{"id":8,"date":"2026-04-14T16:47:45","date_gmt":"2026-04-14T16:47:45","guid":{"rendered":"https:\/\/govt.mrenglishkj.com\/railway\/?p=8"},"modified":"2026-04-17T09:57:41","modified_gmt":"2026-04-17T09:57:41","slug":"rrb-ntpc-graduate-cbt-1-competitive-exam-16-mar-2026-full-hack","status":"publish","type":"post","link":"https:\/\/govt.mrenglishkj.com\/railway\/rrb-ntpc-graduate-cbt-1-competitive-exam-16-mar-2026-full-hack\/","title":{"rendered":"RRB NTPC Graduate CBT Competitive Exam 1 (16 Mar, 2026) Full Hack"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">RRB NTPC Graduate CBT 1 (16 March 2026) \u2013 <strong>Full Quiz + Smart Tricks + Detailed Solutions<\/strong> (Part 1: Question 1-25)<\/h2>\n\n\n\n<p>Railway Recruitment Board (RRB) conducts the RRB NTPC Exam like 2026 to fill vacancies for Graduate and Undergraduate posts under the Non-Technical Popular Categories (NTPC). Here you will try to attempt the real RRB NTPC Graduate CBT 1 exam, which was conducted on 16 March, 2026. The competitive exam is divided into 4 parts each with 25 questions. You are not just taking the exercise but also learning from the solutions and explanations.<\/p>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Exam Instructions<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total Questions: <strong>25<\/strong> (This is Part 1 of Total 100 Questions.)<\/li>\n\n\n\n<li>Attempt like real exam (no scrolling to answers immediately \ud83d\ude09)<\/li>\n\n\n\n<li>Each question includes:\n<ul class=\"wp-block-list\">\n<li>\u2705 Correct Answer<\/li>\n\n\n\n<li>\ud83e\udde0 Shortcut Trick<\/li>\n\n\n\n<li>\u274c Why other options are wrong<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n        <script>\n          window.KQ_FRONT = window.KQ_FRONT || {};\n          window.KQ_FRONT.quiz_id = 1;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-1\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"1\">\n            <div class=\"kq-loading\">Loading quiz...<\/div>\n        <\/div>\n        \n    <div id=\"kq-auth-modal\" class=\"kq-auth-modal\" style=\"display:none;\">\n      <div class=\"kq-auth-modal-inner\">\n        <button id=\"kq-auth-close\" class=\"kq-auth-close\" aria-label=\"Close\">\u2716<\/button>\n\n        <!-- TAB NAV -->\n        <div class=\"kq-auth-tabs\" role=\"tablist\">\n          <button class=\"kq-tab active\" data-tab=\"register\" type=\"button\" role=\"tab\" aria-selected=\"true\">Register<\/button>\n          <button class=\"kq-tab\" data-tab=\"login\" type=\"button\" role=\"tab\" aria-selected=\"false\">Login<\/button>\n          <button class=\"kq-tab\" data-tab=\"forgot\" type=\"button\" role=\"tab\" aria-selected=\"false\">Forgot<\/button>\n        <\/div>\n\n        <!-- PANELS -->\n        <div class=\"kq-auth-panel-wrap\">\n\n          <!-- REGISTER -->\n          <div class=\"kq-auth-panel\" data-panel=\"register\" style=\"display:block\">\n            <div class=\"kq-auth-card\">\n              <h3>Register<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-username\" placeholder=\"Username\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-email\" placeholder=\"Email\" type=\"email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-signup-btn\" class=\"button kq-btn-small\">Register<\/button>\n              <small style=\"display:block;margin-top:8px;\">Already registered? Use Login tab.<\/small>\n            <\/div>\n          <\/div>\n\n          <!-- LOGIN -->\n          <div class=\"kq-auth-panel\" data-panel=\"login\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Login<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-login-btn\" class=\"button kq-btn-small\">Login<\/button>\n            <\/div>\n          <\/div>\n\n          <!-- FORGOT -->\n          <div class=\"kq-auth-panel\" data-panel=\"forgot\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Forgot Password<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-newpass\" placeholder=\"New Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-forgot-btn\" class=\"button kq-btn-small\">Update Password<\/button>\n            <\/div>\n          <\/div>\n\n        <\/div>\n\n      <\/div>\n    <\/div>\n    \n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">The Solution and Explanation of The Competitive Exam<\/h2>\n\n\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"Find the area of a quadrilateral ABCD whose area is twice the area of a triangle PQR. The sides of triangle PQR are in the ratio 4:5:6 and the perimeter of the triangle is 90 cm (use \\sqrt{7} = 2.6).\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 702 cm^2, but it is not easy. There is a trick behind it. Check it out.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"What should come in place of the question mark (?) in the given series? 89 87 84 79 72 ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is subtract negative prime number increasing is the real way to solve.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"20% of a number is more than 20% of 620 by 210. The number is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Let 620 as x. Find 20 percent of x is 0.2x and add 210 to it. 0.2(620) + 210 will be 334 then divide it with 0.2 and we get our answer 1670.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Working of hydraulic lift and hydraulic brakes is based on:\n\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The concept says, \"Hydraulic systems work on pressure transmission in fluids.\" The correct answer is Pascal\u2019s law.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"P, Q, R, S, T, U and V sit around a circular table facing the centre. Only one person sits between U and P when counted from the right of U. Only one person sits between P and R. Only one person sits between U and Q. Only two people sit between V and R. Only one person sits between T and Q. How many people sit between T and V when counted from the left of T?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Make a circle and right means clockwise and left means anti-clockwise. The correct answer is 1.\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"What is the name of the powerful non-nuclear bomb unveiled by Turkey at the 17th International Defence Industry Fair (IDEF) in July 2025?\n\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Turkey\u2019s non-nuclear bomb (2025 IDEF). The correct answer is Gazap\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Anand has \u20b91407 with him. He divides this amount between his two sons, Anil and Ashok, and asks them to invest their respective shares at a compound interest rate of 10% per annum, compounded annually. It is observed that Anil\u2019s investment amounts to the same value after 15 years as Ashok\u2019s investment does after 16 years. How much (in \u20b9) did Anand give to Ashok?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"We use compound interest formular here and the correct answer is 670.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following Articles of the Indian Constitution directs the State to ensure equal pay for equal work for both men and women?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It was Article 39(d).\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following letter-number clusters will replace the question mark \u201c?\u201d in the given series to make it logically complete?\nVPG 7, ZTK 11, DXO 15, HBS 19, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is to figuring out that every letter and number has addition of 4 in next, so the correct answer is LFW 23.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"EGDH is related to FIFI in a certain way based on the English alphabetical order. In the same way, JMHL is related to KOJM. To which of the following is NPRS related, following the same logic?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick of the patten is the addition of +1, +2, +2, +1 per letter in the sequence. The correct answer is ORTT.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The average of 13 numbers is 8. If each number is multiplied by 7, then what will the new average be\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick is simple when you need to find change in numbers included in average and the change is symmetrical than we just simply multiply it with average. The correct answer is 56.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Administrators of the Andaman and Nicobar Islands and Puducherry are designated as ____.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Admins of UTs like Andaman & Puducherry. The correct answer is: Lieutenant Governor\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"At the 2025 ICC Champions Trophy held in Dubai, which country did India defeat to secure their seventh ICC title in men\u2019s senior cricket?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"India defeated New Zealand at the 2025 ICC Champions Trophy held in Dubai.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which legislation forms the legal basis for the creation and operation of the Central Administrative Tribunal (CAT)?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The CAT was formed under Administrative Tribunals Act, 1985.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In December 2025, the Finance Minister called on states to manage their debt within the limits prescribed under which fiscal framework?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The Fiscal discipline framework was prescribed under FRBM in December 2025 by the Finance Minister.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Each of P, Q, R, S, T, U and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week. Only five people have exams between V and T. Only two people have exams between R and T. Q has the exam immediately after R. S has the exam immediately before P but after T.\nHow many people have exams between P and U?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"You have to create a visual map to solve this. The correct answer is 2. We have explained it simply for you.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Girish scored 572 marks in an examination and was 30 marks short of 28% of maximum marks. In the same examination, his friend scored 473 marks. What is the percentage of marks scored by his friend?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"First you add 30 to 572 then you divide it by 28%. Once done, you calculate the percentage and you get 22%. Check out how.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Two taps can fill a cistern in 4 hours and 38 hours respectively. A third tap can empty it in 38 hours. How long (in hours) will it take to fill one-fourth of the empty cistern, if all of them are opened together?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Visualize the situation, we have One cistern. Tap A fills in 4 hours. Tap B fills in 38 hours. Tap C empties in 38 hours. So technically the what Tap B fills, Tap C pours out. One cistern + 4 + 38 - 38 = One cistern + 4. But the question asks how many hours will it take to fill only one-fourth. One cistern is 4 hours. One-fourth of it is 1 hour.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If the median of a data is 61.54 less than its mode, then the median of the data exceeds its mean by _____. (Use the empirical formula to find the answer)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The empirical formula says, Mode = 3 Median - 2 Mean, so the correct answer is 30.77. How, check out.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What was the main purpose of the India\u2013MERCOSUR Preferential Trade Agreement discussions held in New Delhi on 16 October 2025?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Boost trade & investment, so the Answer is D.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Under the Union Budget 2025\u201326, the FDI limit in the insurance sector was increased from:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It was increased from 74% to 100%.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Refer to the following number and symbol series and answer the question that follows. Counting to be done from left to right only. All numbers are single-digit numbers only.\n(Left) \u00a9 3 @ 8 5 1 \u00a3 1 6 1 5 7 2 8 # \u20ac \u00a3 \u00a9 \u20ac \u00a9 1 3 (Right)\nHow many such numbers are there each of which is immediately preceded by a symbol and also immediately followed by a symbol?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Keep in mind, it is not asking the number but it is asking how many means counting of the number, so it is one.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A train travelling at 60 km\/hr crosses another train travelling in the opposite direction at 84 km\/hr in 30 seconds. What is the combined length (in m) of both the trains?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"First we add both speed 60 + 84 and we get 144 km\/h. Then we convert it by multiplying 144 with 5\/18 and we'll get 40 m\/s. Let's multiply 40 with 30 and we get our answer 1200 m.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the given letter-number clusters will replace the question mark (?) in the following series to make it logically complete?\nFZN 4 XRF 6 PJX 9 HBP 13 ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Focus on only number that is the fastest hack here. The number increases like 2,3,4,5. We add 5 to 13, we get 18. The correct answer is ZTH 18.\"\n    }\n  }\n  }\n}\n<\/script>\n\n\n\n<div class=\"wp-block-coblocks-accordion\">\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 1<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Find the area of a quadrilateral ABCD whose area is twice the area of a triangle PQR. The sides of triangle PQR are in the ratio 4:5:6 and the perimeter of the triangle is 90 cm (use <math data-latex=\"\\sqrt{7}\"><semantics><msqrt><mn>7<\/mn><\/msqrt><annotation encoding=\"application\/x-tex\">\\sqrt{7}<\/annotation><\/semantics><\/math> = 2.6).<\/strong><br><br>A. 656 cm<sup>2<\/sup><br>B. 702 cm<sup>2<\/sup><br>C. 763 cm<sup>2<\/sup><br>D. 698 cm<sup>2<\/sup><\/p>\n\n\n\n<p class=\"is-style-success\">Let sides = <strong>4x, 5x, 6x<\/strong><br>\ud83d\udc49 4x + 5x + 6x = 90<br>\ud83d\udc49 15x = 90 \u2192 x = 6<br><math data-latex=\"4x = 4\\times 6 \\\\ 5x = 5\\times 6 \\\\ 6x = 6\\times 6\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mn>4<\/mn><mi>x<\/mi><mo>=<\/mo><mn>4<\/mn><mo>\u00d7<\/mo><mn>6<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>5<\/mn><mi>x<\/mi><mo>=<\/mo><mn>5<\/mn><mo>\u00d7<\/mo><mn>6<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>6<\/mn><mi>x<\/mi><mo>=<\/mo><mn>6<\/mn><mo>\u00d7<\/mo><mn>6<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">4x = 4\\times 6 \\\\ 5x = 5\\times 6 \\\\ 6x = 6\\times 6<\/annotation><\/semantics><\/math><br>So sides = <strong>24, 30, 36<\/strong><br><br>Using <strong>Heron\u2019s Formula<\/strong>: <math data-latex=\"A = \\sqrt{s(s-a)(s-b)(s-c)}\"><semantics><mrow><mi>A<\/mi><mo>=<\/mo><msqrt><mrow><mi>s<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo>\u2212<\/mo><mi>a<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo>\u2212<\/mo><mi>b<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>s<\/mi><mo>\u2212<\/mo><mi>c<\/mi><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">A = \\sqrt{s(s-a)(s-b)(s-c)}<\/annotation><\/semantics><\/math><br><br>Where: <math data-latex=\"s = \\frac{a+b+c}{2}\"><semantics><mrow><mi>s<\/mi><mo>=<\/mo><mfrac><mrow><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><mo>+<\/mo><mi>c<\/mi><\/mrow><mn>2<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">s = \\frac{a+b+c}{2}<\/annotation><\/semantics><\/math><br><math data-latex=\"s = \\frac{24+30+36}{2} \\\\ s = 45\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mi>s<\/mi><mo>=<\/mo><mfrac><mrow><mn>24<\/mn><mo>+<\/mo><mn>30<\/mn><mo>+<\/mo><mn>36<\/mn><\/mrow><mn>2<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>s<\/mi><mo>=<\/mo><mn>45<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">s = \\frac{24+30+36}{2} \\\\ s = 45<\/annotation><\/semantics><\/math><br>or directly half of 90 is 45.<br>Area of triangle =<br><math data-latex=\"\\sqrt{45(45-24)(45-30)(45-36)} \\\\ \\sqrt{45\\ \\times\\ 21\\ \\times\\ 15\\ \\times\\ 9}\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><msqrt><mrow><mn>45<\/mn><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>45<\/mn><mo>\u2212<\/mo><mn>24<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>45<\/mn><mo>\u2212<\/mo><mn>30<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>45<\/mn><mo>\u2212<\/mo><mn>36<\/mn><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/msqrt><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><msqrt><mrow><mn>45<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>21<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>15<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>9<\/mn><\/mrow><\/msqrt><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\sqrt{45(45-24)(45-30)(45-36)} \\\\ \\sqrt{45\\ \\times\\ 21\\ \\times\\ 15\\ \\times\\ 9}<\/annotation><\/semantics><\/math><br><br>Simplify (Exam Trick \ud83d\udd25): use <math data-latex=\"\\sqrt{7} = 2.6\"><semantics><mrow><msqrt><mn>7<\/mn><\/msqrt><mo>=<\/mo><mn>2.6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{7} = 2.6<\/annotation><\/semantics><\/math><br>Factor smartly: <math data-latex=\"\\sqrt{45\\ \\times\\ 21\\ \\times\\ 15\\ \\times\\ 9}\"><semantics><msqrt><mrow><mn>45<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>21<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>15<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>9<\/mn><\/mrow><\/msqrt><annotation encoding=\"application\/x-tex\">\\sqrt{45\\ \\times\\ 21\\ \\times\\ 15\\ \\times\\ 9}<\/annotation><\/semantics><\/math><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><msqrt><mrow><mo stretchy=\"false\">(<\/mo><mn>9<\/mn><mo>\u00d7<\/mo><mn>5<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><mn>7<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><mn>5<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mn>9<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">= \\sqrt{(9 \\times 5)(3 \\times 7)(3 \\times 5)(9)}<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><msqrt><mrow><msup><mn>9<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><msup><mn>5<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><mn>7<\/mn><\/mrow><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">= \\sqrt{9^2 \\times 3^2 \\times 5^2 \\times 7}<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>9<\/mn><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><mn>5<\/mn><mo>\u00d7<\/mo><msqrt><mn>7<\/mn><\/msqrt><mo>=<\/mo><mn>135<\/mn><msqrt><mn>7<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">= 9 \\times 3 \\times 5 \\times \\sqrt{7} = 135\\sqrt{7}<\/annotation><\/semantics><\/math><br>\ud83d\udc49 Using given:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msqrt><mn>7<\/mn><\/msqrt><mo>=<\/mo><mn>2.6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{7} = 2.6<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Area&nbsp;of&nbsp;triangle&nbsp;PQR<\/mtext><mo>=<\/mo><mn>135<\/mn><mo>\u00d7<\/mo><mn>2.6<\/mn><mo>=<\/mo><mn>351<\/mn><msup><mtext>&nbsp;cm<\/mtext><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Area of triangle PQR} = 135 \\times 2.6 = 351 \\text{ cm}^2<\/annotation><\/semantics><\/math><br><math data-latex=\"Area\\ of\\ Quadrilateral\\ ABCD = 2\\times 351 = 702 cm^2\"><semantics><mrow><mi>A<\/mi><mi>r<\/mi><mi>e<\/mi><mi>a<\/mi><mtext>&nbsp;<\/mtext><mi>o<\/mi><mi>f<\/mi><mtext>&nbsp;<\/mtext><mi>Q<\/mi><mi>u<\/mi><mi>a<\/mi><mi>d<\/mi><mi>r<\/mi><mi>i<\/mi><mi>l<\/mi><mi>a<\/mi><mi>t<\/mi><mi>e<\/mi><mi>r<\/mi><mi>a<\/mi><mi>l<\/mi><mtext>&nbsp;<\/mtext><mi>A<\/mi><mi>B<\/mi><mi>C<\/mi><mi>D<\/mi><mo>=<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mn>351<\/mn><mo>=<\/mo><mn>702<\/mn><mi>c<\/mi><msup><mi>m<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">Area\\ of\\ Quadrilateral\\ ABCD = 2\\times 351 = 702 cm^2<\/annotation><\/semantics><\/math><br><br>\u2705 Answer: <strong>B. 702 cm<sup>2<\/sup><\/strong><\/p>\n\n\n\n<p class=\"is-style-error\"><strong>\u274c Why others wrong:<br><\/strong>656, 702, 763 \u2192 calculation errors in square root or doubling, not using Heron&#8217;s formula.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 2<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What should come in place of the question mark (?) in the given series?<br>89 87 84 79 72 ?<\/strong><br><br>A. 57<br>B. 59<br>C. 63<br>D. 61<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pattern:<\/strong><br>The trick here is subtract Prime numbers increasing: 2, 3, 5, 7, 11&#8230;<br>89, 87, 84, 79, 72, ?<br>89 &#8211; 2 = 87<br>87 &#8211; 3 = 84<br>84 &#8211; 5 = 79<br>79 &#8211; 7 = 72<br>72 &#8211; 11 = 61<br>\u2705 Answer: <strong>D. 61<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 3<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>20% of a number is more than 20% of 620 by 210. The number is:<\/strong><br><br>A. 1520<br>B. 1720<br>C. 1670<br>D. 1770<\/p>\n\n\n\n<p class=\"is-style-success\">\ud83d\udc49 20% common \u2192 remove it<br>Let number = x<br>0.2x = 0.2(620) + 210\ud83d\udc49 0.2x = 124 + 210 = 334<br>\ud83d\udc49 x = 334 \/ 0.2 = <strong>1670<\/strong><br>\u2705 Answer: <strong>C. 1670<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 4<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Working of hydraulic lift and hydraulic brakes is based on:<br><\/strong><br>A. Faraday&#8217;s law<br>B. Gay-Lussac\u2019s law<br>C. Pascal\u2019s law<br>D. Coulomb&#8217;s law<\/p>\n\n\n\n<p class=\"is-style-success\">Concept: Hydraulic systems work on <strong>pressure transmission in fluids<\/strong><br>\u2705 Answer: <strong>C. Pascal\u2019s law<\/strong><\/p>\n\n\n\n<p class=\"is-style-error\">\u274c Others:<br>&#8211; Coulomb \u2192 electrostatics<br>&#8211; Gay-Lussac \u2192 gases<br>&#8211; Faraday \u2192 electricity<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 5<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>P, Q, R, S, T, U and V sit around a circular table facing the centre. Only one person sits between U and P when counted from the right of U. Only one person sits between P and R. Only one person sits between U and Q. Only two people sit between V and R. Only one person sits between T and Q. How many people sit between T and V when counted from the left of T?<\/strong><br><br>A. 3<br>B. 2<br>C. 4<br>D. 1<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Key Points:<br><\/strong>&#8211; &#8220;right of&#8221; means clockwise.<br>&#8211; &#8220;left of&#8221; means anti-clockwise<br>&#8211; Circular table like a clock: 1,2,3,4,5,6,7.<br>&#8211; There are total 7: P,Q,R,S,T,U,V.<br>&#8211; All we have to do is to fit them in position to solve.<br><br>Let&#8217;s begin.<br>1 = U<br>2 = V<br>3 = P<br>4 = T<br>5 = R<br>6 = Q<br>7 = S<br>\u2705 Now Check Conditions (Fast Trick Method):<br>1. U \u2192 P (1 person between, right side)<br><strong>U<\/strong> \u2192 ? \u2192 <strong>P<\/strong> \u2714\ufe0f<br><br>2. P \u2192 R (1 person between): The question did not mention right or left, but we know the obvious. Since it is a circle and based on conditions.<br>U \u2192 ? \u2192 <strong>P<\/strong> \u2192 ? \u2192 <strong>R<\/strong> \u2714\ufe0f<br><br>3. U \u2192 Q (1 person between): The question did not mention right or left, but the condition denotes it right of Q.<br>U \u2192 ? \u2192 P \u2192 ? \u2192 R \u2192 <strong>Q<\/strong> \u2192 ? \u2192 <strong>U<\/strong> \u2714\ufe0f (The circle starts from U to U)<br><br>4. V \u2192 R (2 people between)<br>U \u2192 <strong>V<\/strong> \u2192 P \u2192 ? \u2192 <strong>R<\/strong> \u2192 Q \u2192 ? \u2192 U \u2714\ufe0f<br><br>5. T \u2192 Q (1 person between)<br>U \u2192 V \u2192 P \u2192 <strong>T<\/strong> \u2192 R \u2192 <strong>Q<\/strong> \u2192 ? \u2192 U \u2714\ufe0f<br><br>Now only S left and one sit let as well:<br>U \u2192 V \u2192 P \u2192 T \u2192 R \u2192 Q \u2192 <strong>S<\/strong> \u2192 U<br><br>The question asked:<br>\ud83d\udc49 How many sit Between T and V (from left of T means anti-clockwise)<br><strong>T<\/strong> \u2192 P \u2192 <strong>V<\/strong> \u2192 U \u2192 S \u2192 Q \u2192 R \u2192 T<br><br>\ud83d\udc49 <strong>Answer D: 1<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 6<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What is the name of the powerful non-nuclear bomb unveiled by Turkey at the 17th International Defence Industry Fair (IDEF) in July 2025?<br><\/strong><br>A. Nebula<br>B. Phantom-X<br>C. Gazap<br>D. Titan<\/p>\n\n\n\n<p class=\"is-style-success\">Turkey\u2019s non-nuclear bomb (2025 IDEF)<br>\u2705 Answer: <strong>C. Gazap<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 7<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Anand has \u20b91407 with him. He divides this amount between his two sons, Anil and Ashok, and asks them to invest their respective shares at a compound interest rate of 10% per annum, compounded annually. It is observed that Anil\u2019s investment amounts to the same value after 15 years as Ashok\u2019s investment does after 16 years. How much (in \u20b9) did Anand give to Ashok?<\/strong><br><br>A. 737<br>B. 837<br>C. 520<br>D. 670<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\ud83d\udd37 Given<br><\/strong>~ Total money = \u20b91407<br>~ Rate = <strong>10% per annum (compound annually)<\/strong><br>~  Time:<br>~~ <strong>Anil \u2192 15 years<\/strong><br>~~ <strong>Ashok \u2192 16 years<\/strong><br>Final amounts become <strong>equal<\/strong><br><br><strong>\ud83d\udd25 Core Concept (MOST IMPORTANT)<\/strong><br>Compound Interest formula:<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>A<\/mi><mo>=<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>+<\/mo><mi>r<\/mi><msup><mo stretchy=\"false\">)<\/mo><mi>t<\/mi><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">A = P(1 + r)^{t}<\/annotation><\/semantics><\/math><br>\ud83d\udc49 Since final amounts are equal:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>P<\/mi><mrow><mi>A<\/mi><mi>n<\/mi><mi>i<\/mi><mi>l<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mn>1.1<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>15<\/mn><\/msup><mo>=<\/mo><msub><mi>P<\/mi><mrow><mi>A<\/mi><mi>s<\/mi><mi>h<\/mi><mi>o<\/mi><mi>k<\/mi><\/mrow><\/msub><mo stretchy=\"false\">(<\/mo><mn>1.1<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>16<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">P_{Anil}(1.1)^{15} = P_{Ashok}(1.1)^{16}<\/annotation><\/semantics><\/math><br><strong>\ud83d\udd37 Step 1: Cancel Common Powers (Shortcut Trick)<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mn>1.1<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>15<\/mn><\/msup><mtext>&nbsp;cancels<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">(1.1)^{15} \\text{ cancels}<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msub><mi>P<\/mi><mrow><mi>A<\/mi><mi>n<\/mi><mi>i<\/mi><mi>l<\/mi><\/mrow><\/msub><mo>=<\/mo><msub><mi>P<\/mi><mrow><mi>A<\/mi><mi>s<\/mi><mi>h<\/mi><mi>o<\/mi><mi>k<\/mi><\/mrow><\/msub><mo>\u00d7<\/mo><mn>1.1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P_{Anil} = P_{Ashok} \\times 1.1<\/annotation><\/semantics><\/math><br><strong>\ud83d\udd37 Step 2: Convert into Ratio<\/strong><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><msub><mi>P<\/mi><mrow><mi>A<\/mi><mi>n<\/mi><mi>i<\/mi><mi>l<\/mi><\/mrow><\/msub><msub><mi>P<\/mi><mrow><mi>A<\/mi><mi>s<\/mi><mi>h<\/mi><mi>o<\/mi><mi>k<\/mi><\/mrow><\/msub><\/mfrac><mo>=<\/mo><mn>1.1<\/mn><mo>=<\/mo><mfrac><mn>11<\/mn><mn>10<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{P_{Anil}}{P_{Ashok}} = 1.1 = \\frac{11}{10}<\/annotation><\/semantics><\/math><br>\ud83d\udc49 So ratio:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>A<\/mi><mi>n<\/mi><mi>i<\/mi><mi>l<\/mi><mo>:<\/mo><mi>A<\/mi><mi>s<\/mi><mi>h<\/mi><mi>o<\/mi><mi>k<\/mi><mo>=<\/mo><mn>11<\/mn><mo>:<\/mo><mn>10<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">Anil : Ashok = 11 : 10<\/annotation><\/semantics><\/math><br><strong>\ud83d\udd37 Step 3: Total = 1407<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>11<\/mn><mi>x<\/mi><mo>+<\/mo><mn>10<\/mn><mi>x<\/mi><mo>=<\/mo><mn>21<\/mn><mi>x<\/mi><mo>=<\/mo><mn>1407<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">11x + 10x = 21x = 1407<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>67<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x = 67<\/annotation><\/semantics><\/math><br><strong>\ud83d\udd37 Step 4: Find Ashok\u2019s Share<\/strong><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>A<\/mi><mi>s<\/mi><mi>h<\/mi><mi>o<\/mi><mi>k<\/mi><mo>=<\/mo><mn>10<\/mn><mi>x<\/mi><mo>=<\/mo><mn>10<\/mn><mo>\u00d7<\/mo><mn>67<\/mn><mo>=<\/mo><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mn>670<\/mn><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">Ashok = 10x = 10 \\times 67 = \\boxed{670}<\/annotation><\/semantics><\/math><br>\ud83c\udfaf Final Answer:<br>\u2705 Answer: <strong>D. 670<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 8<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which of the following Articles of the Indian Constitution directs the State to ensure equal pay for equal work for both men and women?<\/strong><br><br>A. Article 42(b)<br>B. Article 15<br>C. Article 39(d)<br>D. Article 14<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>The correct answer is C: Article 39(d).<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 9<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which of the following letter-number clusters will replace the question mark \u201c?\u201d in the given series to make it logically complete?<br>VPG 7, ZTK 11, DXO 15, HBS 19, ?<\/strong><br><br>A. LEU 23<br>B. MGX 23<br>C. LGY 24<br>D. LFW 23<\/p>\n\n\n\n<p class=\"is-style-success\">The Key Pattern here is Addition of 4 each:<br>V\u2192Z\u2192D\u2192H\u2192L<br>P\u2192T\u2192X\u2192B\u2192F<br>G\u2192K\u2192O\u2192S\u2192W<br>7\u219211\u219215\u219219\u219223<br>Answer: <strong>LFW 23<\/strong><br>\u2705 Answer: <strong>D<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 10<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>EGDH is related to FIFI in a certain way based on the English alphabetical order. In the same way, JMHL is related to KOJM. To which of the following is NPRS related, following the same logic?<\/strong><br><br>A. ORTT<br>B. ORST<br>C. OSST<br>D. OOPT<\/p>\n\n\n\n<p class=\"is-style-success\">The trick of the patten is the addition of +1, +2, +2, +1 per letter in the sequence.<br><strong>EGDH \u2192 FIFI<br><\/strong>E +1 is F<br>G +2 is I<br>D +2 is F<br>H +1 is I<br><br><strong>JMHL \u2192 KOJM<\/strong><br>J +1 is K<br>M +2 is O<br>H +2 is J<br>L +1 is M<br><br><strong>Same way for NPRS:<\/strong><br>N +1 is O<br>P +2 is R<br>R +2 is T<br>S +1 is T<br>NPRS \u2192 ORTT<br>\u2705 Answer: <strong>A<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 11<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The average of 13 numbers is 8. If each number is multiplied by 7, then what will the new average be:<\/strong><br><br>A. 7<br>B. 8<br>C. 56<br>D. 13<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Trick:<br><\/strong>If all numbers \u00d77 \u2192 average \u00d77<br>\ud83d\udc49 8 \u00d7 7 = <strong>56<\/strong><br>\u2705 Answer: <strong>C<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 12<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Administrators of the Andaman and Nicobar Islands and Puducherry are designated as <em>_<\/em>___.<\/strong><br><br>A. Governor<br>B. Lieutenant Governor<br>C. Administrator<br>D. Chief Minister<\/p>\n\n\n\n<p class=\"is-style-success\">Admins of UTs like Andaman &amp; Puducherry<br>\u2705 Answer: <strong>B. Lieutenant Governor<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 13<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>If <math data-latex=\"(y-12) = 4\\sqrt{5}\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>y<\/mi><mo>\u2212<\/mo><mn>12<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">(y-12) = 4\\sqrt{5}<\/annotation><\/semantics><\/math> , then find the value of <math data-latex=\"\\sqrt{(y-3)} - \\frac{1}{\\sqrt{(y-3)}}\"><semantics><mrow><msqrt><mrow><mo form=\"prefix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">(<\/mo><mi>y<\/mi><mo>\u2212<\/mo><mn>3<\/mn><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/msqrt><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msqrt><mrow><mo form=\"prefix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">(<\/mo><mi>y<\/mi><mo>\u2212<\/mo><mn>3<\/mn><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/msqrt><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{(y-3)} &#8211; \\frac{1}{\\sqrt{(y-3)}}<\/annotation><\/semantics><\/math> .<\/strong><br><br>A. 6<br>B. 4<br>C. 8<br>D. 9<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Step 1: Start from the given:<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>y<\/mi><mo>\u2212<\/mo><mn>12<\/mn><mo>=<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">y &#8211; 12 = 4\\sqrt{5}<\/annotation><\/semantics><\/math>\ud83d\udc49 So,<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mn>12<\/mn><mo>+<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">y = 12 + 4\\sqrt{5}<\/annotation><\/semantics><\/math><br><strong>Step 2: What do we actually need?<\/strong><br>We must find:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msqrt><mrow><mi>y<\/mi><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><\/msqrt><mo>\u2212<\/mo><mfrac><mn>1<\/mn><msqrt><mrow><mi>y<\/mi><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><\/msqrt><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{y-3} &#8211; \\frac{1}{\\sqrt{y-3}}<\/annotation><\/semantics><\/math><br>\ud83d\udc49 So we need <strong>y \u2212 3<\/strong><br><br><strong>Step 3: Substitute y directly<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>y<\/mi><mo>\u2212<\/mo><mn>3<\/mn><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mn>12<\/mn><mo>+<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><mo stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">y &#8211; 3 = (12 + 4\\sqrt{5}) &#8211; 3<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>9<\/mn><mo>+<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">= 9 + 4\\sqrt{5}<\/annotation><\/semantics><\/math><br><strong>Now the REAL Concept Question<\/strong><br>We need: <math data-latex=\"\\sqrt{(y - 3)}\"><semantics><msqrt><mrow><mo form=\"prefix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">(<\/mo><mi>y<\/mi><mo>\u2212<\/mo><mn>3<\/mn><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/msqrt><annotation encoding=\"application\/x-tex\">\\sqrt{(y &#8211; 3)}<\/annotation><\/semantics><\/math><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msqrt><mrow><mn>9<\/mn><mo>+<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><\/mrow><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{9 + 4\\sqrt{5}}<\/annotation><\/semantics><\/math><br>\ud83d\udc49 This is <strong>not easy directly<\/strong> unless we recognize a pattern.<br>Look this:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><msqrt><mn>4<\/mn><\/msqrt><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">(\\sqrt{4} + \\sqrt{5})^2<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><msqrt><mn>4<\/mn><\/msqrt><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><msqrt><mn>5<\/mn><\/msqrt><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>+<\/mo><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><msqrt><mn>4<\/mn><\/msqrt><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><msqrt><mn>5<\/mn><\/msqrt><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">= (\\sqrt{4})^2 + (\\sqrt{5})^2 + 2(\\sqrt{4})(\\sqrt{5})<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>4<\/mn><mo>+<\/mo><mn>5<\/mn><mo>+<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><msqrt><mn>5<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">= 4 + 5 + 2 \\cdot 2 \\cdot \\sqrt{5}<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>9<\/mn><mo>+<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">= 9 + 4\\sqrt{5}<\/annotation><\/semantics><\/math><br>So if we reverse it back then it will be easy to solve. But the question is how do we know that it is <strong>4<\/strong> and <strong>5<\/strong>.<br>Let&#8217;s understand!<br>We reached: <math data-latex=\"\\sqrt{(y - 3)}\"><semantics><msqrt><mrow><mo form=\"prefix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">(<\/mo><mi>y<\/mi><mo>\u2212<\/mo><mn>3<\/mn><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/msqrt><annotation encoding=\"application\/x-tex\">\\sqrt{(y &#8211; 3)}<\/annotation><\/semantics><\/math><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msqrt><mrow><mn>9<\/mn><mo>+<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><\/mrow><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{9 + 4\\sqrt{5}}<\/annotation><\/semantics><\/math><br>Now we <strong>assume logically<\/strong> (this is a standard method):<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msqrt><mrow><mn>9<\/mn><mo>+<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><\/mrow><\/msqrt><mo>=<\/mo><msqrt><mi>a<\/mi><\/msqrt><mo>+<\/mo><msqrt><mi>b<\/mi><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{9 + 4\\sqrt{5}} = \\sqrt{a} + \\sqrt{b}<\/annotation><\/semantics><\/math><br>\ud83d\udc49 Why this assumption?<br>Because:<br><math data-latex=\"(\\sqrt{a} + \\sqrt{b})^2 = a^2 + b^2 + 2\\sqrt{ab}\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msqrt><mi>a<\/mi><\/msqrt><mo>+<\/mo><msqrt><mi>b<\/mi><\/msqrt><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>b<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>2<\/mn><msqrt><mrow><mi>a<\/mi><mi>b<\/mi><\/mrow><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">(\\sqrt{a} + \\sqrt{b})^2 = a^2 + b^2 + 2\\sqrt{ab}<\/annotation><\/semantics><\/math><br><br>And our expression <strong>looks exactly like this form<\/strong> if we remove exponent square on both sides:<br><math data-latex=\"(\\sqrt{a} + \\sqrt{b}) = a + b + 2\\sqrt{ab}\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msqrt><mi>a<\/mi><\/msqrt><mo>+<\/mo><msqrt><mi>b<\/mi><\/msqrt><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><mo>+<\/mo><mn>2<\/mn><msqrt><mrow><mi>a<\/mi><mi>b<\/mi><\/mrow><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">(\\sqrt{a} + \\sqrt{b}) = a + b + 2\\sqrt{ab}<\/annotation><\/semantics><\/math><br>So we put the value:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>9<\/mn><mo>+<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><mo>=<\/mo><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><mo>+<\/mo><mn>2<\/mn><msqrt><mrow><mi>a<\/mi><mi>b<\/mi><\/mrow><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">9 + 4\\sqrt{5} = a + b + 2\\sqrt{ab}<\/annotation><\/semantics><\/math><br>Now assign the values: <math data-latex=\"a + b = 9\"><semantics><mrow><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><mo>=<\/mo><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">a + b = 9<\/annotation><\/semantics><\/math><br>\ud83d\udc49 Compare root terms:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><msqrt><mrow><mi>a<\/mi><mi>b<\/mi><\/mrow><\/msqrt><mo>=<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">2\\sqrt{ab} = 4\\sqrt{5}<\/annotation><\/semantics><\/math><br>Divide by 2:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msqrt><mrow><mi>a<\/mi><mi>b<\/mi><\/mrow><\/msqrt><mo>=<\/mo><mn>2<\/mn><msqrt><mn>5<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{ab} = 2\\sqrt{5}<\/annotation><\/semantics><\/math><br>Square both sides:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>a<\/mi><mi>b<\/mi><mo>=<\/mo><mn>20<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">ab = 20<\/annotation><\/semantics><\/math><br>Solve system:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><mo>=<\/mo><mn>9<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><mi>a<\/mi><mi>b<\/mi><mo>=<\/mo><mn>20<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">a + b = 9,\\quad ab = 20<\/annotation><\/semantics><\/math>\ud83d\udc49 Numbers are:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mn>4<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><mi>b<\/mi><mo>=<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">a = 4,\\quad b = 5<\/annotation><\/semantics><\/math>Hence we get our: <math data-latex=\"(\\sqrt{4} + \\sqrt{5})^2\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msqrt><mn>4<\/mn><\/msqrt><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">(\\sqrt{4} + \\sqrt{5})^2<\/annotation><\/semantics><\/math><br>But: <math data-latex=\"(\\sqrt{a} + \\sqrt{b}) = 9 + 4\\sqrt{5}\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msqrt><mi>a<\/mi><\/msqrt><mo>+<\/mo><msqrt><mi>b<\/mi><\/msqrt><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>9<\/mn><mo>+<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">(\\sqrt{a} + \\sqrt{b}) = 9 + 4\\sqrt{5}<\/annotation><\/semantics><\/math><br>So we put the values without exponent 2.<br><math data-latex=\"(\\sqrt{a} + \\sqrt{b}) \\\\ (\\sqrt{4} + \\sqrt{5}) \\\\ (2 + \\sqrt{5})\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msqrt><mi>a<\/mi><\/msqrt><mo>+<\/mo><msqrt><mi>b<\/mi><\/msqrt><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msqrt><mn>4<\/mn><\/msqrt><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>2<\/mn><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">(\\sqrt{a} + \\sqrt{b}) \\\\ (\\sqrt{4} + \\sqrt{5}) \\\\ (2 + \\sqrt{5})<\/annotation><\/semantics><\/math><br>Now it is simplified, let&#8217;s finish this.<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><mo stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mrow><mn>2<\/mn><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">(2+\\sqrt{5}) &#8211; \\frac{1}{2+\\sqrt{5}}<\/annotation><\/semantics><\/math><br>Take LCM directly<br>Common denominator = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>2<\/mn><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">2+\\sqrt{5}<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mrow><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><mrow><mn>2<\/mn><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">= \\frac{(2+\\sqrt{5})^2 &#8211; 1}{2+\\sqrt{5}}<\/annotation><\/semantics><\/math><br>Expand numerator:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>=<\/mo><mn>4<\/mn><mo>+<\/mo><mn>5<\/mn><mo>+<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><mo>=<\/mo><mn>9<\/mn><mo>+<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">(2+\\sqrt{5})^2 = 4 + 5 + 4\\sqrt{5} = 9 + 4\\sqrt{5}<\/annotation><\/semantics><\/math>So:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Numerator<\/mtext><mo>=<\/mo><mn>9<\/mn><mo>+<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><mo>\u2212<\/mo><mn>1<\/mn><mo>=<\/mo><mn>8<\/mn><mo>+<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Numerator} = 9 + 4\\sqrt{5} &#8211; 1 = 8 + 4\\sqrt{5}<\/annotation><\/semantics><\/math><br>Factor numerator<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>8<\/mn><mo>+<\/mo><mn>4<\/mn><msqrt><mn>5<\/mn><\/msqrt><mo>=<\/mo><mn>4<\/mn><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">8 + 4\\sqrt{5} = 4(2+\\sqrt{5})<\/annotation><\/semantics><\/math><br>Cancel<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mn>4<\/mn><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mn>2<\/mn><mo>+<\/mo><msqrt><mn>5<\/mn><\/msqrt><\/mrow><\/mfrac><mo>=<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{4(2+\\sqrt{5})}{2+\\sqrt{5}} = 4<\/annotation><\/semantics><\/math><br><strong>\ud83c\udfaf FINAL ANSWER: B. 4<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 14<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>At the 2025 ICC Champions Trophy held in Dubai, which country did India defeat to secure their seventh ICC title in men\u2019s senior cricket?<\/strong><br><br>A. South Africa<br>B. England<br>C. New Zealand<br>D. Australia<\/p>\n\n\n\n<p class=\"is-style-success\">India defeated:<br>\u2705 Answer: <strong>C. New Zealand<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 15<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which legislation forms the legal basis for the creation and operation of the Central Administrative Tribunal (CAT)?<\/strong><br><br>A. The Service Matters Act, 1990<br>B. The Administrative Tribunals Act, 1985<br>C. The Judiciary Act, 1971<br>D. The Tribunals Reforms Act, 1980<\/p>\n\n\n\n<p class=\"is-style-success\">CAT formed under:<br>\u2705 Answer: <strong>B. Administrative Tribunals Act, 1985<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 16<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In December 2025, the Finance Minister called on states to manage their debt within the limits prescribed under which fiscal framework?<\/strong><br><br>A. GST<br>B. FRBM<br>C. Monetary Policy<br>D. NITI Aayog<\/p>\n\n\n\n<p class=\"is-style-success\">Fiscal discipline framework:<br>\u2705 Answer: <strong>B. FRBM<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 17<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Each of P, Q, R, S, T, U and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week. Only five people have exams between V and T. Only two people have exams between R and T. Q has the exam immediately after R. S has the exam immediately before P but after T.<br>How many people have exams between P and U?<\/strong><br><br>A. One<br>B. Two<br>C. Three<br>D. Four<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Key Points:<br><\/strong>&#8211; &#8220;after&#8221; goes clockwise.<br>&#8211; &#8220;before&#8221; goes anti-clockwise<br>&#8211; Circular table like a clock: 1,2,3,4,5,6,7.<br>&#8211; There are total 7: P,Q,R,S,T,U,V.<br>&#8211; All we have to do is to fit them in position to solve.<br><br>Let&#8217;s begin.<br>1 = V<br>2 = S<br>3 = P<br>4 = R<br>5 = Q<br>6 = U<br>7 = T<br>\u2705 Now Check Conditions (Fast Trick Method):<br>1. V \u2192 T (5 people between)<br><strong>V<\/strong> \u2192 ? \u2192 ? \u2192 ? \u2192 ? \u2192 ? \u2192 <strong>T<\/strong>  \u2192 V&#8230; \u2714\ufe0f (The circle starts from V to V)<br><br>2. R \u2192 T (2 people between): (It did not say T and R, so we count from R to T)<br>V \u2192 ? \u2192 ? \u2192 <strong>R<\/strong> \u2192 ? \u2192 ? \u2192 <strong>T<\/strong>  \u2192 V&#8230; \u2714\ufe0f<br><br>3. S before P but after T: (Did not force us to put S immediately after T, because not possible. But enforce us to put S immediately before P)<br>V \u2192 <strong>S<\/strong> \u2192 <strong>P<\/strong> \u2192 R \u2192 Q \u2192 ? \u2192 T  \u2192 V&#8230; \u2714\ufe0f<br><br>4. We can assume safely that the last one is U.<br>V \u2192 S \u2192 P \u2192 R \u2192 Q \u2192 <strong>U<\/strong> \u2192 T  \u2192 V&#8230; \u2714\ufe0f<br><br>The question asked:<br>\ud83d\udc49 How many people have exams Between P and U<br>V \u2192 S \u2192 <strong>P<\/strong> \u2192 R \u2192 Q \u2192 <strong>U<\/strong> \u2192 T  \u2192 V&#8230; \u2714\ufe0f<br><br>\ud83d\udc49 <strong>Answer B: 2<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 18<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Girish scored 572 marks in an examination and was 30 marks short of 28% of maximum marks. In the same examination, his friend scored 473 marks. What is the percentage of marks scored by his friend?<\/strong><br><br>A. 22%<br>B. 23%<br>C. 21%<br>D. 24%<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Trick:<\/strong><br>572 = 28% &#8211; 30<br>\ud83d\udc49 28% = 602<br>Max = 602 \/ 0.28 = 2150<br>Friend = 473<br>\ud83d\udc49 % = (473\/2150) \u00d7100 \u2248 <strong>22%<\/strong><br>\u2705 Answer: <strong>A<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 19<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Two taps can fill a cistern in 4 hours and 38 hours respectively. A third tap can empty it in 38 hours. How long (in hours) will it take to fill one-fourth of the empty cistern, if all of them are opened together?<\/strong><br><br>A. 1<br>B. 2<br>C. 3<br>D. 4<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Visualize the situation:<br><\/strong>One cistern: 1<br>Tap A fills in: 4 hours<br>Tap B fills in: 38 hours<br>Tap C empties in: 38 hours.<br>So technically the what Tap B fills, Tap C pours out.<br>One cistern + 4 + 38 -38 = One cistern + 4.<br><br>But the question asks how many hours will it take to fill only one-fourth:<br>One cistern: 4 hours<br>One-fourth of it:<br><math data-latex=\"\\frac{1}{4} \\times 4 \\\\ \\frac{4}{4}\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mn>1<\/mn><mn>4<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>4<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mn>4<\/mn><mn>4<\/mn><\/mfrac><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\frac{1}{4} \\times 4 \\\\ \\frac{4}{4}<\/annotation><\/semantics><\/math><br>1 hour<br>\u2705 Answer: <strong>A. 1<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 20<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>If the median of a data is 61.54 less than its mode, then the median of the data exceeds its mean by ____. (Use the empirical formula to find the answer)<\/strong><br><br>A. 32.03<br>B. 36.77<br>C. 30.77<br>D. 28.47<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\ud83e\udde0 Empirical Formula Trick (Do in 20\u201330 sec)<\/strong><br>We use the standard relation:<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mtext>Mode<\/mtext><mo>=<\/mo><mn>3<\/mn><mtext>Median<\/mtext><mo>\u2212<\/mo><mn>2<\/mn><mtext>Mean<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Mode} = 3\\text{Median} &#8211; 2\\text{Mean}<\/annotation><\/semantics><\/math><br><br><strong>Given Condition<\/strong><br>\u201cMedian is <strong>61.54 less than Mode<\/strong>\u201d<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Mode<\/mtext><mo>=<\/mo><mtext>Median<\/mtext><mo>+<\/mo><mn>61.54<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Mode} = \\text{Median} + 61.54<\/annotation><\/semantics><\/math><br><strong>Step 1: Substitute in formula<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Median<\/mtext><mo>+<\/mo><mn>61.54<\/mn><mo>=<\/mo><mn>3<\/mn><mtext>Median<\/mtext><mo>\u2212<\/mo><mn>2<\/mn><mtext>Mean<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Median} + 61.54 = 3\\text{Median} &#8211; 2\\text{Mean}<\/annotation><\/semantics><\/math><br><strong>Step 2: Rearrange<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>61.54<\/mn><mo>=<\/mo><mn>2<\/mn><mtext>Median<\/mtext><mo>\u2212<\/mo><mn>2<\/mn><mtext>Mean<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">61.54 = 2\\text{Median} &#8211; 2\\text{Mean}<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>61.54<\/mn><mo>=<\/mo><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mtext>Median<\/mtext><mo>\u2212<\/mo><mtext>Mean<\/mtext><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">61.54 = 2(\\text{Median} &#8211; \\text{Mean})<\/annotation><\/semantics><\/math><br><strong>Step 3: Final value<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Median<\/mtext><mo>\u2212<\/mo><mtext>Mean<\/mtext><mo>=<\/mo><mfrac><mn>61.54<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>30.77<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Median} &#8211; \\text{Mean} = \\frac{61.54}{2} = 30.77<\/annotation><\/semantics><\/math><br><strong>\ud83c\udfaf FINAL ANSWER: C. 30.77\u200b<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 21<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What was the main purpose of the India\u2013MERCOSUR Preferential Trade Agreement discussions held in New Delhi on 16 October 2025?<\/strong><br><br>A. To establish a common currency<br>B. To coordinate defense policies<br>C. To standardize education systems<br>D. To promote trade and investment<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Boost trade &amp; investment<br>\u2705 Answer: D<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 22<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Under the Union Budget 2025\u201326, the FDI limit in the insurance sector was increased from:<\/strong><br><br>A. 26% to 49%<br>B. 51% to 100%<br>C. 74% to 100%<br>D. 49% to 74%<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>74% \u2192 100%<br>\u2705 Answer: C<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 23<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Refer to the following number and symbol series and answer the question that follows. Counting to be done from left to right only. All numbers are single-digit numbers only.<br>(Left) \u00a9 3 @ 8 5 1 \u00a3 1 6 1 5 7 2 8 # \u20ac \u00a3 \u00a9 \u20ac \u00a9 1 3 (Right)<br>How many such numbers are there each of which is immediately preceded by a symbol and also immediately followed by a symbol?<\/strong><br><br>A. 1<br>B. 0<br>C. 2<br>D. 3<\/p>\n\n\n\n<p class=\"is-style-success\">It asked us how many such numbers: it asks counting of it, not value.<br>So there is only one number that is between symbols.<br><strong>\u00a9 3 @<\/strong><br>\ud83d\udc49 Only <strong>1 number<\/strong><br>\u2705 Answer: <strong>A<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 24<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>A train travelling at 60 km\/hr crosses another train travelling in the opposite direction at 84 km\/hr in 30 seconds. What is the combined length (in m) of both the trains?<\/strong><br><br>A. 1000<br>B. 1300<br>C. 1200<br>D. 1100<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Trick:<\/strong><br>Relative speed = 60 + 84 = 144 km\/h<br>\ud83d\udc49 Convert \u2192 144 \u00d7 5\/18 = 40 m\/s<br>Distance = speed \u00d7 time<br>\ud83d\udc49 40 \u00d7 30 = <strong>1200 m<\/strong><br>\u2705 Answer: <strong>C<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 25<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which of the given letter-number clusters will replace the question mark (?) in the following series to make it logically complete?<br>FZN 4 XRF 6 PJX 9 HBP 13 ?<\/strong><br><br>A. ZKW 21<br>B. LFR 17<br>C. ZTH 18<br>D. XHD 19<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>The fastest trick:<br><\/strong>Focus only on number here, not pattern.<br>It increases like 2,3,4,5&#8230;<br>FZN 4 (4 + 2 = <strong>6<\/strong>)<br>XRF <strong>6<\/strong> (6 + 3 = <strong>9<\/strong>)<br>PJX <strong>9<\/strong> (9 + 4 = <strong>13<\/strong>)<br>HBP <strong>13<\/strong> (13 + 5 = <strong>18<\/strong>)<br><br>There is only one option with 18.<br><strong>\u2705 Answer: C. ZTH 18<\/strong><\/p>\n<\/div><\/details><\/div>\n<\/div>\n\n\n\n<!--nextpage-->\n\n\n\n<h2 class=\"wp-block-heading\">RRB NTPC Graduate CBT 1 (16 March 2026) \u2013 <strong>Full Test, Quick Tricks, Detailed Solutions<\/strong> (Part 2: Question 26-50)<\/h2>\n\n\n\n<p>This test contains questions from 26 to 50. Railway Recruitment Board (RRB) conducts the RRB NTPC Exam like 2026 to fill vacancies for Graduate and Undergraduate posts under the Non-Technical Popular Categories (NTPC). Here you will try to attempt the real RRB NTPC Graduate CBT 1 exam, which was conducted on 16 March, 2026. The competitive exam is divided into 4 parts each with 25 questions. You are not just taking the exercise but also learning from the solutions and explanations.<\/p>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Exam Instructions<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total Questions: <strong>25<\/strong> (This is Part 2 of Total 100 Questions.)<\/li>\n\n\n\n<li>Attempt like real exam (no scrolling to answers immediately \ud83d\ude09)<\/li>\n\n\n\n<li>Each question includes:\n<ul class=\"wp-block-list\">\n<li>\u2705 Correct Answer<\/li>\n\n\n\n<li>\ud83e\udde0 Shortcut Trick<\/li>\n\n\n\n<li>\u274c Why other options are wrong<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n        <script>\n          window.KQ_FRONT = window.KQ_FRONT || {};\n          window.KQ_FRONT.quiz_id = 7;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-7\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"7\">\n            <div class=\"kq-loading\">Loading quiz...<\/div>\n        <\/div>\n        \n    <div id=\"kq-auth-modal\" class=\"kq-auth-modal\" style=\"display:none;\">\n      <div class=\"kq-auth-modal-inner\">\n        <button id=\"kq-auth-close\" class=\"kq-auth-close\" aria-label=\"Close\">\u2716<\/button>\n\n        <!-- TAB NAV -->\n        <div class=\"kq-auth-tabs\" role=\"tablist\">\n          <button class=\"kq-tab active\" data-tab=\"register\" type=\"button\" role=\"tab\" aria-selected=\"true\">Register<\/button>\n          <button class=\"kq-tab\" data-tab=\"login\" type=\"button\" role=\"tab\" aria-selected=\"false\">Login<\/button>\n          <button class=\"kq-tab\" data-tab=\"forgot\" type=\"button\" role=\"tab\" aria-selected=\"false\">Forgot<\/button>\n        <\/div>\n\n        <!-- PANELS -->\n        <div class=\"kq-auth-panel-wrap\">\n\n          <!-- REGISTER -->\n          <div class=\"kq-auth-panel\" data-panel=\"register\" style=\"display:block\">\n            <div class=\"kq-auth-card\">\n              <h3>Register<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-username\" placeholder=\"Username\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-email\" placeholder=\"Email\" type=\"email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-signup-btn\" class=\"button kq-btn-small\">Register<\/button>\n              <small style=\"display:block;margin-top:8px;\">Already registered? Use Login tab.<\/small>\n            <\/div>\n          <\/div>\n\n          <!-- LOGIN -->\n          <div class=\"kq-auth-panel\" data-panel=\"login\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Login<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-login-btn\" class=\"button kq-btn-small\">Login<\/button>\n            <\/div>\n          <\/div>\n\n          <!-- FORGOT -->\n          <div class=\"kq-auth-panel\" data-panel=\"forgot\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Forgot Password<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-newpass\" placeholder=\"New Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-forgot-btn\" class=\"button kq-btn-small\">Update Password<\/button>\n            <\/div>\n          <\/div>\n\n        <\/div>\n\n      <\/div>\n    <\/div>\n    \n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">The Solution and Explanation of The Competitive Exam<\/h2>\n\n\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"A boat can row 36 km downstream in the same time as it takes to row 24 km upstream. If the speed of the stream is 3 km\/h, what is the speed of the boat in still water?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 15 km\/h. There is a trick behind it. Check it out.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Manoj starts from Point A and drives 25 km towards South. He then takes a left turn, drives 17 km, turns left and drives 28 km. He then takes a left turn and drives 20 km. He takes a final left turn, drives 3 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90 degrees turns only unless specified)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Always draw simple axes to quickly solve this, visual representation is the key. The correct answer is 3 km to the east.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language, A + B means \u2018A is the mother of B\u2019 A - B means \u2018A is the wife of B\u2019 A \u00d7 B means \u2018A is the sister of B\u2019 A \u00f7 B means \u2018A is the father of B\u2019 Based on the above, how is S related to P if \u2018S - K \u00f7 T \u00d7 V + P\u2019?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is visual representation, so the correct answer is Mother's mother.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"A tower stands vertically on the ground. From a point on the ground which is 28.6 m away from the foot of a tower, the angle of elevation of the top of the tower is found to be 45\u00b0. Find the height of the tower.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The concept says, tan 45 degree means both height and base is same, so the correct answer is 28.6.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language, \u2018BELI\u2019 is coded as \u20186315\u2019 and \u2018EVIL\u2019 is coded as \u20189653\u2019. What is the code for \u2018V\u2019 in the given code language?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The question is not about position but what is the value of V. We can see clearly the in first code the only value and number unique is (B = 1). The same way in second code the unique is (V =9).\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"The mean marks of the following distribution is:\n$$ \\begin{array}{|c|c|} \\hline \\textbf{Marks Obtained} & \\textbf{No. of Students} \\\\ \\hline {81} & {15} \\\\ \\hline {35} & {4} \\\\ \\hline {73} & {3} \\\\ \\hline {56} & {16} \\\\ \\hline \\end{array} $$\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 65. Check out how to do it.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which two neighbors combined have a land border with India longer than China\u2019s border?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Bangladesh and Pakistan. Check other solutions as well.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What is the maximum value that must be assigned to A so that the 8-digit number 816A0408 is divisible by 4?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 9, check out why 9 here.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which major technological advancement characterizes the fourth generation of computers?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is Microprocessors. The others are 1st, 2nd, and 3rd Gen\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"VASE is related to ZEOA in a certain way based on the English alphabetical order. In the same way, DIKW is related to HMGS. To which of the following is LQCO related, following the same logic?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick of the patten is the +4, +4, -4, -4 per letter in the sequence. The correct answer is PUYK.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Based on the English alphabetical order, three of the following four are alike in a certain way and thus form a group. Which is the one that does not belong to that group? (Note: The odd one out is not based on the number of consonants\/vowels or their position in the letter cluster.)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"In order to solve this one you need options, check out them first. The correct answer is DZV.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Read the given statements and conclusions carefully.\nAssuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.\nStatements: Some canals are rivers. Some rivers are oceans. Some oceans are ponds.\nConclusions: (I) All ponds are rivers. (II) All oceans are canals.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is neither follows, but how, you should check this out from here.\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which institution released the policy report titled Internationalisation of Higher Education in India: Prospects, Potential, and Policy Recommendations in December 2025?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It was NITI Aayog that released the policy.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Evaluate: (-9) - (-56) \u00f7 (-14) + (-4) \u00d7 7\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is -41. Check out how to solve it quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In which language was the Sangam literature of South India, composed between 300 BCE and 300 CE, primarily written?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is Tamil.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Seven people F, G, H, I, V, W, and X are sitting around a circular table facing the centre of the table. I sits second to the right of W. I sits third to the left of F. V sits third to the left of X. G is an immediate neighbour of both W and F. How many people sit between H and G when counted from the left of H?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"You have to create a visual map to solve this. The correct answer is 3. We have explained it simply for you.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Consider a hypothetical population of rabbits experiencing logistic growth. If the carrying capacity of their environment is 1000 individuals and the current population is 500, what would you expect to happen to the population?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The question itself says the environment can keep up with 1000 individuals, so it is obvious the rabbits will grow to the level. Check out how.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which postulate of Dalton's Atomic Theory was proven wrong by the discovery of subatomic particles?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Option based, check the explanation to figure it out.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which postulate of Dalton's Atomic Theory was proven wrong by the discovery of subatomic particles?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is an option based, in order to figure it out, check the explanation. How, check out.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Three friends X, Y and Z started a business by investing a sum of money in the ratio of 4 : 2 : 5. After 6 months, X withdraws half of his capital. If the sum invested by Z is \u20b923,000, then out of a total annual profit of \u20b937,000, what is the difference between X's and Y's profit?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 3700, let's learn the trick to find out quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"At present, Sharad is three times as old as his son, and his daughter is 3 years younger than the son. If the sum of the ages of these three people 3 years ago was 63 years, then Sharad's present age (in years) is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Sharad is 45, how, let's check out and learn the trick to solve it quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Below are given two sets of numbers. In each set of numbers, a certain mathematical operation on the first number results in the second number. Similarly, certain mathematical operation on the second number results in the third number and so on. Which of the given options follows the same set of operations as in question?\n(NOTE \u2013 A two\/three-digit number cannot be broken into individual digits for operations, e.g., if 37 is followed by 10, the operation cannot be 3+7 as a two-digit number cannot be broken into individual digits.)\n7 - 21 - 31 - 62; 9 - 27 - 37 - 74\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The pattern here is the first digit then multiply it by 3, next add 10 then at last double it. That is how we get 7, 21, 31, 62 and 9, 27, 37, 74. Check out the correct answer.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Find the area of a regular hexagon whose side measures 14\u221a3 cm.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Apply the formula of hexagon and input the value of a inside of it and you get your answer.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which sector uses computers for online transactions, payroll processing, inventory control, and data analysis?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Only Business and Commerce matches all the description in the question.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"By selling an article at 6\/15 of its actual selling price, Hitesh incurs a loss of 28%. If he sells it at 89% of its actual selling price, then the profit percentage is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Need calculation skill to solve this one fastest, learn how to do it quickly and the answer is 60.2%.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If both the roots of the quadratic equation $A(8x^2 + 4) + Bx + 4x^2 \u2212 8 = 0$ and $3A(2x^2 + 1) + Kx + 3x^2 \u2212 6 = 0$ are common, then what is the value of $9B^2 \u2212 16K^2$?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Though it looks fiendish to solve but there is simple trick to solve it in no time. Let's learn and the correct answer is 0.\"\n    }\n  }\n  }\n}\n<\/script>\n\n\n\n<div class=\"wp-block-coblocks-accordion\">\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 26<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>A boat can row 36 km downstream in the same time as it takes to row 24 km upstream. If the speed of the stream is 3 km\/h, what is the speed of the boat in still water?<\/strong><br><br>A. 15 km\/h<br>B. 12 km\/h<br>C. 21 km\/h<br>D. 18 km\/h<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\ud83e\udde0 Core Concept:<\/strong><br>Let boat speed = <strong>b<\/strong><br>\ud83d\udc49 Downstream = b + 3<br>\ud83d\udc49 Upstream = b \u2212 3<br>Time equal:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>36<\/mn><mrow><mi>b<\/mi><mo>+<\/mo><mn>3<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>24<\/mn><mrow><mi>b<\/mi><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{36}{b+3} = \\frac{24}{b-3}<\/annotation><\/semantics><\/math><br>Cross multiply:<br>36(b \u2212 3) = 24(b + 3)<br>36b \u2212 108 = 24b + 72<br>\ud83d\udc49 12b = 180<br>Divide both sides by 12:<br>\ud83d\udc49 b = <strong>15<\/strong><br>\u2705 Answer: <strong>A. 15 km\/h<\/strong><\/p>\n\n\n\n<p class=\"is-style-error\"><strong>\u274c Why others wrong:<br><\/strong>12 \u2192 ignored stream<br>18, 21 \u2192 wrong cross multiplication<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 27<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Manoj starts from Point A and drives 25 km towards South. He then takes a left turn, drives 17 km, turns left and drives 28 km. He then takes a left turn and drives 20 km. He takes a final left turn, drives 3 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90 degrees turns only unless specified)<\/strong><br><br>A. 2 km to the west<br>B. 2 km to the east<br>C. 3 km to the west<br>D. 3 km to the east<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Trick:<\/strong><br>Always draw simple axes \ud83d\udc47<br>&#8211; Start A<br>&#8211; South 25 \u2192 (0, -25)<br>&#8211; Left (East) 17 \u2192 (17, -25)<br>&#8211; Left (North) 28 \u2192 (17, 3)<br>&#8211; Left (West) 20 \u2192 (-3, 3)<br>&#8211; Left (South) 3 \u2192 (-3, 0)<br> Final point P = (-3, 0)<br>\ud83d\udc49 A = (0,0)<br>So distance = 3 km toward <strong>East<\/strong><br>\u2705 Answer: <strong>D. 3 km toward <strong>East<\/strong><\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 28<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In a certain code language,<br>A + B means \u2018A is the mother of B\u2019<br>A &#8211; B means \u2018A is the wife of B\u2019<br>A \u00d7 B means \u2018A is the sister of B\u2019<br>A \u00f7 B means \u2018A is the father of B\u2019<br>Based on the above, how is S related to P if \u2018S &#8211; K \u00f7 T \u00d7 V + P\u2019?<\/strong><br><br>A. Mother\u2019s sister<br>B. Father\u2019s mother<br>C. Father\u2019s sister<br>D. Mother\u2019s mother<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Expression:<br><\/strong>S &#8211; K \u00f7 T \u00d7 V + P<br>Break step-by-step:<br>S &#8211; K \u2192 S is wife of K<br>K \u00f7 T \u2192 K is father of T<br>\ud83d\udc49 S = mother of T<br>T \u00d7 V \u2192 T is sister of V<br>\ud83d\udc49 S = mother of V<br>V + P \u2192 V is mother of P<br>\ud83d\udc49 S = grandmother of P<br>\u2705 Answer: <strong>D. Mother&#8217;s mother<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 29<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>A tower stands vertically on the ground. From a point on the ground which is 28.6 m away from the foot of a tower, the angle of elevation of the top of the tower is found to be 45\u00b0. Find the height of the tower.<br><\/strong><br>A. 22.6 m<br>B. 28.6 m<br>C. 24.6 m<br>D. 26.6 m<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Why we use Tan here: Because there is asked only about height and base, not hypotenuse.<br><\/strong>The tangent of an angle is defined as the ratio of the length of the&nbsp;<strong>opposite side<\/strong>&nbsp;to the length of the&nbsp;<strong>adjacent side<\/strong>:<br><math data-latex=\"tan (45\\degree) = \\frac{opposite}{adjacent}\"><semantics><mrow><mi>t<\/mi><mi>a<\/mi><mi>n<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>45<\/mn><mi>\u00b0<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><mi>o<\/mi><mi>p<\/mi><mi>p<\/mi><mi>o<\/mi><mi>s<\/mi><mi>i<\/mi><mi>t<\/mi><mi>e<\/mi><\/mrow><mrow><mi>a<\/mi><mi>d<\/mi><mi>j<\/mi><mi>a<\/mi><mi>c<\/mi><mi>e<\/mi><mi>n<\/mi><mi>t<\/mi><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">tan (45\\degree) = \\frac{opposite}{adjacent}<\/annotation><\/semantics><\/math><br>It is considered same on both sides. Meaning if opposite is 1 then adjacent is 1 as well.<br><math data-latex=\"tan (45\\degree) = \\frac{1}{1}\"><semantics><mrow><mi>t<\/mi><mi>a<\/mi><mi>n<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>45<\/mn><mi>\u00b0<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>1<\/mn><mn>1<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">tan (45\\degree) = \\frac{1}{1}<\/annotation><\/semantics><\/math><br><math data-latex=\"tan (45\\degree) = 1\"><semantics><mrow><mi>t<\/mi><mi>a<\/mi><mi>n<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>45<\/mn><mi>\u00b0<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">tan (45\\degree) = 1<\/annotation><\/semantics><\/math><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><\/semantics><\/math>Hence if the base is 28.6 then the height will be the same as well.<br>\ud83d\udc49 height = base = <strong>28.6 m<\/strong><br>\u2705 Answer: <strong>B. 28.6 m<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 30<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In a certain code language, \u2018BELI\u2019 is coded as \u20186315\u2019 and \u2018EVIL\u2019 is coded as \u20189653\u2019. What is the code for \u2018V\u2019 in the given code language?<br><\/strong><br>A. 6<br>B. 3<br>C. 9<br>D. 7<\/p>\n\n\n\n<p class=\"is-style-success\">BELI \u2192 6315<br>EVIL \u2192 9653<br>Common letter = <strong>V appears in both? No<\/strong><br><strong>Look at E and L<br><\/strong>From first word: E = 3, L = 1<br>From second word: E = 9, L = 3<br>\ud83d\udc49 So mapping is NOT fixed per position<br>\ud83d\udc49 But value must be same<br>Look both have these but different positions assigned.<br>B<strong>ELI<\/strong> \u2192 <strong>63<\/strong>1<strong>5<\/strong><br><strong>E<\/strong>V<strong>IL<\/strong> \u2192 9<strong>653<\/strong><br>The question is not about position but what is the value of V. We can see clearly the in first code the only value and number unique is (B = 1). The same way in second code the unique is (V =9).<br>\u2705 Answer: <strong>C. 9<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 31<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The mean marks of the following distribution is:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Marks Obtained<\/th><th class=\"has-text-align-center\" data-align=\"center\">No. of Students<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">81<\/td><td class=\"has-text-align-center\" data-align=\"center\">15<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">35<\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">73<\/td><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">56<\/td><td class=\"has-text-align-center\" data-align=\"center\">16<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"is-style-info\">A. 51<br>B. 60<br>C. 65<br>D. 74<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Calculation (Shortcut)<\/strong><br>Formula:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Mean<\/mtext><mo>=<\/mo><mfrac><mrow><mi mathvariant=\"normal\">\u03a3<\/mi><mi>f<\/mi><mi>x<\/mi><\/mrow><mrow><mi mathvariant=\"normal\">\u03a3<\/mi><mi>f<\/mi><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Mean} = \\frac{\\Sigma fx}{\\Sigma f}<\/annotation><\/semantics><\/math><br>Compute:<br>81\u00d715 = 1215<br>35\u00d74 = 140<br>73\u00d73 = 219<br>56\u00d716 = 896<br>Total = 2470<br>Students = 38<br>Mean = 2470\/38 = <strong>65<\/strong><br>\u2705 Answer: <strong>C. 65<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 32<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which two neighbors combined have a land border with India longer than China\u2019s border?<br><\/strong><br>A. Bangladesh and Pakistan<br>B. Bhutan and Afghanistan<br>C. Nepal and Myanmar<br>D. Pakistan and Nepal<\/p>\n\n\n\n<p class=\"is-style-success\">\ud83d\udc49 Bangladesh (~4096 km)<br>\ud83d\udc49 Pakistan (~3323 km)<br>Combined &gt; China (~3488 km)<br><strong>\u2705 Answer: A. Bangladesh and Pakistan<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 33<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What is the maximum value that must be assigned to A so that the 8-digit number 816A0408 is divisible by 4?<\/strong><br><br>A. 5<br>B. 7<br>C. 9<br>D. 4<\/p>\n\n\n\n<p class=\"is-style-success\">The question asked what is the value of A and it must be max digit.<br>Last 2 digits = 08<br>\ud83d\udc49 Always divisible by 4<br>So any digit works as long as it is max.<br>Max one digit = 9<br>\u2705 Answer: <strong>C. 9<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 34<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which major technological advancement characterizes the fourth generation of computers?<\/strong><br><br>A. Microprocessors<br>B. Transistors<br>C. Vacuum tubes<br>D. Integrated circuits<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: A. Microprocessors<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Gen<\/th><th class=\"has-text-align-center\" data-align=\"center\">Tech<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">1st<\/td><td class=\"has-text-align-center\" data-align=\"center\">Vacuum tubes<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">2nd<\/td><td class=\"has-text-align-center\" data-align=\"center\">Transistors<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">3rd<\/td><td class=\"has-text-align-center\" data-align=\"center\">Integrated circuits (IC)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">4th<\/td><td class=\"has-text-align-center\" data-align=\"center\">Microprocessors<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 35<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>VASE is related to ZEOA in a certain way based on the English alphabetical order. In the same way, DIKW is related to HMGS. To which of the following is LQCO related, following the same logic?<\/strong><br><br>A. QUXL<br>B. QVZL<br>C. OTXJ<br>D. PUYK<\/p>\n\n\n\n<p class=\"is-style-success\">The trick and pattern here is +4, +4, -4, -4.<br>L (+4) \u2192 P<br>Q (+4) \u2192 U<br>C (-4) \u2192 Y<br>O (-4) \u2192 K<br><strong>\u2705 Answer: D. PUYK<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 36<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Based on the English alphabetical order, three of the following four are alike in a certain way and thus form a group. Which is the one that does not belong to that group? (Note: The odd one out is not based on the number of consonants\/vowels or their position in the letter cluster.)<\/strong><br><br>A. BXS<br>B. DZV<br>C. PLG<br>D. WSN<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Trick:<br><\/strong>The last two letters in option A, C, D. Look closely the difference is -5 in next letter.<br>A. X (-5) = S<br>B. Z (-4) = V<br>C. L (-5) = G<br>D. S (-5) = N<br>\ud83d\udc49 Only option B is -4, so it does not belong here.<br>\u2705 Answer: <strong>B<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 37<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Read the given statements and conclusions carefully.<br>Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.<br>Statements:<\/strong><br><strong>&#8211; Some canals are rivers.<br>&#8211; Some rivers are oceans.<br>&#8211; Some oceans are ponds.<br>Conclusions:<br>(I) All ponds are rivers.<br>(II) All oceans are canals.<\/strong><br><br>A. Neither conclusion (I) nor (II) follows<br>B. Both conclusions (I) and (II) follow<br>C. Only conclusion (I) follows<br>D. Only conclusion (II) follows<\/p>\n\n\n\n<p class=\"is-style-success\">The statement is talking about Some, not all, which conlusion does. We cannot assume it ourselves, so:<br><strong>\u2705 Answer: A. Neither follows<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 38<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which institution released the policy report titled Internationalisation of Higher Education in India: Prospects, Potential, and Policy Recommendations in December 2025?<\/strong><br><br>A. All India Council for Technical Education<br>B. University Grants Commission<br>C. Ministry of Education<br>D. NITI Aayog<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: D. NITI Aayog<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 39<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Evaluate: (-9) &#8211; (-56) \u00f7 (-14) + (-4) \u00d7 7<br><\/strong><br>A. -40<br>B. -41<br>C. -43<br>D. -44<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Simplification<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>\u2212<\/mo><mn>9<\/mn><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>56<\/mn><mo>\u00f7<\/mo><mo>\u2212<\/mo><mn>14<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>4<\/mn><mo>\u00d7<\/mo><mn>7<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">-9 &#8211; (-56 \u00f7 -14) + (-4 \u00d7 7)<\/annotation><\/semantics><\/math>\ud83d\udc49 -56 \u00f7 -14 = 4<br>\ud83d\udc49 -4 \u00d7 7 = -28<br>= -9 &#8211; 4 &#8211; 28 = <strong>-41<\/strong><br>\u2705 Answer: <strong>B. -41<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 40<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In which language was the Sangam literature of South India, composed between 300 BCE and 300 CE, primarily written?<\/strong><br><br>A. Sanskrit<br>B. Pali<br>C. Tamil<br>D. Prakrit<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>C. Tamil<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 41<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Seven people F, G, H, I, V, W, and X are sitting around a circular table facing the centre of the table. I sits second to the right of W. I sits third to the left of F. V sits third to the left of X. G is an immediate neighbour of both W and F. How many people sit between H and G when counted from the left of H?<\/strong><br><br>A. One<br>B. Zero<br>C. Three<br>D. Two<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Key Points:<br><\/strong>&#8211; &#8220;right of&#8221; goes clockwise.<br>&#8211; &#8220;left of&#8221; goes anti-clockwise<br>&#8211; Circular table like a clock: 1,2,3,4,5,6,7.<br>&#8211; There are total 7: F,G,H,I,V,W,X.<br>&#8211; All we have to do is to fit them in position to solve.<br><br>Let&#8217;s begin.<br>1 = W<br>2 = V<br>3 = I<br>4 = H<br>5 = X<br>6 = F<br>7 = G<br>\u2705 Now Check Conditions (Fast Trick Method):<br>1. I \u2192 W (2nd to right of W)<br><strong>W<\/strong> \u2192 ? \u2192 <strong>I<\/strong> \u2192 ? \u2192 ? \u2192 ? \u2192 ? \u2192 W&#8230; \u2714\ufe0f (The circle starts from W to W)<br><br>2. I \u2192 F (3rd left of F)<br>W \u2192 ? \u2192 <strong>I<\/strong> \u2192 ? \u2192 ? \u2192 <strong>F<\/strong> \u2192 ? \u2192 W&#8230; \u2714\ufe0f<br><br>3. V \u2192 X (Hard to predict right now, so wait for next)<br>W \u2192 ? \u2192 I \u2192 ? \u2192 ? \u2192 F \u2192 ? \u2192 W&#8230; \u2714\ufe0f<br><br>4. G \u2192 W, F (middle of W and F)<br>W \u2192 ? \u2192 I \u2192 ? \u2192 ? \u2192 F \u2192 <strong>G<\/strong> \u2192 W&#8230; \u2714\ufe0f<br><br>3. V \u2192 X (3rd left of X)<br>W \u2192 <strong>V<\/strong> \u2192 I \u2192 ? \u2192 <strong>X<\/strong> \u2192 F \u2192 G \u2192 W&#8230; \u2714\ufe0f<br><br>Now only one left which will be H.<br>W \u2192 V \u2192 I \u2192 H \u2192 X \u2192 F \u2192 G \u2192 W &#8230; \u2714\ufe0f<br>The question asked:<br>\ud83d\udc49 How many people have sit Between H and G (left of H)<br>W \u2192 V \u2192 I \u2192 <strong>H<\/strong> \u2192 X \u2192 F \u2192 <strong>G<\/strong> \u2192 W &#8230; \u2714\ufe0f<br>Left of H:<br><strong>H<\/strong> \u2192 I \u2192 V \u2192 W \u2192 <strong>G<\/strong> \u2192 F \u2192 X \u2192  H&#8230; \u2714\ufe0f<br>\ud83d\udc49 <strong>Answer C: Three<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 42<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Consider a hypothetical population of rabbits experiencing logistic growth. If the carrying capacity of their environment is 1000 individuals and the current population is 500, what would you expect to happen to the population?<\/strong><br><br>A. The population will decline rapidly due to resource depletion.<br>B. The population will continue to grow exponentially without any constraints.<br>C. The population will experience a sudden crash followed by a rapid rebound.<br>D. The population growth will slow down and eventually stabilize near the carrying capacity.<\/p>\n\n\n\n<p class=\"is-style-success\">The question itself says the environment can keep up with 1000 individuals, so it is obvious the rabbits will grow to the level. &#8220;Population slows as it reaches carrying capacity&#8221;<br><strong>\u2705 Answer: D. The population growth will slow down and eventually stabilize near the carrying capacity.<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 43<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which postulate of Dalton&#8217;s Atomic Theory was proven wrong by the discovery of subatomic particles?<\/strong><br><br>A. Isotopes of the same element have different masses.<br>B. Atoms retain their identity in chemical reactions.<br>C. Atoms of different elements have different masses.<br>D. Matter consists of indivisible atoms.<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Wrong postulate:<br><\/strong>\ud83d\udc49 Atoms indivisible \u274c (electrons discovered)<br><strong>\u2705 Answer: D. Matter consists of indivisible atoms.<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 44<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Three friends X, Y and Z started a business by investing a sum of money in the ratio of 4 : 2 : 5. After 6 months, X withdraws half of his capital. If the sum invested by Z is \u20b923,000, then out of a total annual profit of \u20b937,000, what is the difference between X&#8217;s and Y&#8217;s profit?<\/strong><br><br>A. \u20b93700<br>B. \u20b95015<br>C. \u20b93065<br>D. \u20b94255<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Ratio:<br><\/strong>X:Y:Z = 4:2:5<br>Z = 23000 \u2192 unit = 4600<br>X = 18400<br>Y = 9200<br>After 6 months X becomes half<br>Effective:<br>X = 4\u00d76 + 2\u00d76 = 36<br>Y = 2\u00d712 = 24<br>Ratio = 36:24 = 3:2<br>Profit difference = <strong>\u20b93700<\/strong><br>\u2705 Answer: <strong>A. 3700<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 45<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>At present, Sharad is three times as old as his son, and his daughter is 3 years younger than the son. If the sum of the ages of these three people 3 years ago was 63 years, then Sharad&#8217;s present age (in years) is:<\/strong><br><br>A. 50<br>B. 55<br>C. 45<br>D. 35<\/p>\n\n\n\n<p class=\"is-style-success\">Let son = x<br>Sharad = 3x<br>Daughter = x\u22123<br>3 years ago:<br>(3x\u22123)+(x\u22123)+(x\u22126)=63<br>\ud83d\udc49 5x\u221212=63<br>\ud83d\udc49 x=15<br>Sharad (3x) = 45<br><strong>\ud83c\udfaf FINAL ANSWER: C. 30.77\u200b<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 46<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Below are given two sets of numbers. In each set of numbers, a certain mathematical operation on the first number results in the second number. Similarly, certain mathematical operation on the second number results in the third number and so on. Which of the given options follows the same set of operations as in question?<br>(NOTE \u2013 A two\/three-digit number cannot be broken into individual digits for operations, e.g., if 37 is followed by 10, the operation cannot be 3+7 as a two-digit number cannot be broken into individual digits.)<br>7 &#8211; 21 &#8211; 31 &#8211; 62; 9 &#8211; 27 &#8211; 37 &#8211; 74<\/strong><br><br>A. 11-33-43-86<br>B. 12-36-46-82<br>C. 8-32-42-84<br>D. 6-18-28-76<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pattern:<br><\/strong>\u00d73, +10, \u00d72<br>Let&#8217;s check:<br>7, 21 (7&#215;3), 31 (21+10), 62 (31&#215;2)<br>9, 27 (9&#215;3), 37 (27+10), 74 (37&#215;2)<br>Options A: 11, 33 (11&#215;3), 43 (33+10), 86 (43&#215;2)<br>Check options \u2192 only A fits<br><strong>\u2705 Answer: A. 11-33-43-86<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 47<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Find the area of a regular hexagon whose side measures 14\u221a3 cm.<\/strong><br><br>A. 509\u221a3 cm<sup>2<\/sup><br>B. 294\u221a3 cm<sup>2<\/sup><br>C. 882\u221a3 cm<sup>2<\/sup><br>D. 441\u221a3 cm<sup>2<\/sup><\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Hexagon area: <\/strong><math data-latex=\"\\frac{3\\sqrt{3}}{2}  a^2\"><semantics><mrow><mfrac><mrow><mn>3<\/mn><msqrt><mn>3<\/mn><\/msqrt><\/mrow><mn>2<\/mn><\/mfrac><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{3\\sqrt{3}}{2}  a^2<\/annotation><\/semantics><\/math><br>We have given: <math data-latex=\"a = 14\\sqrt{3}\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mn>14<\/mn><msqrt><mn>3<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">a = 14\\sqrt{3}<\/annotation><\/semantics><\/math><strong><br><\/strong>Let&#8217;s put in:<br><math data-latex=\"\\frac{3\\sqrt{3}}{2}\\ \\times \\   (14\\sqrt{3})^2 \\\\ \\frac{3\\sqrt{3}}{2}\\ \\times \\   ((14)^2(\\sqrt{3})^2) \\\\ \\frac{3\\sqrt{3}}{2}\\ \\times \\   (196\\times3) \\\\ \\frac{3\\sqrt{3}}{2}\\ \\times \\  588 \\\\ 3\\sqrt{3}\\ \\times \\  294 \\\\ 294\\ \\times \\  3\\sqrt{3} \\\\ 882\\sqrt{3}\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mrow><mn>3<\/mn><msqrt><mn>3<\/mn><\/msqrt><\/mrow><mn>2<\/mn><\/mfrac><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>14<\/mn><msqrt><mn>3<\/mn><\/msqrt><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mrow><mn>3<\/mn><msqrt><mn>3<\/mn><\/msqrt><\/mrow><mn>2<\/mn><\/mfrac><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>14<\/mn><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msqrt><mn>3<\/mn><\/msqrt><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mrow><mn>3<\/mn><msqrt><mn>3<\/mn><\/msqrt><\/mrow><mn>2<\/mn><\/mfrac><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>196<\/mn><mo>\u00d7<\/mo><mn>3<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mrow><mn>3<\/mn><msqrt><mn>3<\/mn><\/msqrt><\/mrow><mn>2<\/mn><\/mfrac><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>588<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>3<\/mn><msqrt><mn>3<\/mn><\/msqrt><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>294<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>294<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>3<\/mn><msqrt><mn>3<\/mn><\/msqrt><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>882<\/mn><msqrt><mn>3<\/mn><\/msqrt><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\frac{3\\sqrt{3}}{2}\\ \\times \\   (14\\sqrt{3})^2 \\\\ \\frac{3\\sqrt{3}}{2}\\ \\times \\   ((14)^2(\\sqrt{3})^2) \\\\ \\frac{3\\sqrt{3}}{2}\\ \\times \\   (196\\times3) \\\\ \\frac{3\\sqrt{3}}{2}\\ \\times \\  588 \\\\ 3\\sqrt{3}\\ \\times \\  294 \\\\ 294\\ \\times \\  3\\sqrt{3} \\\\ 882\\sqrt{3}<\/annotation><\/semantics><\/math><strong><br>\u2705 Answer: C<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 48<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which sector uses computers for online transactions, payroll processing, inventory control, and data analysis?<\/strong><br><br>A. Manufacturing Plants<br>B. Research<br>C. Service Industry<br>D. Business and Commerce<\/p>\n\n\n\n<p class=\"is-style-success\">Business &amp; commerce uses all listed functions<br><strong>\u2705 Answer: D. Business and Commerce<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 49<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>By selling an article at 6\/15 of its actual selling price, Hitesh incurs a loss of 28%. If he sells it at 89% of its actual selling price, then the profit percentage is:<\/strong><br><br>A. 59.2%<br>B. 60.5%<br>C. 60.2%<br>D. 60.7%<\/p>\n\n\n\n<p class=\"is-style-success\">Let actual SP (Selling Price) = 100<br>6\/15 SP = 40<br>Loss 28% \u2192 CP = 40 \/ 0.72 = 55.56<br>New SP = 89<br>Profit = (89\u221255.56)\/55.56 \u00d7100 \u2248 60.2%<br><strong>\u2705 Answer: C. 60.2%<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 50<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>If both the roots of the quadratic equation <\/strong><math data-latex=\"A(8x^2 + 4) + Bx + 4x^2 \u2212 8 = 0\"><semantics><mrow><mi>A<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>8<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>4<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>B<\/mi><mi>x<\/mi><mo>+<\/mo><mn>4<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>8<\/mn><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">A(8x^2 + 4) + Bx + 4x^2 \u2212 8 = 0<\/annotation><\/semantics><\/math><strong> and <\/strong><math data-latex=\"3A(2x^2 + 1) + Kx + 3x^2 \u2212 6 = 0\"><semantics><mrow><mn>3<\/mn><mi>A<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>2<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>K<\/mi><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>6<\/mn><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3A(2x^2 + 1) + Kx + 3x^2 \u2212 6 = 0<\/annotation><\/semantics><\/math> <strong>are common, then what is the value of <\/strong><math data-latex=\"9B^2 \u2212 16K^2\"><semantics><mrow><mn>9<\/mn><msup><mi>B<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>16<\/mn><msup><mi>K<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">9B^2 \u2212 16K^2<\/annotation><\/semantics><\/math> <strong>?<\/strong><br><br>A. -1<br>B. 1<br>C. 2<br>D. 0<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>The fastest trick:<br><\/strong>Make equation standard.<br>\ud83d\udc49 Expression like:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>9<\/mn><msup><mi>B<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>16<\/mn><msup><mi>K<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">9B^2 &#8211; 16K^2<\/annotation><\/semantics><\/math>\ud83d\udc49 Recognize:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mi>B<\/mi><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mn>4<\/mn><mi>K<\/mi><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">(3B)^2 &#8211; (4K)^2<\/annotation><\/semantics><\/math><br>Compare ratios \u2192 get: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>B<\/mi><mo>:<\/mo><mi>K<\/mi><mo>=<\/mo><mn>4<\/mn><mo>:<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">B : K = 4 : 3<\/annotation><\/semantics><\/math>Direct observe: (put values of ration in B and K)<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>9<\/mn><msup><mi>B<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><mn>16<\/mn><msup><mi>K<\/mi><mn>2<\/mn><\/msup><mo>\u21d2<\/mo><mtext>difference&nbsp;=&nbsp;0<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">9B^2 = 16K^2 \\Rightarrow \\text{difference = 0}<\/annotation><\/semantics><\/math><br>\u23f1\ufe0f Time: <strong>20\u201325 sec<\/strong><br><br><strong>Want to learn Math then look:<br><\/strong>\ud83d\udd34 Given<br>Two quadratic equations:<br>(1)<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>A<\/mi><mo stretchy=\"false\">(<\/mo><mn>8<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>4<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>B<\/mi><mi>x<\/mi><mo>+<\/mo><mn>4<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>8<\/mn><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">A(8x^2 + 4) + Bx + 4x^2 &#8211; 8 = 0<\/annotation><\/semantics><\/math>(2)<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>3<\/mn><mi>A<\/mi><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>K<\/mi><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>6<\/mn><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3A(2x^2 + 1) + Kx + 3x^2 &#8211; 6 = 0<\/annotation><\/semantics><\/math>\ud83d\udc49 Both have <strong>same roots<\/strong><br><br><strong>\ud83e\udde0 Core Concept (VERY IMPORTANT)<\/strong><br>\ud83d\udc49 If two quadratic equations have <strong>same roots<\/strong>, then:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><msub><mi>a<\/mi><mn>1<\/mn><\/msub><msub><mi>a<\/mi><mn>2<\/mn><\/msub><\/mfrac><mo>=<\/mo><mfrac><msub><mi>b<\/mi><mn>1<\/mn><\/msub><msub><mi>b<\/mi><mn>2<\/mn><\/msub><\/mfrac><mo>=<\/mo><mfrac><msub><mi>c<\/mi><mn>1<\/mn><\/msub><msub><mi>c<\/mi><mn>2<\/mn><\/msub><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{a_1}{a_2} = \\frac{b_1}{b_2} = \\frac{c_1}{c_2}<\/annotation><\/semantics><\/math><br><br>\ud83d\udc49 (Coefficients are proportional)<br><br><strong>Equation (1):<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>A<\/mi><mo stretchy=\"false\">(<\/mo><mn>8<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>4<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>B<\/mi><mi>x<\/mi><mo>+<\/mo><mn>4<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>8<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">A(8x^2 + 4) + Bx + 4x^2 &#8211; 8<\/annotation><\/semantics><\/math>Expand:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>8<\/mn><mi>A<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>4<\/mn><mi>A<\/mi><mo>+<\/mo><mi>B<\/mi><mi>x<\/mi><mo>+<\/mo><mn>4<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>8<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">8Ax^2 + 4A + Bx + 4x^2 &#8211; 8<\/annotation><\/semantics><\/math>Group terms:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mn>8<\/mn><mi>A<\/mi><mo>+<\/mo><mn>4<\/mn><mo stretchy=\"false\">)<\/mo><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>B<\/mi><mi>x<\/mi><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mn>4<\/mn><mi>A<\/mi><mo>\u2212<\/mo><mn>8<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(8A + 4)x^2 + Bx + (4A &#8211; 8) = 0<\/annotation><\/semantics><\/math><br><strong>Equation (2):<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>3<\/mn><mi>A<\/mi><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>K<\/mi><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3A(2x^2 + 1) + Kx + 3x^2 &#8211; 6<\/annotation><\/semantics><\/math>Expand:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>6<\/mn><mi>A<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>3<\/mn><mi>A<\/mi><mo>+<\/mo><mi>K<\/mi><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">6Ax^2 + 3A + Kx + 3x^2 &#8211; 6<\/annotation><\/semantics><\/math>Group terms:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mn>6<\/mn><mi>A<\/mi><mo>+<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>K<\/mi><mi>x<\/mi><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mi>A<\/mi><mo>\u2212<\/mo><mn>6<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(6A + 3)x^2 + Kx + (3A &#8211; 6) = 0<\/annotation><\/semantics><\/math><br><strong>Step 2: Apply proportionality<\/strong><br>Compare coefficients:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mn>8<\/mn><mi>A<\/mi><mo>+<\/mo><mn>4<\/mn><\/mrow><mrow><mn>6<\/mn><mi>A<\/mi><mo>+<\/mo><mn>3<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mi>B<\/mi><mi>K<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>4<\/mn><mi>A<\/mi><mo>\u2212<\/mo><mn>8<\/mn><\/mrow><mrow><mn>3<\/mn><mi>A<\/mi><mo>\u2212<\/mo><mn>6<\/mn><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{8A + 4}{6A + 3} = \\frac{B}{K} = \\frac{4A &#8211; 8}{3A &#8211; 6}<\/annotation><\/semantics><\/math><br><strong>Step 3: Solve ratio (first = third)<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mn>8<\/mn><mi>A<\/mi><mo>+<\/mo><mn>4<\/mn><\/mrow><mrow><mn>6<\/mn><mi>A<\/mi><mo>+<\/mo><mn>3<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>4<\/mn><mi>A<\/mi><mo>\u2212<\/mo><mn>8<\/mn><\/mrow><mrow><mn>3<\/mn><mi>A<\/mi><mo>\u2212<\/mo><mn>6<\/mn><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{8A + 4}{6A + 3} = \\frac{4A &#8211; 8}{3A &#8211; 6}<\/annotation><\/semantics><\/math><br><strong>Simplify both:<\/strong><br>Left:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>8<\/mn><mi>A<\/mi><mo>+<\/mo><mn>4<\/mn><mo>=<\/mo><mn>4<\/mn><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mi>A<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><mn>6<\/mn><mi>A<\/mi><mo>+<\/mo><mn>3<\/mn><mo>=<\/mo><mn>3<\/mn><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mi>A<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">8A + 4 = 4(2A + 1), \\quad 6A + 3 = 3(2A + 1)<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mrow><mn>4<\/mn><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mi>A<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mn>3<\/mn><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mi>A<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">= \\frac{4(2A+1)}{3(2A+1)} = \\frac{4}{3}<\/annotation><\/semantics><\/math>Right:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>4<\/mn><mi>A<\/mi><mo>\u2212<\/mo><mn>8<\/mn><mo>=<\/mo><mn>4<\/mn><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u2212<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><mn>3<\/mn><mi>A<\/mi><mo>\u2212<\/mo><mn>6<\/mn><mo>=<\/mo><mn>3<\/mn><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u2212<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">4A &#8211; 8 = 4(A &#8211; 2), \\quad 3A &#8211; 6 = 3(A &#8211; 2)<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mrow><mn>4<\/mn><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u2212<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mn>3<\/mn><mo stretchy=\"false\">(<\/mo><mi>A<\/mi><mo>\u2212<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">= \\frac{4(A-2)}{3(A-2)} = \\frac{4}{3}<\/annotation><\/semantics><\/math>\ud83d\udc49 Both sides equal automatically \u2714\ufe0f<br>\ud83d\udc49 So condition satisfied for all valid A<br><br><strong>Step 4: Use middle ratio<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mi>B<\/mi><mi>K<\/mi><\/mfrac><mo>=<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{B}{K} = \\frac{4}{3}<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>B<\/mi><mo>:<\/mo><mi>K<\/mi><mo>=<\/mo><mn>4<\/mn><mo>:<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">B : K = 4 : 3<\/annotation><\/semantics><\/math><br><strong>Step 5: Put values<\/strong><br>Let:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>B<\/mi><mo>=<\/mo><mn>4<\/mn><mi>t<\/mi><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><mi>K<\/mi><mo>=<\/mo><mn>3<\/mn><mi>t<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">B = 4t,\\quad K = 3t<\/annotation><\/semantics><\/math><br><strong>Step 6: Find required value<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>9<\/mn><msup><mi>B<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>16<\/mn><msup><mi>K<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">9B^2 &#8211; 16K^2<\/annotation><\/semantics><\/math>Substitute:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>9<\/mn><mo stretchy=\"false\">(<\/mo><mn>4<\/mn><mi>t<\/mi><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>16<\/mn><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mi>t<\/mi><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">= 9(4t)^2 &#8211; 16(3t)^2<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>9<\/mn><mo>\u22c5<\/mo><mn>16<\/mn><msup><mi>t<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>16<\/mn><mo>\u22c5<\/mo><mn>9<\/mn><msup><mi>t<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">= 9 \\cdot 16t^2 &#8211; 16 \\cdot 9t^2<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>144<\/mn><msup><mi>t<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>144<\/mn><msup><mi>t<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">= 144t^2 &#8211; 144t^2<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 0<\/annotation><\/semantics><\/math><strong>\u2705 Answer: D. 0<\/strong><\/p>\n<\/div><\/details><\/div>\n<\/div>\n\n\n\n<!--nextpage-->\n\n\n\n<h2 class=\"wp-block-heading\">RRB NTPC Graduate CBT 1 (16 March 2026) \u2013 <strong>Exercise With Fastest Solutions<\/strong> (Part 3: Question 51-75)<\/h2>\n\n\n\n<p>This is the part 3 which contains questions from 51 to 75. Railway Recruitment Board (RRB) conducts the RRB NTPC Exam like 2026 to fill vacancies for Graduate and Undergraduate posts under the Non-Technical Popular Categories (NTPC). Here you will try to attempt the real RRB NTPC Graduate CBT 1 exam, which was conducted on 16 March, 2026. The competitive exam is divided into 4 parts each with 25 questions. You are not just taking the exercise but also learning from the solutions and explanations.<\/p>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Exam Instructions<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total Questions: <strong>25<\/strong> (This is Part 3 of Total 100 Questions.)<\/li>\n\n\n\n<li>Attempt like real exam (no scrolling to answers immediately \ud83d\ude09)<\/li>\n\n\n\n<li>Each question includes:\n<ul class=\"wp-block-list\">\n<li>\u2705 Correct Answer<\/li>\n\n\n\n<li>\ud83e\udde0 Shortcut Trick<\/li>\n\n\n\n<li>\u274c Why other options are wrong<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n        <script>\n          window.KQ_FRONT = window.KQ_FRONT || {};\n          window.KQ_FRONT.quiz_id = 9;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-9\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"9\">\n            <div class=\"kq-loading\">Loading quiz...<\/div>\n        <\/div>\n        \n    <div id=\"kq-auth-modal\" class=\"kq-auth-modal\" style=\"display:none;\">\n      <div class=\"kq-auth-modal-inner\">\n        <button id=\"kq-auth-close\" class=\"kq-auth-close\" aria-label=\"Close\">\u2716<\/button>\n\n        <!-- TAB NAV -->\n        <div class=\"kq-auth-tabs\" role=\"tablist\">\n          <button class=\"kq-tab active\" data-tab=\"register\" type=\"button\" role=\"tab\" aria-selected=\"true\">Register<\/button>\n          <button class=\"kq-tab\" data-tab=\"login\" type=\"button\" role=\"tab\" aria-selected=\"false\">Login<\/button>\n          <button class=\"kq-tab\" data-tab=\"forgot\" type=\"button\" role=\"tab\" aria-selected=\"false\">Forgot<\/button>\n        <\/div>\n\n        <!-- PANELS -->\n        <div class=\"kq-auth-panel-wrap\">\n\n          <!-- REGISTER -->\n          <div class=\"kq-auth-panel\" data-panel=\"register\" style=\"display:block\">\n            <div class=\"kq-auth-card\">\n              <h3>Register<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-username\" placeholder=\"Username\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-email\" placeholder=\"Email\" type=\"email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-signup-btn\" class=\"button kq-btn-small\">Register<\/button>\n              <small style=\"display:block;margin-top:8px;\">Already registered? Use Login tab.<\/small>\n            <\/div>\n          <\/div>\n\n          <!-- LOGIN -->\n          <div class=\"kq-auth-panel\" data-panel=\"login\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Login<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-login-btn\" class=\"button kq-btn-small\">Login<\/button>\n            <\/div>\n          <\/div>\n\n          <!-- FORGOT -->\n          <div class=\"kq-auth-panel\" data-panel=\"forgot\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Forgot Password<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-newpass\" placeholder=\"New Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-forgot-btn\" class=\"button kq-btn-small\">Update Password<\/button>\n            <\/div>\n          <\/div>\n\n        <\/div>\n\n      <\/div>\n    <\/div>\n    \n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">The Solution and Explanation of The Competitive Exam<\/h2>\n\n\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"If $a : b = 2 : 3$, then ($7a^3 - 2b^3$) : ($b^3 - a^3$) is____?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 2 : 19, but it is not easy. There is a trick behind it. Check it out.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"In a triangle PQR, \u2220QOR = 130\u00b0, where O is the in-centre of triangle PQR. The measure of \u2220QPR is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 80 degree and learn the real way to solve.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Three printing machines, P, Q and R, when each is working alone, can print one lakh books in, respectively, 8 hours, 16 hours and 24 hours. These machines print books in turns of one hour each, starting with P, followed by Q and then by R. However, after a total of 9 hours, P stops functioning, but Q and R continue working alternately for an hour each, with Q working during the 10th hour, till the printing of all the one lakh books is completed. In how many hours in all did machines Q and R complete printing the remaining books?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 6 hours. Let's learn the trick to solve it in no time.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Which sector's share in GDP increased significantly by 1990, reflecting a shift in the Indian economy?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Out of all the options, Services is the right one\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Consider the following statements about Thawar Chand Gehlot.\n1. He is the first person from Madhya Pradesh to serve as the Governor of Karnataka.\n2. He is the 19th Governor of Karnataka. Which of the above statements is\/are correct?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is both 1 and 2, but how, let's learn.\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"There is a wooden block in the form of a cube whose each side is 8 meters long. The maximum possible number of cylinders with a diameter of 1 meter and a height of 4 meters were cut from this block. The cylinders are to be painted at the rate of \u20b914. per square meter. What is the total amount (in \u20b9) needed to paint all the cylinders if we paint the entire surface of each cylinder? (Take $\\pi = \\frac{22}{7}$)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 25,344, let's learn how to solve it quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"This question is based on the five, three-digit numbers given below.\n(Left) 458 652 748 351 591 (Right)\n(Example: 697 \u2013 First digit = 6, second digit = 9 and third digit = 7)\nNOTE - All operations to be done from left to right. What will be the resultant if third digit of the highest number is multiplied with the third digit of lowest number?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 8. Let's learn how to solve it in 3 seconds.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The sum of two numbers is 56. Their difference is $\\frac{1}{7}$ of their sum. Their LCM is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 96. Let's learn the trick to solve it in 3 seconds.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language, \u2018CARD\u2019 is coded as \u20184628\u2019 and \u2018NEAT\u2019 is coded as \u20183574\u2019. What is the code for \u2018A\u2019 in that language?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 4. Let's learn the trick to solve it in 3 seconds.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What is the primary function of the water vascular system in echinoderms, such as starfish?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Locomotion and feeding\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which Harappan city, around 2500 BCE, is noted for its dockyard, indicating advanced architectural planning for trade?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Lothal is the right answer to choose.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language,\nA @ B means \u2018A is the son of B\u2019,\nA # B means \u2018A is the sister of B\u2019, \nA + B means \u2018A is the wife of B\u2019\nand A % B means \u2018A is the father of B\u2019.\nBased on the above, how is E related to B if \u2018E + R @ D% N # B\u2019?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Brother's wife, let's learn the simple trick to solve it quickly.\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"$\\frac{\\sqrt[3]{6859}}{\\sqrt[4]{256}} \\times \\frac{2}{57} \\times 168$ = ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 28, let's learn the mathematics trick to solve it in no time.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"According to the Banking Laws (Amendment) Act, 2025, the threshold for \u2018substantial interest\u2019 in a bank was revised from \u20b95 lakh to which of the following amounts?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is \u20b92 crore.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A, B, C, D, E and F live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2, and so on till the topmost floor is numbered 6. Only five people live above D. Only two people live above A. C lives below F but above A. B does not live on an even numbered floor. How many people live below C?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Four. Let's learn the right trick to solve it quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The splitting of the ancient Indo\u2013Brahma river into the Indus, Ganga, and Brahmaputra drainage systems is believed to have been primarily caused by which geological event?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Pleistocene upheaval. We have explained it simply for you.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"When was the India European Free Trade Association (EFTA) Trade and Economic Partnership Agreement (TEPA) signed, which came into effect on 1 October 2025?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"March 2024.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which cultural and musical group celebrated its 10th anniversary in December 2025?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Robir Kiran\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The summer solstice occurs when the Sun is directly overhead at which of the following latitudes?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Tropic of Cancer\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"At what rate (in percentage) per year will a sum of money double itself in 16 years on simple interest?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 6.25. Let's learn the way to solve it in 3 second.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Select the set in which the numbers are related in the same way as are the numbers of the following sets.\n(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 \u2013 Operations on 13 such as adding \/ subtracting \/ multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)\n(20, 46, 2)\n(32, 136, 24)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is the 2nd value is double of 1st value addition with triple of 3rd value. The correct answer is (6, 42, 10).\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A file name is highlighted, and you want to copy it to another folder while keeping it in the original folder as well. Which pair of steps matches this task?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"For copy we press Press Ctrl + C and keep the original file intact then for paste we press Ctrl + V to the point we want to put the copied file.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"There are 78 members in group A, 22 members in group B and 34 members in group C. All the members of these groups went to a restaurant. The average amounts spent on each member of groups A, B and C are \u20b9136, \u20b9383 and \u20b9457, respectively. The overall average amount (in \u20b9) spent per member is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 258, let's learn the trick to solve it quickly\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In 2025, which Indian High Court issued the pioneering 'Policy Regarding the Use of AI Tools in District Judiciary', becoming the first in the country to frame comprehensive guidelines for artificial intelligence (AI) use in judicial work?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Kerala High Court\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following sectors observed a negative growth rate in Real GVA (Gross Value Added) during Q1 of FY 2025-26 as per the report published by NSO and MoSPI?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Mining & Quarrying\"\n    }\n  }\n  }\n}\n<\/script>\n\n\n\n<div class=\"wp-block-coblocks-accordion\">\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 51<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>If <\/strong><math data-latex=\"a : b = 2 : 3\"><semantics><mrow><mi>a<\/mi><mo lspace=\"0.2222em\" rspace=\"0.2222em\">:<\/mo><mi>b<\/mi><mo>=<\/mo><mn>2<\/mn><mo lspace=\"0.2222em\" rspace=\"0.2222em\">:<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">a : b = 2 : 3<\/annotation><\/semantics><\/math><strong>, then (<\/strong><math data-latex=\"7a^3 - 2b^3\"><semantics><mrow><mn>7<\/mn><msup><mi>a<\/mi><mn>3<\/mn><\/msup><mo>\u2212<\/mo><mn>2<\/mn><msup><mi>b<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">7a^3 &#8211; 2b^3<\/annotation><\/semantics><\/math><strong>) : (<\/strong><math data-latex=\"b^3 - a^3\"><semantics><mrow><msup><mi>b<\/mi><mn>3<\/mn><\/msup><mo>\u2212<\/mo><msup><mi>a<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">b^3 &#8211; a^3<\/annotation><\/semantics><\/math><strong>) is____?<\/strong><br><br>A. 2 : 19<br>B. 3 : 11<br>C. 13 : 6<br>D. 3 : 14<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Given:<br><\/strong>a : b = 2 : 3 \u2192 let a = 2k, b = 3k<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mn>7<\/mn><msup><mi>a<\/mi><mn>3<\/mn><\/msup><mo>\u2212<\/mo><mn>2<\/mn><msup><mi>b<\/mi><mn>3<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><mo>:<\/mo><mo stretchy=\"false\">(<\/mo><msup><mi>b<\/mi><mn>3<\/mn><\/msup><mo>\u2212<\/mo><msup><mi>a<\/mi><mn>3<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(7a^3 &#8211; 2b^3) : (b^3 &#8211; a^3)<\/annotation><\/semantics><\/math>Substitute: a\u00b3 = 8k\u00b3, b\u00b3 = 27k\u00b3<br>Numerator:<br>= 7\u00d78 \u2212 2\u00d727 = 56 \u2212 54 = 2<br>Denominator:<br>= 27 \u2212 8 = 19<br>\u2705 Answer: <strong>A. 2 : 19<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 52<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In a triangle PQR, \u2220QOR = 130\u00b0, where O is the in-centre of triangle PQR. The measure of \u2220QPR is:<\/strong><br><br>A. 70\u00b0<br>B. 80\u00b0<br>C. 60\u00b0<br>D. 50\u00b0<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Key Formula:<br><\/strong>Angle at in-centre:  <math data-latex=\"\\angle{BIC} = 90\\degree + \\frac{A}{2}\"><semantics><mrow><mi>\u2220<\/mi><mrow><mi>B<\/mi><mi>I<\/mi><mi>C<\/mi><\/mrow><mo>=<\/mo><mn>90<\/mn><mi>\u00b0<\/mi><mo>+<\/mo><mfrac><mi>A<\/mi><mn>2<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\angle{BIC} = 90\\degree + \\frac{A}{2}<\/annotation><\/semantics><\/math><br>Here: <math data-latex=\"130 = 90 + \\frac{\\angle{P}}{2}\"><semantics><mrow><mn>130<\/mn><mo>=<\/mo><mn>90<\/mn><mo>+<\/mo><mfrac><mrow><mi>\u2220<\/mi><mi>P<\/mi><\/mrow><mn>2<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">130 = 90 + \\frac{\\angle{P}}{2}<\/annotation><\/semantics><\/math><br>\ud83d\udc49 <math data-latex=\"\\frac{\\angle{P}}{2} = 130 - 90 \\\\ \\frac{\\angle{P}}{2} = 40 \\\\ \\angle{P} = 40 \\times 2\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mrow><mi>\u2220<\/mi><mi>P<\/mi><\/mrow><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>130<\/mn><mo>\u2212<\/mo><mn>90<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mrow><mi>\u2220<\/mi><mi>P<\/mi><\/mrow><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>40<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>\u2220<\/mi><mi>P<\/mi><mo>=<\/mo><mn>40<\/mn><mo>\u00d7<\/mo><mn>2<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\frac{\\angle{P}}{2} = 130 &#8211; 90 \\\\ \\frac{\\angle{P}}{2} = 40 \\\\ \\angle{P} = 40 \\times 2<\/annotation><\/semantics><\/math><br>\ud83d\udc49 P = <strong>80\u00b0<\/strong><br>\u2705 Answer: <strong>B. <strong>80\u00b0<\/strong><\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 53<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Three printing machines, P, Q and R, when each is working alone, can print one lakh books in, respectively, 8 hours, 16 hours and 24 hours. These machines print books in turns of one hour each, starting with P, followed by Q and then by R. However, after a total of 9 hours, P stops functioning, but Q and R continue working alternately for an hour each, with Q working during the 10th hour, till the printing of all the one lakh books is completed. In how many hours in all did machines Q and R complete printing the remaining books?<\/strong><br><br>A. 9<br>B. 6<br>C. 12<br>D. 15<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Rates:<\/strong><br>P = 1\/8<br>Q = 1\/16<br>R = 1\/24<br><strong>First 9 hours (P,Q,R cycle):<\/strong><br>1 cycle (3 hrs):<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>1<\/mn><mn>8<\/mn><\/mfrac><mo>+<\/mo><mfrac><mn>1<\/mn><mn>16<\/mn><\/mfrac><mo>+<\/mo><mfrac><mn>1<\/mn><mn>24<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>11<\/mn><mn>48<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{8} + \\frac{1}{16} + \\frac{1}{24} = \\frac{11}{48}<\/annotation><\/semantics><\/math>3 cycles (9 hrs):<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>33<\/mn><mn>48<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>11<\/mn><mn>16<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">= \\frac{33}{48} = \\frac{11}{16}<\/annotation><\/semantics><\/math>Remaining:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>1<\/mn><mo>\u2212<\/mo><mfrac><mn>11<\/mn><mn>16<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>5<\/mn><mn>16<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">1 &#8211; \\frac{11}{16} = \\frac{5}{16}<\/annotation><\/semantics><\/math><br><strong>Now Q &amp; R alternate:<\/strong><br>2 hrs work (1 cycle = 2 hours):<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>1<\/mn><mn>16<\/mn><\/mfrac><mo>+<\/mo><mfrac><mn>1<\/mn><mn>24<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>5<\/mn><mn>48<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{16} + \\frac{1}{24} = \\frac{5}{48}<\/annotation><\/semantics><\/math>Time:<br><math data-latex=\"\\frac{\\frac{5}{16}}{\\frac{5}{48}} = \\frac{5 \\times 48}{5 \\times 16} = \\frac{240}{80} = \"><semantics><mrow><mfrac><mfrac><mn>5<\/mn><mn>16<\/mn><\/mfrac><mfrac><mn>5<\/mn><mn>48<\/mn><\/mfrac><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>5<\/mn><mo>\u00d7<\/mo><mn>48<\/mn><\/mrow><mrow><mn>5<\/mn><mo>\u00d7<\/mo><mn>16<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>240<\/mn><mn>80<\/mn><\/mfrac><mo>=<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{\\frac{5}{16}}{\\frac{5}{48}} = \\frac{5 \\times 48}{5 \\times 16} = \\frac{240}{80} = <\/annotation><\/semantics><\/math>3 cycles = 6 hours (3 x 2)<br>\u2705 Answer: <strong>B. 6<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 54<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which sector&#8217;s share in GDP increased significantly by 1990, reflecting a shift in the Indian economy?<br><\/strong><br>A. Industry<br>B. Services<br>C. Agriculture<br>D. Mining<\/p>\n\n\n\n<p class=\"is-style-success\">\ud83d\udc49 Post-1990 \u2192 Service sector boom<br>\u2705 Answer: <strong>B. Services<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 55<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Consider the following statements about Thawar Chand Gehlot.<br>1. He is the first person from Madhya Pradesh to serve as the Governor of Karnataka.<br>2. He is the 19th Governor of Karnataka. Which of the above statements is\/are correct?<\/strong><br><br>A. Both 1 and 2<br>B. Neither 1 nor 2<br>C. Only 2<br>D. Only 1<\/p>\n\n\n\n<p class=\"is-style-success\">19th Governor \u2714\ufe0f<br>First from MP \u2714\ufe0f<br><strong>\u2705 Answer: A. Both 1 and 2<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 56<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>There is a wooden block in the form of a cube whose each side is 8 meters long. The maximum possible number of cylinders with a diameter of 1 meter and a height of 4 meters were cut from this block. The cylinders are to be painted at the rate of \u20b914. per square meter. What is the total amount (in \u20b9) needed to paint all the cylinders if we paint the entire surface of each cylinder? (Take <\/strong><math data-latex=\"\\pi = \\frac{22}{7}\"><semantics><mrow><mi>\u03c0<\/mi><mo>=<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\pi = \\frac{22}{7}<\/annotation><\/semantics><\/math><strong>)<br><\/strong><br>A. 24,527<br>B. 23,455<br>C. 25,344<br>D. 24,325<\/p>\n\n\n\n<p class=\"is-style-success\">Cube side = 8 m<br>Number of cylinders:<br>Along length = 8 \/ 1 = 8<br>Width = 8<br>Height = 8 \/ 4 = 2<br>\ud83d\udc49 Total = 8 \u00d7 8 \u00d7 2 = 128<br><br><strong>Surface area of 1 cylinder:<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><mi>\u03c0<\/mi><mi>r<\/mi><mo stretchy=\"false\">(<\/mo><mi>h<\/mi><mo>+<\/mo><mi>r<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>0.5<\/mn><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mn>4.5<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">2\\pi r(h+r) = 2 \u00d7 \\frac{22}{7} \u00d7 0.5 \u00d7 (4.5)<\/annotation><\/semantics><\/math>= 14.14 m\u00b2 approx<br>Total area:<br>= 128 \u00d7 14.14 \u2248 1810<br>Cost:<br>= 1810 \u00d7 14 \u2248 <strong>25,344<\/strong><br>\u2705 Answer: <strong>C. 25,344<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 57<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>This question is based on the five, three-digit numbers given below.<br>(Left) 458 652 748 351 591 (Right)<br>(Example: 697 \u2013 First digit = 6, second digit = 9 and third digit = 7)<br>NOTE &#8211; All operations to be done from left to right. What will be the resultant if third digit of the highest number is multiplied with the third digit of lowest number?<\/strong><br><br>A. 8<br>B. 7<br>C. 6<br>D. 5<\/p>\n\n\n\n<p class=\"is-style-success\">Highest = 748 \u2192 last digit = 8<br>Lowest = 351 \u2192 last digit = 1<br>\ud83d\udc49 8 \u00d7 1 = 8<br>\u2705 Answer: <strong>A. 8<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 58<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The sum of two numbers is 56. Their difference is <\/strong><math data-latex=\"\\frac{1}{7}\"><semantics><mfrac><mn>1<\/mn><mn>7<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{1}{7}<\/annotation><\/semantics><\/math><strong> of their sum. Their LCM is:<\/strong><br><br>A. 96<br>B. 63<br>C. 72<br>D. 84<\/p>\n\n\n\n<p class=\"is-style-success\">Sum = 56<br>Difference = 8<br>Solve:<br>x + y = 56<br>x \u2212 y = 8<br>\ud83d\udc49 x = 32, y = 24<br>LCM = 96<br><strong>The correct answer is A: 96<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 59<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In a certain code language, \u2018CARD\u2019 is coded as \u20184628\u2019 and \u2018NEAT\u2019 is coded as \u20183574\u2019. What is the code for \u2018A\u2019 in that language?<\/strong><br><br>A. 4<br>B. 6<br>C. 3<br>D. 7<\/p>\n\n\n\n<p class=\"is-style-success\">C<strong>A<\/strong>RD = <strong>4<\/strong>628<br>NE<strong>A<\/strong>T = 357<strong>4<\/strong><br>Common letter = <strong>A and 4 appears in both<\/strong><br>\ud83d\udc49 A = <strong>4<\/strong><br>\u2705 Answer: <strong>A. 4<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 60<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What is the primary function of the water vascular system in echinoderms, such as starfish?<\/strong><br><br>A. Reproduction<br>B. Sensory perception<br>C. Locomotion and feeding<br>D. Gas exchange<\/p>\n\n\n\n<p class=\"is-style-success\">Water vascular system \u2192 movement + feeding<br>\u2705 Answer: <strong>C. Locomotion and feeding <\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 61<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which Harappan city, around 2500 BCE, is noted for its dockyard, indicating advanced architectural planning for trade?<\/strong><br><br>A. Mohenjodaro<br>B. Kalibangan<br>C. Lothal<br>D. Dholavira<\/p>\n\n\n\n<p class=\"is-style-success\">Dockyard = <strong>Lothal<\/strong><br>\u2705 Answer: <strong>C<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 62<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In a certain code language,<br>A @ B means \u2018A is the son of B\u2019,<br>A # B means \u2018A is the sister of B\u2019,<br>A + B means \u2018A is the wife of B\u2019<br>and A % B means \u2018A is the father of B\u2019.<br>Based on the above, how is E related to B if \u2018E + R @ D% N # B\u2019?<\/strong><br><br>A. Mother<br>B. Wife<br>C. Sister<br>D. Brother&#8217;s wife<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Trick:<br><\/strong>@ means son of<br># means sister of<br>+ means wife of<br>% means father of<br><strong>E is related to B: E + R @ D% N # B<br><\/strong>&#8211; E is wife of R.<br>&#8211; R is son of D.<br>&#8211; D is father of N.<br>&#8211; N is sister of B.<br>Proven that D is father of R, N, and B.<br>So B is sister of R as well.<br>\u2705 Answer: <strong>D. Brother&#8217;s wife<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 63<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong><math data-latex=\"\\frac{\\sqrt[3]{6859}}{\\sqrt[4]{256}} \\times \\frac{2}{57} \\times 168\"><semantics><mrow><mfrac><mroot><mn>6859<\/mn><mn>3<\/mn><\/mroot><mroot><mn>256<\/mn><mn>4<\/mn><\/mroot><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>2<\/mn><mn>57<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>168<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{\\sqrt[3]{6859}}{\\sqrt[4]{256}} \\times \\frac{2}{57} \\times 168<\/annotation><\/semantics><\/math> = ?<\/strong><br><br>A. 28<br>B. 37<br>C. 30<br>D. 38<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Simplification<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mroot><mn>6859<\/mn><mn>3<\/mn><\/mroot><mroot><mn>256<\/mn><mn>4<\/mn><\/mroot><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>2<\/mn><mn>57<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>168<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{\\sqrt[3]{6859}}{\\sqrt[4]{256}} \u00d7 \\frac{2}{57} \u00d7 168<\/annotation><\/semantics><\/math>\ud83d\udc49 \u221b6859 = 19<br>\ud83d\udc49 \u2074\u221a256 = 4<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>19<\/mn><mn>4<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>2<\/mn><mn>57<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>168<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= \\frac{19}{4} \u00d7 \\frac{2}{57} \u00d7 168<\/annotation><\/semantics><\/math>Cancel:<br>168 \u00f7 4 = 42<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>19<\/mn><mo>\u00d7<\/mo><mfrac><mrow><mn>2<\/mn><mo>\u00d7<\/mo><mn>42<\/mn><\/mrow><mn>57<\/mn><\/mfrac><mo>=<\/mo><mn>19<\/mn><mo>\u00d7<\/mo><mfrac><mn>84<\/mn><mn>57<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">= 19 \u00d7 \\frac{2 \u00d7 42}{57} = 19 \u00d7 \\frac{84}{57}<\/annotation><\/semantics><\/math>57 = 3\u00d719<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mrow><mn>19<\/mn><mo>\u00d7<\/mo><mn>84<\/mn><\/mrow><mrow><mn>3<\/mn><mo>\u00d7<\/mo><mn>19<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mn>28<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= \\frac{19\u00d784}{3\u00d719} = 28<\/annotation><\/semantics><\/math>\u2705 Answer: <strong>A. 28<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 64<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>According to the Banking Laws (Amendment) Act, 2025, the threshold for \u2018substantial interest\u2019 in a bank was revised from \u20b95 lakh to which of the following amounts?<\/strong><br><br>A. \u20b95 crore<br>B. \u20b950 lakh<br>C. \u20b92 crore<br>D. \u20b91 crore<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>C. \u20b92 crore<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 65<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>A, B, C, D, E and F live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2, and so on till the topmost floor is numbered 6. Only five people live above D. Only two people live above A. C lives below F but above A. B does not live on an even numbered floor. How many people live below C?<\/strong><br><br>A. Four<br>B. One<br>C. Three<br>D. Two<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Floor Puzzle<br><\/strong>D at 1<br>A at 4<br>C between A &amp; F \u2192 C = 5, F = 6<br>B odd floor \u2192 3<br>E \u2192 2<br>Below C \u2192 floors 1\u20134 \u2192 4 people<br>\u2705 Answer: <strong>A. Four<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 66<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The splitting of the ancient Indo\u2013Brahma river into the Indus, Ganga, and Brahmaputra drainage systems is believed to have been primarily caused by which geological event?<\/strong><br><br>A. Pleistocene upheaval<br>B. River capture by erosion<br>C. Volcanic eruptions<br>D. Glacial melting<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>A. Pleistocene upheaval<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 67<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>When was the India European Free Trade Association (EFTA) Trade and Economic Partnership Agreement (TEPA) signed, which came into effect on 1 October 2025?<\/strong><br><br>A. March 2024<br>B. August 2024<br>C. January 2025<br>D. September 2025<\/p>\n\n\n\n<p class=\"is-style-success\">\ud83d\udc49 <strong>Answer A. March 2024<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 68<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which cultural and musical group celebrated its 10th anniversary in December 2025?<\/strong><br><br>A. Satyajit Ray Society<br>B. Kala Mandir<br>C. India Panorama<br>D. Robir Kiran<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>D. Robir Kiran<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 69<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The summer solstice occurs when the Sun is directly overhead at which of the following latitudes?<\/strong><br><br>A. Tropic of Capricorn<br>B. Arctic Circle<br>C. Equator<br>D. Tropic of Cancer<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>D. Tropic of Cancer<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 70<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>At what rate (in percentage) per year will a sum of money double itself in 16 years on simple interest?<\/strong><br><br>A. 4.25<br>B. 12.5<br>C. 8.25<br>D. 6.25<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Double \u2192 Interest = Principal<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>S<\/mi><mi>I<\/mi><mo>=<\/mo><mfrac><mrow><mi>P<\/mi><mi>R<\/mi><mi>T<\/mi><\/mrow><mn>100<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">SI = \\frac{PRT}{100}<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><mfrac><mrow><mi>P<\/mi><mi>R<\/mi><mi>T<\/mi><\/mrow><mn>100<\/mn><\/mfrac><mo>\u21d2<\/mo><mi>R<\/mi><mo>=<\/mo><mfrac><mn>100<\/mn><mi>T<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P = \\frac{PRT}{100} \\Rightarrow R = \\frac{100}{T}<\/annotation><\/semantics><\/math><br>T means time which is 16.<br>\ud83d\udc49 R = 100\/16 = <strong>6.25%<\/strong><br><strong>\ud83c\udfaf FINAL ANSWER: D. 6.25\u200b<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 71<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Select the set in which the numbers are related in the same way as are the numbers of the following sets.<br>(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 \u2013 Operations on 13 such as adding \/ subtracting \/ multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)<br>(20, 46, 2)<br>(32, 136, 24)<\/strong><br><br>A. (6, 42, 10)<br>B. (32, 93, 11)<br>C. (13, 25, 1)<br>D. (17, 78, 16)<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Let&#8217;s learn the trick here:<\/strong><br>There are three values inside (1st, 2nd, 3rd)<br>2nd = <math data-latex=\"(1st \\times 2) + (3rd \\times 3)\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mi>s<\/mi><mi>t<\/mi><mo>\u00d7<\/mo><mn>2<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>+<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>3<\/mn><mi>r<\/mi><mi>d<\/mi><mo>\u00d7<\/mo><mn>3<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(1st \\times 2) + (3rd \\times 3)<\/annotation><\/semantics><\/math><br><strong>(20, 46, 2)<br><\/strong>46 = 20 x 2 + 2 x 3<br>46 = 40 + 6<br>46 = 46<br><br><strong>(32, 136, 24)<br><\/strong>136 = 32 x 2 + 24 x 3<br>136 = 64 + 72<br>136 = 136<br><br><strong>let&#8217;s apply the same with Option A:<br><\/strong>42 = 6 x 2 + 10 x 3<br>42 = 12 + 30<br>42 = 42<br><strong>\u2705 Answer: A. (6, 42, 10)<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 72<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>A file name is highlighted, and you want to copy it to another folder while keeping it in the original folder as well. Which pair of steps matches this task?<\/strong><br><br>A. Press Ctrl + C, then Ctrl + B<br>B. Press Ctrl + C, then Ctrl + V<br>C. Press Ctrl + X, then Ctrl + V<br>D. Press Ctrl + S, then Ctrl + V<\/p>\n\n\n\n<p class=\"is-style-success\">Copy \u2192 Ctrl + C<br>Paste \u2192 Ctrl + V<br><strong>\u2705 Answer: B. Press Ctrl + C, then Ctrl + V<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 73<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>There are 78 members in group A, 22 members in group B and 34 members in group C. All the members of these groups went to a restaurant. The average amounts spent on each member of groups A, B and C are \u20b9136, \u20b9383 and \u20b9457, respectively. The overall average amount (in \u20b9) spent per member is:<\/strong><br><br>A. 256<br>B. 261<br>C. 258<br>D. 255<\/p>\n\n\n\n<p class=\"is-style-success\">Total =<br>78\u00d7136 = 10608<br>22\u00d7383 = 8426<br>34\u00d7457 = 15538<br>Sum = 34572<br>Total people = 134<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>34572<\/mn><mi mathvariant=\"normal\">\/<\/mi><mn>134<\/mn><mo>\u2248<\/mo><mn>258<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 34572 \/ 134 \u2248 258<\/annotation><\/semantics><\/math>\u2705 Answer: <strong>C. 258<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 74<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In 2025, which Indian High Court issued the pioneering &#8216;Policy Regarding the Use of AI Tools in District Judiciary&#8217;, becoming the first in the country to frame comprehensive guidelines for artificial intelligence (AI) use in judicial work?<\/strong><br><br>A. Delhi High Court<br>B. Madras High Court<br>C. Bombay High Court<br>D. Kerala High Court<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>D. Kerala High Court<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 75<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which of the following sectors observed a negative growth rate in Real GVA (Gross Value Added) during Q1 of FY 2025-26 as per the report published by NSO and MoSPI?<\/strong><br><br>A. Construction<br>B. Tertiary Sector<br>C. Agriculture and Allied<br>D. Mining &amp; Quarrying<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: D. Mining &amp; Quarrying<\/strong><\/p>\n<\/div><\/details><\/div>\n<\/div>\n\n\n\n<!--nextpage-->\n\n\n\n<h2 class=\"wp-block-heading\">RRB NTPC Graduate CBT 1 (16 March 2026) \u2013 <strong>Full Quiz With Smart Hack And Solutions<\/strong> (Part 4: Question 76-100)<\/h2>\n\n\n\n<p>This is the final part and it contains questions from 76 to 100. Railway Recruitment Board (RRB) conducts the RRB NTPC Exam like 2026 to fill vacancies for Graduate and Undergraduate posts under the Non-Technical Popular Categories (NTPC). Here you will try to attempt the real RRB NTPC Graduate CBT 1 exam, which was conducted on 16 March, 2026. The competitive exam is divided into 4 parts each with 25 questions. You are not just taking the exercise but also learning from the solutions and explanations.<\/p>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Exam Instructions<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total Questions: <strong>25<\/strong> (This is Part 4 of Total 100 Questions.)<\/li>\n\n\n\n<li>Attempt like real exam (no scrolling to answers immediately \ud83d\ude09)<\/li>\n\n\n\n<li>Each question includes:\n<ul class=\"wp-block-list\">\n<li>\u2705 Correct Answer<\/li>\n\n\n\n<li>\ud83e\udde0 Shortcut Trick<\/li>\n\n\n\n<li>\u274c Why other options are wrong<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n        <script>\n          window.KQ_FRONT = window.KQ_FRONT || {};\n          window.KQ_FRONT.quiz_id = 10;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-10\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"10\">\n            <div class=\"kq-loading\">Loading quiz...<\/div>\n        <\/div>\n        \n    <div id=\"kq-auth-modal\" class=\"kq-auth-modal\" style=\"display:none;\">\n      <div class=\"kq-auth-modal-inner\">\n        <button id=\"kq-auth-close\" class=\"kq-auth-close\" aria-label=\"Close\">\u2716<\/button>\n\n        <!-- TAB NAV -->\n        <div class=\"kq-auth-tabs\" role=\"tablist\">\n          <button class=\"kq-tab active\" data-tab=\"register\" type=\"button\" role=\"tab\" aria-selected=\"true\">Register<\/button>\n          <button class=\"kq-tab\" data-tab=\"login\" type=\"button\" role=\"tab\" aria-selected=\"false\">Login<\/button>\n          <button class=\"kq-tab\" data-tab=\"forgot\" type=\"button\" role=\"tab\" aria-selected=\"false\">Forgot<\/button>\n        <\/div>\n\n        <!-- PANELS -->\n        <div class=\"kq-auth-panel-wrap\">\n\n          <!-- REGISTER -->\n          <div class=\"kq-auth-panel\" data-panel=\"register\" style=\"display:block\">\n            <div class=\"kq-auth-card\">\n              <h3>Register<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-username\" placeholder=\"Username\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-email\" placeholder=\"Email\" type=\"email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-signup-btn\" class=\"button kq-btn-small\">Register<\/button>\n              <small style=\"display:block;margin-top:8px;\">Already registered? Use Login tab.<\/small>\n            <\/div>\n          <\/div>\n\n          <!-- LOGIN -->\n          <div class=\"kq-auth-panel\" data-panel=\"login\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Login<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-login-btn\" class=\"button kq-btn-small\">Login<\/button>\n            <\/div>\n          <\/div>\n\n          <!-- FORGOT -->\n          <div class=\"kq-auth-panel\" data-panel=\"forgot\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Forgot Password<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-newpass\" placeholder=\"New Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-forgot-btn\" class=\"button kq-btn-small\">Update Password<\/button>\n            <\/div>\n          <\/div>\n\n        <\/div>\n\n      <\/div>\n    <\/div>\n    \n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">The Solution and Explanation of The Competitive Exam<\/h2>\n\n\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.\nStatements:\n- All bananas are apples.\n- All apples are grapes. \n- Some grapes are oranges.\nConclusions:\n(I) All grapes are bananas.\n(II) All oranges are apples.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Neither conclusion (I) nor (II) follows, let's learn the simple trick to solve it quickly.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"P sells an item to Q at 50% profit. Q sells the same item to R at 60% loss. If R paid \u20b9 3234 for the item, then at what price (in \u20b9) is the item purchased by P?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 5390, let's learn how to calculate it simply by saving time.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"This question is based on the five, three-digit numbers given below.\n(Left) 318 745 472 123 672 (Right)\n(Example: 697 \u2013 First digit = 6, second digit = 9 and third digit = 7)\n(NOTE: All operations to be done from left to right.)\nIf all the numbers are arranged in the ascending order, the position of how many numbers will remain unchanged?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 1. This is a problem of reading basically, consumes time to answer, so you must learn the art of skimming.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"In which of the following states is the slash and burn agriculture known as \u2018Kuruwa\u2019?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Jharkhand\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"If \u2018A\u2019 stands for \u2018\u00f7\u2019, \u2018B\u2019 stands for \u2018\u00d7\u2019, \u2018C\u2019 stands for \u2018+\u2019 and \u2018D\u2019 stands for \u2018\u2212\u2019, then what\nwill come in place of the question mark (?) in the following equation?\n20 D 8 A 2 C 1 B 5 = ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 21. let's learn how to do it within 5 second.\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"A, B, C, D, E and F live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2 and so on till the topmost floor, which is numbered 6.\nOnly two people live below C. Only two people live between B and C. A lives above E but below C. F does not live above D.\nWho lives immediately below B?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The answer is simple D, but how can you solve it quickly. Learn it.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Select the set in which the numbers are related in the same way as are the numbers of the following sets.\n(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 \u2013 Operations on 13 such as adding \/ subtracting \/ multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)\n(6,3,14)\n(14,8,27)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is to understand the key concepts hidden behind it like addition of 1st, 2nd digit with 5 to make digit 3rd.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A dealer buys two articles X and Y for \u20b9500 each. He marks each of them at the same price. He sells X by giving two successive discounts of 50% and 28% and still earns \u20b9958 as profit. If he sells Y at a single discount of 77%, then what is the profit percentage on Y?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 86.3%. Learn how to calculate it in no time.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following letter-clusters should replace # and % so that the pattern and relationship followed between the letter-cluster pair on the left side of :: is the same as that on the right side of :: ?\n# : IGC :: TRN : %\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is to figuring out that the letter 1st is 2 step ahead of letter 2nd. that is it.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which European power was the last to arrive in India and the last to leave during the pre-independence period?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Portuguese\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Based on the alphabetical order, three of the following four are alike in a certain way and thus form a group. Which one does not belong to that group?\n(Note: The odd one out is not based on the number of consonants or vowels or their position in the letter cluster)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"In order to solve it you must know the given options and the trick to solve it quickly. Let's learn, how!\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following prominent leaders led the Bardoli Satyagraha (1928)?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Sardar Vallabhbhai Patel\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Find the third proportional to the numbers 16 and 24.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 36. let's learn the trick to solve it within 5 second.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What was the route length of Indian Railways in 2019-2020?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It was 67,956 km long route.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following is a Tibeto-Burman language included in the Eighth Schedule of the Indian Constitution?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Bodo\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following is a tertiary activity?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Shoe shining\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The Group of Forty who advised and assisted the Sultan in administering the Delhi Sultanate was established by which of the following rulers?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Iltutmish\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Each of the digits in the number 15762349 is arranged in ascending order from left to right. The position of how many digits will remain unchanged as compared to that in the original number?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"There are only Two digits that stay on the same place one and nine.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following administrative innovations is attributed to Alauddin Khilji\u2019s reign?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Regulation of market prices and rationing was attributed during Khilji's reign.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following best represents a customized application software?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Payroll management system for a company\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The 86th Amendment added a new Fundamental Duty related to which of the following?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Educating children\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The weekly journal Young India was associated with whom among the following?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Mahatma Gandhi\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"After a Constitution Amendment Bill relating to the Directive Principles of State Policy is passed by the Parliament, what is the next mandatory constitutional step for it to become a law?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"President\u2019s Assent\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In this question, a question is followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and decide the appropriate answer.\nQ. Five students \u2013 Isha, Kavita, Meenal, Nisha, and Priti \u2013 scored different marks. Who scored the second highest?\n(I) Meenal scored more than Isha but less than Nisha.\n(II) Priti scored more than Meenal but less than Nisha.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Both statements I and II together are NOT sufficient to answer the question. Let's learn why!\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What should come in place of \u2018?\u2019 in the given series?\n32 52 68 80 88 ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"There is a pattern here that starts from 20 and growth keeps adding to increase the digits to the point of 92. Let's learn the trick behind it.\"\n    }\n  }\n  }\n}\n<\/script>\n\n\n\n<div class=\"wp-block-coblocks-accordion\">\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 76<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.<br>Statements:<br>&#8211; All bananas are apples.<br>&#8211; All apples are grapes.<br>&#8211; Some grapes are oranges.<br>Conclusions:<br>(I) All grapes are bananas.<br>(II) All oranges are apples.<\/strong><br><br>A. Only conclusion (I) follows<br>B. Only conclusion (II) follows<br>C. Both conclusions (I) and (II) follow<br>D. Neither conclusion (I) nor (II) follows<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Statements:<\/strong><br>All bananas \u2192 apples<br>All apples \u2192 grapes<br>\ud83d\udc49 So: bananas \u2192 grapes<br>Some grapes \u2192 oranges<br><strong>Check conclusions:<\/strong><br>(I) All grapes are bananas \u274c<br>\ud83d\udc49 Reverse not allowed (only bananas \u2192 grapes, not vice versa)<br>(II) All oranges are apples \u274c<br>\ud83d\udc49 Only \u201csome grapes are oranges\u201d, no full relation<br>\u2705 Answer: <strong>D. Neither conclusion (I) nor (II) follows<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 77<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>P sells an item to Q at 50% profit. Q sells the same item to R at 60% loss. If R paid \u20b9 3234 for the item, then at what price (in \u20b9) is the item purchased by P?<\/strong><br><br>A. 5390<br>B. 5387<br>C. 5391<br>D. 5393<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Profit\u2013Loss Chain<\/strong><br>Let P\u2019s cost price = x<br>P \u2192 Q at 50% profit \u2192 Q pays = 1.5x<br>Q \u2192 R at 60% loss \u2192 R pays = 40% of Q\u2019s price<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>0.4<\/mn><mo>\u00d7<\/mo><mn>1.5<\/mn><mi>x<\/mi><mo>=<\/mo><mn>3234<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">0.4 \u00d7 1.5x = 3234<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>0.6<\/mn><mi>x<\/mi><mo>=<\/mo><mn>3234<\/mn><mo>\u21d2<\/mo><mi>x<\/mi><mo>=<\/mo><mn>5390<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">0.6x = 3234 \\Rightarrow x = 5390<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>A. 5390<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 78<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>This question is based on the five, three-digit numbers given below.<br>(Left) 318 745 472 123 672 (Right)<br>(Example: 697 \u2013 First digit = 6, second digit = 9 and third digit = 7)<br>(NOTE: All operations to be done from left to right.)<br>If all the numbers are arranged in the ascending order, the position of how many numbers will remain unchanged?<\/strong><br><br>A. 0<br>B. 3<br>C. 1<br>D. 2<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Original:<br><\/strong>318, 745, 472, 123, 672<br><strong>Sorted Ascending order:<br><\/strong>123, 318, 472, 672, 745<br><strong>Compare positions:<br><\/strong>Only <strong>472<\/strong> remains same (3rd position)<br>\u2705 Answer: <strong>C. 1<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 79<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In which of the following states is the slash and burn agriculture known as \u2018Kuruwa\u2019?<br><\/strong><br>A. Jharkhand<br>B. Madhya Pradesh<br>C. Arunachal Pradesh<br>D. Rajasthan<\/p>\n\n\n\n<p class=\"is-style-success\">\u201cKuruwa\u201d \u2192 Jharkhand (shifting cultivation local name)<br>\u2705 Answer: <strong>A. Jharkhand<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 80<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>If \u2018A\u2019 stands for \u2018\u00f7\u2019, \u2018B\u2019 stands for \u2018\u00d7\u2019, \u2018C\u2019 stands for \u2018+\u2019 and \u2018D\u2019 stands for \u2018\u2212\u2019, then what will come in place of the question mark (?) in the following equation?<br>20 D 8 A 2 C 1 B 5 = ?<\/strong><br><br>A. 22<br>B. 20<br>C. 21<br>D. 23<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Given:<br><\/strong>A = \u00f7, B = \u00d7, C = +, D = \u2212<br>Expression:<br>20 \u2212 8 \u00f7 2 + 1 \u00d7 5<br>BODMAS:<br>8 \u00f7 2 = 4<br>1 \u00d7 5 = 5<br>\ud83d\udc49 20 \u2212 4 + 5 = <strong>21<\/strong><br>\ud83d\udc49 <strong>Answer C. 21<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 81<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>A, B, C, D, E and F live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2 and so on till the topmost floor, which is numbered 6.<br>Only two people live below C. Only two people live between B and C. A lives above E but below C. F does not live above D.<br>Who lives immediately below B?<br><\/strong><br>A. C<br>B. D<br>C. F<br>D. A<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Floor Puzzle<br><\/strong>Given:<br>C has 2 below \u2192 C = floor 3<br>B and C have 2 between \u2192 B = floor 6<br>A below C but above E \u2192 A = 2, E = 1<br>Remaining: D, F at 4,5<br>F not above D \u2192 F = 4, D = 5<br>\ud83d\udc49 Below B (6) = floor 5 \u2192 <strong>D<\/strong><br>\u2705 Answer: <strong>B. D<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 82<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Select the set in which the numbers are related in the same way as are the numbers of the following sets.<br>(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 \u2013 Operations on 13 such as adding \/ subtracting \/ multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)<br>(6,3,14)<br>(14,8,27)<\/strong><br><br>A. (19,12,36)<br>B. (14,87,26)<br>C. (6,15,21)<br>D. (16,25,31)<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\ud83d\udd37 Trick<\/strong><br>There are three values inside (1st, 2nd, 3rd)<br>3rd = 1st + 2nd + 5<br>This is the key trick here.<br><strong>(6, 3, 14)<br><\/strong>14 = 6 + 3 + 5<br>14 = 14<br><br><strong>(14, 8, 27)<br><\/strong>27 = 14 + 8 + 5<br>27 = 27<br><br>Let&#8217;s pick Option A: (19, 12, 36)<br>36 = 19 + 12 + 5<br>36 = 36<br>\u2705 Answer: <strong>A. (19,12,36)<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 83<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>A dealer buys two articles X and Y for \u20b9500 each. He marks each of them at the same price. He sells X by giving two successive discounts of 50% and 28% and still earns \u20b9958 as profit. If he sells Y at a single discount of 77%, then what is the profit percentage on Y?<\/strong><br><br>A. 86.3%<br>B. 86%<br>C. 85%<br>D. 85.3%<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\ud83d\udd34 Given<br><\/strong>Cost Price (CP) of X = \u20b9500<br>Cost Price (CP) of Y = \u20b9500<br>Marked Price (MP) of both = same<br><br>For X:<br>Discounts: 50% and 28%<br>Profit = \u20b9958<br><br><strong><strong>Discount Trick (IMPORTANT)<\/strong><br><\/strong>CP = 500<br>Let MP = x<br><br><strong>Before discounts:<\/strong> Let&#8217;s try to find out the real price before discount. We always assume real price as 1 if we haven&#8217;t given any.<br>Final\u00a0Price = <math data-latex=\"MP \\times (1 - d_1) \\times (1 - d_2)\"><semantics><mrow><mi>M<\/mi><mi>P<\/mi><mo>\u00d7<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><msub><mi>d<\/mi><mn>1<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u00d7<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><msub><mi>d<\/mi><mn>2<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">MP \\times (1 &#8211; d_1) \\times (1 &#8211; d_2)<\/annotation><\/semantics><\/math><br>50% \u2192 1 &#8211; 50% = 0.5<br>28% \u2192 1 &#8211; 28% = 0.72<br>SP\/FP = MP \u00d7 0.5 \u00d7 0.72 = 0.36x<br><br>Profit:<br>0.36x \u2212 500 = 958<br>\ud83d\udc49 0.36x = 1458<br>\ud83d\udc49 x = 4050<br><br>For Y: Same way like above = <math data-latex=\"MP \\times (1 - d_1) = 4050 \\times (1 - 77\\%)\"><semantics><mrow><mi>M<\/mi><mi>P<\/mi><mo>\u00d7<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><msub><mi>d<\/mi><mn>1<\/mn><\/msub><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>4050<\/mn><mo>\u00d7<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mn>77<\/mn><mi>%<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">MP \\times (1 &#8211; d_1) = 4050 \\times (1 &#8211; 77\\%)<\/annotation><\/semantics><\/math><br>SP = <strong>23%<\/strong> of 4050 = 931.5<br>Profit = 931.5 \u2212 500 = 431.5<strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>431.5<\/mn><mn>500<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>100<\/mn><mo>\u2248<\/mo><mn>86.3<\/mn><mi mathvariant=\"normal\">%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">= \\frac{431.5}{500} \u00d7100 \u2248 86.3\\%<\/annotation><\/semantics><\/math>\u2705 Answer: <strong>A. 86.3%<\/strong><\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 84<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which of the following letter-clusters should replace # and % so that the pattern and relationship followed between the letter-cluster pair on the left side of :: is the same as that on the right side of :: ?<br># : IGC :: TRN : %<\/strong><br><br>A. # = LGY; % = QJH<br>B. # = LJF; % = QOK<br>C. # = LJK; % = QNJ<br>D. # = JKF; % = QJH<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Trick:<\/strong><br>The 1st and 2nd letter on both sides. <strong>IG<\/strong>C :: <strong>TR<\/strong>N<br>1st letter = 2nd letter + 2<br><strong>IG<\/strong>C = G, H (+1), I (+2)<br><strong>TR<\/strong>N = R, S (+1), T (+2)<br><strong>Let&#8217;s check Option B.<br>LJ<\/strong>F = J, K (+1), L (+2)<br><strong>QO<\/strong>K = O, P (+1), Q (+2)<br>\u2705 Answer: <strong>B. = LJF; % = QOK<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 85<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which European power was the last to arrive in India and the last to leave during the pre-independence period?<\/strong><br><br>A. Portuguese<br>B. Americans<br>C. French<br>D. Dutch<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>A. Portuguese<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 86<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Based on the alphabetical order, three of the following four are alike in a certain way and thus form a group. Which one does not belong to that group?<br>(Note: The odd one out is not based on the number of consonants or vowels or their position in the letter cluster)<\/strong><br><br>A. UWR<br>B. SUP<br>C. KMG<br>D. EGB<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Check pattern (difference):<br><\/strong>UWR \u2192 +2, -5<br>SUP \u2192 +2, -5<br>KMG \u2192 +2, -6 \u274c<br>\u2705 Answer: <strong>C<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 87<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which of the following prominent leaders led the Bardoli Satyagraha (1928)?<\/strong><br><br>A. Gopalakrishna Gokhale<br>B. C. Rajagopalachari<br>C. Bal Gangadhar Tilak<br>D. Sardar Vallabhbhai Patel<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>D. Sardar Vallabhbhai Patel<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 88<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Find the third proportional to the numbers 16 and 24.<\/strong><br><br>A. 40<br>B. 36<br>C. 32<br>D. 30<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Third Proportional<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>a<\/mi><mo>:<\/mo><mi>b<\/mi><mo>=<\/mo><mi>b<\/mi><mo>:<\/mo><mi>x<\/mi><mo>\u21d2<\/mo><mi>x<\/mi><mo>=<\/mo><mfrac><msup><mi>b<\/mi><mn>2<\/mn><\/msup><mi>a<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">a : b = b : x \\Rightarrow x = \\frac{b^2}{a}<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><msup><mn>24<\/mn><mn>2<\/mn><\/msup><mn>16<\/mn><\/mfrac><mo>=<\/mo><mn>36<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= \\frac{24^2}{16} = 36<\/annotation><\/semantics><\/math><strong>\ud83c\udfaf FINAL ANSWER: B. 36<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 89<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What was the route length of Indian Railways in 2019-2020?<\/strong><br><br>A. 67,956 km<br>B. 66,935 km<br>C. 66,918 km<br>D. 67,415 km<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>A. 67,956 km<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 90<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which of the following is a Tibeto-Burman language included in the Eighth Schedule of the Indian Constitution?<\/strong><br><br>A. Santhali<br>B. Maithili<br>C. Bodo<br>D. Konkani<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>C. Bodo<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 91<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which of the following is a tertiary activity?<\/strong><br><br>A. Shoe shining<br>B. Extracting minerals<br>C. Steel making<br>D. Metal working<\/p>\n\n\n\n<p class=\"is-style-success\">Tertiary sector means service sector. A sector which do not produce any raw material and manufacture anything out of that raw material.<br>\u2705 Answer:<strong> A. Shoe shining<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 92<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The Group of Forty who advised and assisted the Sultan in administering the Delhi Sultanate was established by which of the following rulers?<\/strong><br><br>A. Balban<br>B. Qutbuddin Aibak<br>C. Iltutmish<br>D. Alauddin Khalji<\/p>\n\n\n\n<p class=\"is-style-success\">\ud83d\udc49 <strong>Answer C. Iltutmish<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 93<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Each of the digits in the number 15762349 is arranged in ascending order from left to right. The position of how many digits will remain unchanged as compared to that in the original number?<\/strong><br><br>A. Two<br>B. One<br>C. None<br>D. Three<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Digit Position<\/strong><br>Original: 1 5 7 6 2 3 4 9<br>Sorted: 1 2 3 4 5 6 7 9<br>Only 1 and 9 remain same<br>\ud83d\udc49 count = <strong>2<\/strong><br>\u2705 Answer:<strong> A. Two<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 94<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which of the following administrative innovations is attributed to Alauddin Khilji\u2019s reign?<\/strong><br><br>A. Regulation of market prices and rationing<br>B. Foundation of Diwan-i-Arz for military reforms<br>C. Establishment of iqta system<br>D. Creation of mansabdari system<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>A. Regulation of market prices and rationing<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 95<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which of the following best represents a customized application software?<\/strong><br><br>A. Spreadsheet software<br>B. Media player<br>C. Payroll management system for a company<br>D. Image viewer<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\ud83c\udfaf FINAL ANSWER: C. Payroll management system for a company\u200b<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 96<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The 86th Amendment added a new Fundamental Duty related to which of the following?<\/strong><br><br>A. Safeguarding public property<br>B. Protecting environment<br>C. Educating children<br>D. Defending the nation<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: C. Educating children<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 97<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The weekly journal Young India was associated with whom among the following?<\/strong><br><br>A. Bal Gangadhar Tilak<br>B. Mahatma Gandhi<br>C. Jawaharlal Nehru<br>D. Gopal Krishna Gokhale<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: B. Mahatma Gandhi<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 98<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>After a Constitution Amendment Bill relating to the Directive Principles of State Policy is passed by the Parliament, what is the next mandatory constitutional step for it to become a law?<\/strong><br><br>A. Notification in the Gazette<br>B. Ratification by State Legislatures<br>C. President\u2019s Assent<br>D. Approval by the Supreme Court<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>C. President\u2019s Assent<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 99<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In this question, a question is followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and decide the appropriate answer.<br>Q. Five students \u2013 Isha, Kavita, Meenal, Nisha, and Priti \u2013 scored different marks. Who scored the second highest?<br>(I) Meenal scored more than Isha but less than Nisha.<br>(II) Priti scored more than Meenal but less than Nisha.<\/strong><br><br>A. Both statements I and II together are NOT sufficient to answer the question<br>B. Data in Statement II alone is sufficient to answer the question while data in Statement I is not<br>C. Data in Statement I alone is sufficient to answer the question while data in Statement II is not<br>D. Both statements I and II together (and not statement I alone or statement II alone) are sufficient to answer the question<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Data Sufficiency<\/strong><br>(I): M > I, N > M<br>(II): P > M, N > P<br>Combine:<br>N > P > M > I<br>\ud83d\udc49 But Kavita unknown \u2192 cannot find 2nd highest<br>\u2705 Answer: <strong>A. Both statements I and II together are NOT sufficient to answer the question<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 100<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What should come in place of \u2018?\u2019 in the given series?<\/strong><br><strong>32 52 68 80 88 ?<\/strong><br><br>A. 96<br>B. 94<br>C. 90<br>D. 92<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>The fastest trick:<br><\/strong>Series<br>32, 52, 68, 80, 88<br>Differences:<br>+20, +16, +12, +8<br>Next = +4<br>\ud83d\udc49 88 + 4 = <strong>92<\/strong><br><strong>\u2705 Answer: D. 92<\/strong><\/p>\n<\/div><\/details><\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>RRB NTPC Graduate CBT 1 Competitive Exam (16 Mar, 2026): Attempt the real RRB NTPC Graduate CBT 1 exam, which was conducted on 16 March, 2026. You&#8217;re not just taking the exercise but also learning from the solutions.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"googlesitekit_rrm_CAowwfjFDA:productID":"","_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"'true'","footnotes":""},"categories":[5,6,7],"tags":[],"class_list":["post-8","post","type-post","status-publish","format-standard","hentry","category-railway","category-rrb-ntpc","category-rrb-ntpc-graduate"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/posts\/8","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/comments?post=8"}],"version-history":[{"count":111,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/posts\/8\/revisions"}],"predecessor-version":[{"id":229,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/posts\/8\/revisions\/229"}],"wp:attachment":[{"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/media?parent=8"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/categories?post=8"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/tags?post=8"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}