{"id":51,"date":"2026-04-15T17:34:11","date_gmt":"2026-04-15T17:34:11","guid":{"rendered":"https:\/\/govt.mrenglishkj.com\/railway\/?p=51"},"modified":"2026-04-16T17:20:22","modified_gmt":"2026-04-16T17:20:22","slug":"rrb-ntpc-graduate-cbt-1-competitive-exam-1-quick-hack","status":"publish","type":"post","link":"https:\/\/govt.mrenglishkj.com\/railway\/rrb-ntpc-graduate-cbt-1-competitive-exam-1-quick-hack\/","title":{"rendered":"RRB NTPC Graduate CBT 1 Competitive Exam 1: Quick Hack"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">RRB NTPC Graduate CBT 1 (Practice Free test 1) \u2013 <strong>Exercise, Tricks, Solutions<\/strong> (Part 1: Question 1-25)<\/h2>\n\n\n\n<p>Are you preparing for RRB NTPC exams? You are in a right place. You can prepare for any competitive exams here for free. There are no hidden charges. We even give you rewards if you perform well to motivate you in your study. Here you will try to attempt RRB NTPC Graduate CBT 1 exam practice test 1. 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 = 4;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-4\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"4\">\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\">Answers of The RRB NTPC Competitive Exam Questions<\/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\": \"The area of a quadrilateral WXYZ is three times the area of triangle LMN. The sides of triangle LMN are in the ratio 3 : 5 : 7, and its perimeter is 60 cm. Find the area of quadrilateral WXYZ. (Use \u221a3 = 1.73)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"This is a tricky one but there is a way to solve it quickly, check out here. The correct answer is 207.6.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"What should come in place of the question mark (?) in the given series? 75, 73, 70, 65, 58, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is subtract negative prime number increasing is the real way to solve. The correct answer is 47.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"25% of a number is 150 more than 25% of 800. Find the number.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"25% of 800 = 200. 25% of number is 150 more = 200 + 150 = 350\nSince it was only 25% of the total value that means it was one-fourth. When we multiply it by 4 then we get the full value. So the number is = 350 \u00d7 4 = 1400\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"A medical lift in a hospital raises a patient chair using fluid pressure in a sealed system. Which law explains its working?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"In a closed fluid, pressure applied at one point is transmitted equally in all directions. That is exactly the principle behind hydraulic lifts and similar fluid-based machines. The correct answer is Pascal\u2019s law.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Six friends A, B, C, D, E and F sit around a circular table facing the centre. D sits immediately right of A. There is one person between A and B. There is one person between B and C. E sits immediately left of A. How many people sit between E and D when counted from the left of E?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Make a circle and right means clockwise and left means anti-clockwise. The correct answer is 3.\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"Which weapon was reported in July 2025 as T\u00fcrkiye\u2019s most powerful non-nuclear aerial bomb unveiled at IDEF 2025?\",\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\": \"Meera divides \u20b92100 between two fixed deposits, X and Y. Both earn 10% per annum compounded annually. After 5 years, the amount in X becomes equal to the amount in Y after 6 years. How much did she invest in Y?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"We use compound interest formular here and the correct answer is 1000.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which Article of the Indian Constitution directs the State to promote the educational and economic interests of the weaker sections, especially the Scheduled Castes and Scheduled Tribes?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It was Article 46.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which letter-number cluster will replace the question mark?\nFJQ 6, HLS 9, JNU 12, LPW 15, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is to figuring out that every letter has addition of 2 and number has addition of 3 in next, so the correct answer is NRY 18.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code, each letter is shifted alternately by +2 and -1. How is BRISK written?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick of the patten is to alternatively +2, -1, +2, -1 per letter in the sequence. The correct answer is DQKRM.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The average of 10 numbers is 9. If each number is multiplied by 4 and then 6 is subtracted from each result, what will be the new average?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick is simple multiply 9 and 4 then subtract 6. The correct answer is 30.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Under Article 239, a Union Territory is administered by a ________.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Administrator.\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which team did the Indian Women\u2019s Cricket Team defeat to win their maiden ODI World Cup in Nov 2025?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"India defeated South Africa at the 2025 ODI World Cup.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which Act provides the legal basis for the Central Administrative Tribunal?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The CAT was formed under Administrative Tribunals Act, 1985.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The fiscal discipline law that underpins India\u2019s debt and deficit management is known as the:\",\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\": \"Seven people W, X, Y, Z, A, B, and C are waiting for their food to serve on a round table facing to center. The waiter serves the food to W first then A. There are three people between W and A. C is in the middle of W and A with one person on both sides. B gets the food who is sitting after A. The waiter serves Z who is sitting before W. How many people waiter has not served yet?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"You don't have to create a visual map to solve this. All you have to do is to understand what it asked. The correct answer is 3. We have explained it simply for you.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Arjun scored 452 marks in an examination and was 28 marks short of 30% of the maximum marks. His friend scored 400 marks. What percentage of the maximum marks did his friend score?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"First you add 28 to 452 then you divide it by 30%. Once done, you calculate the percentage and you get 25%. Check out how.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A pipe fills a tank in 6 hours, another pipe fills it in 12 hours, and a drain empties it in 8 hours. If all are opened together, how long will it take to fill half the tank?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 4 hours. Let's check out how it is done.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If the mode of a data set is 74.8 and the median is 58.4, then by how much does the median exceed the mean? (Use the empirical relation.)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The empirical formula says, Mode = 3 Median - 2 Mean, so the correct answer is 8.2. How, check out.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which country handed over the BRICS presidency to India for 2026?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It was South Africa.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which ISRO mission involves uncrewed test flights planned for 2026?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is called Gaganyaan.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which country has developed the 'second living drug' Qartemi for blood cancer?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is India.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Two trains are moving in opposite directions at 72 km\/h and 54 km\/h. They cross each other in 24 seconds. What is the combined length of both trains?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"First we add both speed 72 + 54 and we get 126 km\/h. Then we convert it by multiplying 126 with 5\/18 and we'll get 35 m\/s. Let's multiply 35 with 24 and we get our answer 840 m.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which letter-number cluster will replace the question mark in the series?\nADL 5, CFN 8, EHP 11, GJR 14, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is ILT 17. Let's check how to get it simply and quickly\"\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>The area of a quadrilateral WXYZ is <strong>three times<\/strong> the area of triangle LMN. The sides of triangle LMN are in the ratio <strong>3 : 5 : 7<\/strong>, and its perimeter is <strong>60 cm<\/strong>.<br>Find the area of quadrilateral WXYZ. (use <math data-latex=\"\\sqrt{3}\"><semantics><msqrt><mn>3<\/mn><\/msqrt><annotation encoding=\"application\/x-tex\">\\sqrt{3}<\/annotation><\/semantics><\/math> = 1.73).<\/strong><br><br>A. 103.8 cm<sup>2<\/sup><br>B. 207.6 cm<sup>2<\/sup><br>C. 248.6 cm<sup>2<\/sup><br>D. 319.8 cm<sup>2<\/sup><\/p>\n\n\n\n<p class=\"is-style-success\">Let sides = <strong>3x, 5x, 7x<\/strong><br>\ud83d\udc49 3x + 5x + 7x = 60<br>\ud83d\udc49 15x = 60 \u2192 x = 4<br><math data-latex=\"3x = 3\\times 4 \\\\ 5x = 5\\times 4 \\\\ 7x = 7\\times 4\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mn>3<\/mn><mi>x<\/mi><mo>=<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><mn>4<\/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>4<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>7<\/mn><mi>x<\/mi><mo>=<\/mo><mn>7<\/mn><mo>\u00d7<\/mo><mn>4<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">3x = 3\\times 4 \\\\ 5x = 5\\times 4 \\\\ 7x = 7\\times 4<\/annotation><\/semantics><\/math><br>So sides = <strong>12, 20, 28<\/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{12+20+28}{2} \\\\ s = 30\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mi>s<\/mi><mo>=<\/mo><mfrac><mrow><mn>12<\/mn><mo>+<\/mo><mn>20<\/mn><mo>+<\/mo><mn>28<\/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>30<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">s = \\frac{12+20+28}{2} \\\\ s = 30<\/annotation><\/semantics><\/math><br>Or directly half of 60 is 30.<br>Area of triangle =<br><math data-latex=\"\\sqrt{30(30-12)(30-20)(30-28)} \\\\ \\sqrt{30\\ \\times\\ 18\\ \\times\\ 10\\ \\times\\ 2}\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><msqrt><mrow><mn>30<\/mn><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>30<\/mn><mo>\u2212<\/mo><mn>12<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>30<\/mn><mo>\u2212<\/mo><mn>20<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>30<\/mn><mo>\u2212<\/mo><mn>28<\/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>30<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>18<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>10<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>2<\/mn><\/mrow><\/msqrt><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\sqrt{30(30-12)(30-20)(30-28)} \\\\ \\sqrt{30\\ \\times\\ 18\\ \\times\\ 10\\ \\times\\ 2}<\/annotation><\/semantics><\/math><br><br>Simplify (Exam Trick \ud83d\udd25): use <math data-latex=\"\\sqrt{3} = 1.73\"><semantics><mrow><msqrt><mn>3<\/mn><\/msqrt><mo>=<\/mo><mn>1.73<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{3} = 1.73<\/annotation><\/semantics><\/math><br>Factor smartly: <math data-latex=\"\\sqrt{30\\ \\times\\ 18\\ \\times\\ 10\\ \\times\\ 2}\"><semantics><msqrt><mrow><mn>30<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>18<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>10<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>2<\/mn><\/mrow><\/msqrt><annotation encoding=\"application\/x-tex\">\\sqrt{30\\ \\times\\ 18\\ \\times\\ 10\\ \\times\\ 2}<\/annotation><\/semantics><\/math><br><math data-latex=\"\\sqrt{(6\\ \\times\\ 5)(6\\ \\times\\ 3)(5\\ \\times\\ 2)(2)}\"><semantics><msqrt><mrow><mo form=\"prefix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">(<\/mo><mn>6<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>5<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>6<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>3<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>5<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>2<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>2<\/mn><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/msqrt><annotation encoding=\"application\/x-tex\">\\sqrt{(6\\ \\times\\ 5)(6\\ \\times\\ 3)(5\\ \\times\\ 2)(2)}<\/annotation><\/semantics><\/math><br><math data-latex=\"\\sqrt{6^2\\ \\times\\ 5^2\\ \\times\\ 2^2\\ \\times\\ 3} \\\\ 6\\ \\times\\  5\\ \\times\\ 2\\ \\times\\ \\sqrt{3} \\\\ 60\\ \\times 1.73\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><msqrt><mrow><msup><mn>6<\/mn><mn>2<\/mn><\/msup><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><msup><mn>5<\/mn><mn>2<\/mn><\/msup><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>3<\/mn><\/mrow><\/msqrt><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>6<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>5<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>2<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><msqrt><mn>3<\/mn><\/msqrt><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>60<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mn>1.73<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\sqrt{6^2\\ \\times\\ 5^2\\ \\times\\ 2^2\\ \\times\\ 3} \\\\ 6\\ \\times\\ 5\\ \\times\\ 2\\ \\times\\ \\sqrt{3} \\\\ 60\\ \\times 1.73<\/annotation><\/semantics><\/math><br>The exponent 2 cuts the square root and we have given the value of square root 3 already in question.<br>Area of triangle LMN = <math data-latex=\"60\\ \\times\\ 1.73 = 103.8\"><semantics><mrow><mn>60<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>1.73<\/mn><mo>=<\/mo><mn>103.8<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">60\\ \\times\\ 1.73 = 103.8<\/annotation><\/semantics><\/math><br>Area of Quadrilateral WXYZ = <math data-latex=\"2\\ \\times\\ 103.8 = 207.6\"><semantics><mrow><mn>2<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>103.8<\/mn><mo>=<\/mo><mn>207.6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2\\ \\times\\ 103.8 = 207.6<\/annotation><\/semantics><\/math><br><br>\u2705 Answer: <strong>B. 207.6 cm<sup>2<\/sup><\/strong><\/p>\n\n\n\n<p class=\"is-style-error\"><strong>\u274c Why others wrong:<br><\/strong> calculation errors in square root or doubling or without using heron or no factorizing.<\/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><strong>What should come in place of the question mark (?) in the given series?<\/strong><br>75, 73, 70, 65, 58, ?<\/strong><br><br>A. 47<br>B. 49<br>C. 51<br>D. 53<\/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>75, 73, 70, 65, 58, ?<br>75 &#8211; 2 = 73<br>73 &#8211; 3 = 70<br>70 &#8211; 5 = 65<br>65 &#8211; 7 = 58<br>58 &#8211; 11 = 47<br>\u2705 Answer: <strong>A. 47<\/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>25% of a number is 150 more than 25% of 800. Find the number.<\/strong><br><br>A. 1400<br>B. 1600<br>C. 1800<br>D. 2000<\/p>\n\n\n\n<p class=\"is-style-success\">25% of 800 = 200<br>Given:<br>25% of number is 150 more = 200 + 150 = 350<br>Since it was only 25% of the total value that means it was one-fourth. When we multiply it by 4 then we get the full value.<br>So the number is = 350 \u00d7 4 = <strong>1400<\/strong><br>\u2705 Answer: <strong>A. 1400<\/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>A medical lift in a hospital raises a patient chair using fluid pressure in a sealed system. Which law explains its working?<br><\/strong><br>A. Newton\u2019s first law<br>B. Pascal\u2019s law<br>C. Archimedes\u2019 principle<br>D. Boyle\u2019s law<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Correct answer: B. Pascal\u2019s law<\/strong><br><strong>Solution:<\/strong><br>In a closed fluid, pressure applied at one point is transmitted equally in all directions. That is exactly the principle behind hydraulic lifts and similar fluid-based machines.<\/p>\n\n\n\n<p class=\"is-style-error\"><strong>Why the others are incorrect:<\/strong><br>A. Newton\u2019s first law is about inertia, not fluid pressure.<br>C. Archimedes\u2019 principle explains buoyancy, not hydraulic systems.<br>D. Boyle\u2019s law relates pressure and volume of gases, not force transmission in a liquid.<\/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>Six friends A, B, C, D, E and F sit around a circular table facing the centre. D sits immediately right of A. There is one person between A and B. There is one person between B and C. E sits immediately left of A. How many people sit between E and D when counted from the left of E?<\/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>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.<br>&#8211; There are total 6: A,B,C,D,E,F.<br>&#8211; All we have to do is to fit them in position to solve.<br><br>Let&#8217;s begin.<br>1 = A<br>2 = D<br>3 = B<br>4 = F<br>5 = C<br>6 = E<br>\u2705 Now Check Conditions (Fast Trick Method):<br>1. A \u2192 D (1 person between, right side)<br><strong>A<\/strong> \u2192 <strong>D<\/strong> \u2714\ufe0f<br><br>2. A \u2192 B (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><strong>A<\/strong> \u2192 D \u2192 <strong>B<\/strong> \u2714\ufe0f<br><br>3. B \u2192 C (1 person between): The question did not mention right or left, but the condition denotes left of E.<br>A \u2192 D \u2192 <strong>B<\/strong> \u2192 ? \u2192 <strong>C<\/strong> \u2192 ? \u2192 A \u2714\ufe0f (The circle starts from A to A)<br><br>4. E \u2192 A (left of A)<br>A \u2192 D \u2192 B \u2192 ? \u2192 C \u2192 <strong>E<\/strong> \u2192 <strong>A<\/strong> \u2714\ufe0f<br><br>Now only F left and one sit let as well:<br>A \u2192 D \u2192 B \u2192 <strong>F<\/strong> \u2192 C \u2192 E \u2192 A \u2714\ufe0f<br><br>The question asked:<br>\ud83d\udc49 How many sit Between E and D (from left of E means anti-clockwise)<br><strong>E<\/strong> \u2192 C \u2192 F \u2192 B \u2192 <strong>D<\/strong> \u2192A \u2192 E \u2714\ufe0f<br><br>\ud83d\udc49 <strong>Answer C: 3<\/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>Which weapon was reported in July 2025 as T\u00fcrkiye\u2019s most powerful non-nuclear aerial bomb unveiled at IDEF 2025?<br><\/strong><br>A. Gazap<br>B. Nebula<br>C. Titan<br>D. Phantom-X<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Correct answer: A. Gazap<\/strong><br><strong>Solution:<\/strong><br>T\u00fcrkiye unveiled <strong>GAZAP<\/strong> at IDEF 2025 as its most powerful conventional\/non-nuclear aerial bomb.<\/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>Meera divides \u20b92100 between two fixed deposits, X and Y. Both earn 10% per annum compounded annually. After 5 years, the amount in X becomes equal to the amount in Y after 6 years. How much did she invest in Y?<\/strong><br><br>A. \u20b9900<br>B. \u20b91000<br>C. \u20b91100<br>D. \u20b91200<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution:<\/strong><br>Let the amount invested in X be \u20b9x and in Y be \u20b9y.<br>Given:<br>x + y = 2100<br>Also,<br>x(1.1)<sup>5<\/sup> = y(1.1)<sup>6<\/sup><br>Divide both sides by (1.1)<sup>5<\/sup>:<br>x = 1.1y<br>Substitute into the total:<br>1.1y + y = 2100<br>2.1y = 2100<br>y = 2100\/2.1<br>y = 1000<br>So, Meera invested <strong>\u20b91000 in Y<\/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 Article of the Indian Constitution directs the State to promote the educational and economic interests of the weaker sections, especially the Scheduled Castes and Scheduled Tribes?<\/strong><br><br>A. Article 39(d)<br>B. Article 46<br>C. Article 42<br>D. Article 14<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Correct answer: B. Article 46<\/strong><br><strong>Solution:<\/strong><br>Article 46 states that the State shall promote with special care the educational and economic interests of the weaker sections of the people, especially the Scheduled Castes and Scheduled Tribes.<\/p>\n\n\n\n<p class=\"is-style-error\"><strong>Why the others are incorrect:<\/strong><br>A. Article 39(d) is about equal pay for equal work.<br>C. Article 42 is about just and humane conditions of work and maternity relief.<br>D. Article 14 guarantees equality before law.<\/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 letter-number cluster will replace the question mark?<br>FJQ 6, HLS 9, JNU 12, LPW 15, ?<\/strong><br><br>A. NRY 18<br>B. NRX 18<br>C. NQY 18<br>D. MSY 18<\/p>\n\n\n\n<p class=\"is-style-success\">The Key Pattern here is Addition of 2 each letters and 3 in each number:<br>F\u2192H\u2192J\u2192L\u2192N<br>J\u2192L\u2192N\u2192P\u2192R<br>Q\u2192S\u2192U\u2192W\u2192Y<br>6\u21929\u219212\u219215\u219218<br>Answer: <strong>NRY 18<\/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 10<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In a certain code, each letter is shifted alternately by +2 and -1. How is BRISK written?<\/strong><br><br>A. DQKRM<br>B. DPKRM<br>C. DQKRN<br>D. EQKRM<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Correct answer: A. DQKRM<\/strong><br><strong>Solution:<\/strong><br>Apply the shifts letter by letter:<br>B \u2192 D (+2)<br>R \u2192 Q (-1)<br>I \u2192 K (+2)<br>S \u2192 R (-1)<br>K \u2192 M (+2)<br>So BRISK becomes <strong>DQKRM<\/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 10 numbers is 9. If each number is multiplied by 4 and then 6 is subtracted from each result, what will be the new average?<\/strong><br><br>A. 24<br>B. 30<br>C. 36<br>D. 42<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Correct answer: B. 30<\/strong><br><strong>Solution:<\/strong><br>If every number is multiplied by 4, the average also becomes 4 times as large:<br>9 \u00d7 4 = 36<br>Then 6 is subtracted from each number, so the average decreases by 6:<br>36 &#8211; 6 = 30<br>So the new average is <strong>30<\/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>Under Article 239, a Union Territory is administered by a <strong><em>__<\/em><\/strong>_.<\/strong><br><br>A. Administrator<br>B. Governor<br>C. Chief Minister<br>D. Speaker<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Correct answer: A. Administrator<\/strong><br><strong>Solution:<\/strong><br>The official rule is that Union Territories are administered under Article 239, and the Government of India notes that such administrators may be called Administrator, Lieutenant Governor, or Chief Commissioner depending on the UT. The constitutional term asked here is <strong>Administrator<\/strong>.<\/p>\n\n\n\n<p class=\"is-style-error\"><strong>Why the others are incorrect:<\/strong><br>B. Governor is the head of a State, not the standard term for Union Territory administration.<br>C. Chief Minister heads an elected State government.<br>D. Speaker is the presiding officer of a legislature.<\/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 <\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>+<\/mo><mfrac><mn>1<\/mn><mi>x<\/mi><\/mfrac><mo>=<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x + \\frac{1}{x} = 6<\/annotation><\/semantics><\/math><strong>, find the value of <\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">x^2 + \\frac{1}{x^2}<\/annotation><\/semantics><\/math><strong>.<br><\/strong><br>A. 34<br>B. 32<br>C. 36<br>D. 30<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\ud83d\udd34 Step 0: What are we given?<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>+<\/mo><mfrac><mn>1<\/mn><mi>x<\/mi><\/mfrac><mo>=<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x + \\frac{1}{x} = 6<\/annotation><\/semantics><\/math>We need:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">x^2 + \\frac{1}{x^2}<\/annotation><\/semantics><\/math><br>\ud83d\udc49 Problem: we have <strong>powers 1<\/strong>, but we need <strong>powers 2<\/strong><br>\ud83d\udc49 So we must somehow <strong>convert power 1 \u2192 power 2<\/strong><br><strong>\ud83e\udde0 Step 1: WHY we square?<\/strong><br>To go from:<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>\u2192<\/mo><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">x \u2192 x^2<\/annotation><\/semantics><\/math><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mn>1<\/mn><mi>x<\/mi><\/mfrac><mo>\u2192<\/mo><mfrac><mn>1<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{x} \u2192 \\frac{1}{x^2}<\/annotation><\/semantics><\/math><br>\ud83d\udc49 The <strong>only natural operation<\/strong> is <strong>square<\/strong><br>Because:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mspace width=\"1em\"><\/mspace><mtext>and<\/mtext><mspace width=\"1em\"><\/mspace><msup><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>1<\/mn><mi>x<\/mi><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><mn>2<\/mn><\/msup><mo>=<\/mo><mfrac><mn>1<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">(x)^2 = x^2 \\quad \\text{and} \\quad \\left(\\frac{1}{x}\\right)^2 = \\frac{1}{x^2}<\/annotation><\/semantics><\/math>\u2714\ufe0f That\u2019s why we square the whole equation.<br><strong>\ud83d\udfe2 Step 2: Apply squaring<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>+<\/mo><mfrac><mn>1<\/mn><mi>x<\/mi><\/mfrac><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mn>6<\/mn><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">(x + \\frac{1}{x})^2 = 6^2<\/annotation><\/semantics><\/math>\ud83d\udc49 Left side squared<br>\ud83d\udc49 Right side also MUST be squared (rule of equations \u2696\ufe0f)<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>36<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 36<\/annotation><\/semantics><\/math><br><strong>\ud83e\udde0 Step 3: Where did this identity come from?<\/strong><br>Now we expand using basic formula:<br>\ud83d\udc49 YES \u2014 this is from:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><msup><mo 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><mi>a<\/mi><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">(a + b)^2 = a^2 + b^2 + 2ab<\/annotation><\/semantics><\/math>Apply here:<br>Let:<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">a = x<\/annotation><\/semantics><\/math><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>b<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mi>x<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">b = \\frac{1}{x}<\/annotation><\/semantics><\/math><br>Then:<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>+<\/mo><mfrac><mn>1<\/mn><mi>x<\/mi><\/mfrac><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mi>x<\/mi><mo>\u22c5<\/mo><mfrac><mn>1<\/mn><mi>x<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">(x + \\frac{1}{x})^2 = x^2 + \\frac{1}{x^2} + 2\\cdot x \\cdot \\frac{1}{x}<\/annotation><\/semantics><\/math><br><br><strong>\ud83e\udde0 Step 4: Where did 2 come from?<\/strong><br>From this part:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><mi>a<\/mi><mi>b<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">2ab<\/annotation><\/semantics><\/math>Now substitute:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><mo>\u22c5<\/mo><mi>x<\/mi><mo>\u22c5<\/mo><mfrac><mn>1<\/mn><mi>x<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">2 \\cdot x \\cdot \\frac{1}{x}<\/annotation><\/semantics><\/math>\ud83d\udc49 <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math> cancels:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>1<\/mn><mo>=<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 2 \\cdot 1 = 2<\/annotation><\/semantics><\/math>\u2714\ufe0f That\u2019s where the <strong>+2<\/strong> comes from<br><br><strong>\ud83d\udfe1 Step 5: Final expanded form<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>2<\/mn><mo>=<\/mo><mn>36<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x^2 + \\frac{1}{x^2} + 2 = 36<\/annotation><\/semantics><\/math><br><strong>\ud83e\udde0 Step 6: Why we \u201cshift\u201d 2?<\/strong><br>We want ONLY:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">x^2 + \\frac{1}{x^2}<\/annotation><\/semantics><\/math>So remove extra <strong>+2<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>=<\/mo><mn>36<\/mn><mo>\u2212<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x^2 + \\frac{1}{x^2} = 36 &#8211; 2<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>34<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 34<\/annotation><\/semantics><\/math><strong>\u2705 Final Answer: A. 34<\/strong><br><br><strong>\u26a1 Ultra Short Exam Method<\/strong><br>See:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>+<\/mo><mfrac><mn>1<\/mn><mi>x<\/mi><\/mfrac><mo>=<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x + \\frac{1}{x} = 6<\/annotation><\/semantics><\/math>Direct formula:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mi>g<\/mi><mi>i<\/mi><mi>v<\/mi><mi>e<\/mi><mi>n<\/mi><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x^2 + \\frac{1}{x^2} = (given)^2 &#8211; 2<\/annotation><\/semantics><\/math>Put value:<br><math data-latex=\"6^2 - 2 \\\\ 36 - 2 = 34\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><msup><mn>6<\/mn><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>2<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>36<\/mn><mo>\u2212<\/mo><mn>2<\/mn><mo>=<\/mo><mn>34<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">6^2 &#8211; 2 \\\\ 36 &#8211; 2 = 34<\/annotation><\/semantics><\/math><\/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><strong>Which team did the Indian Women\u2019s Cricket Team defeat to win their maiden ODI World Cup in Nov 2025?<\/strong><\/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>A. South Africa<\/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 Act provides the legal basis for the Central Administrative Tribunal?<\/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>The fiscal discipline law that underpins India\u2019s debt and deficit management is known as the:<\/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>Seven people W, X, Y, Z, A, B, and C are waiting for their food to serve on a round table facing to center. The waiter serves the food to W first then A. There are three people between W and A. C is in the middle of W and A with one person on both sides. B gets the food who is sitting after A. The waiter serves Z who is sitting before W. How many people waiter has not served yet?<\/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>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: W,X,Y,Z,A,B,C.<br>&#8211; All we have to do is to find who did not get food. That is the trick here.<br><br>Let&#8217;s begin.<br>1 = W<br>2 = ? (X or Y)<br>3 = C<br>4 = ? (X or Y)<br>5 = A<br>6 = B<br>7 = Z<br><br>The question asked:<br>\ud83d\udc49 How many people did not get food?<br>It is clear X and Y were not mentioned at all in question and the question tells only position of C. hence there are three people C,X,Y who did not get food.<br><br>\ud83d\udc49 <strong>Answer C: 3<\/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>Arjun scored 452 marks in an examination and was 28 marks short of 30% of the maximum marks. His friend scored 400 marks. What percentage of the maximum marks did his friend score?<\/strong><br><br>A. 24%<br>B. 25%<br>C. 26%<br>D. 27%<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Correct answer: B. 25%<\/strong><br><strong>Solution:<\/strong><br>If 452 is 28 short of 30%, then 30% of the maximum marks is:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>452<\/mn><mo>+<\/mo><mn>28<\/mn><mo>=<\/mo><mn>480<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">452+28=480<\/annotation><\/semantics><\/math><br>So the maximum marks are:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mn>480<\/mn><mo>\u00d7<\/mo><mn>100<\/mn><\/mrow><mn>30<\/mn><\/mfrac><mo>=<\/mo><mn>1600<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{480\\times 100}{30}=1600<\/annotation><\/semantics><\/math><br>Friend\u2019s percentage:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>400<\/mn><mn>1600<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>100<\/mn><mo>=<\/mo><mn>25<\/mn><mi mathvariant=\"normal\">%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{400}{1600}\\times 100=25\\%<\/annotation><\/semantics><\/math><\/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>A pipe fills a tank in 6 hours, another pipe fills it in 12 hours, and a drain empties it in 8 hours. If all are opened together, how long will it take to fill half the tank?<\/strong><br><br>A. 3 hours<br>B. 4 hours<br>C. 5 hours<br>D. 6 hours<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Correct answer: B. 4 hours<\/strong><br><strong>Solution:<\/strong><br>Net rate per hour:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>1<\/mn><mn>6<\/mn><\/mfrac><mo>+<\/mo><mfrac><mn>1<\/mn><mn>12<\/mn><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mn>8<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>4<\/mn><mn>24<\/mn><\/mfrac><mo>+<\/mo><mfrac><mn>2<\/mn><mn>24<\/mn><\/mfrac><mo>\u2212<\/mo><mfrac><mn>3<\/mn><mn>24<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>3<\/mn><mn>24<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>8<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{6}+\\frac{1}{12}-\\frac{1}{8} = \\frac{4}{24}+\\frac{2}{24}-\\frac{3}{24} = \\frac{3}{24} = \\frac{1}{8}<\/annotation><\/semantics><\/math><br>So the tank fills at <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mn>1<\/mn><mn>8<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{8}<\/annotation><\/semantics><\/math>\u200b per hour.<br>To fill half the tank:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mn>1<\/mn><mi mathvariant=\"normal\">\/<\/mi><mn>2<\/mn><\/mrow><mrow><mn>1<\/mn><mi mathvariant=\"normal\">\/<\/mi><mn>8<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mn>4<\/mn><mtext>&nbsp;hours<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1\/2}{1\/8}=4 \\text{ hours}<\/annotation><\/semantics><\/math><\/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 mode of a data set is 74.8 and the median is 58.4, then by how much does the median exceed the mean? (Use the empirical relation.)<\/strong><br><br>A. 7.2<br>B. 8.2<br>C. 9.2<br>D. 10.2<\/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>Correct answer: B. 8.2<\/strong><br><strong>Solution:<\/strong><br>Using the empirical formula:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Mode<\/mtext><mo>=<\/mo><mn>3<\/mn><mo stretchy=\"false\">(<\/mo><mtext>Median<\/mtext><mo stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mtext>Mean<\/mtext><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Mode} = 3(\\text{Median}) &#8211; 2(\\text{Mean})<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>74.8<\/mn><mo>=<\/mo><mn>3<\/mn><mo stretchy=\"false\">(<\/mo><mn>58.4<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mtext>Mean<\/mtext><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">74.8 = 3(58.4) &#8211; 2(\\text{Mean})<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>74.8<\/mn><mo>=<\/mo><mn>175.2<\/mn><mo>\u2212<\/mo><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mtext>Mean<\/mtext><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">74.8 = 175.2 &#8211; 2(\\text{Mean})<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mtext>Mean<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>100.4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2(\\text{Mean}) = 100.4<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Mean<\/mtext><mo>=<\/mo><mn>50.2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Mean} = 50.2<\/annotation><\/semantics><\/math>So,<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Median<\/mtext><mo>\u2212<\/mo><mtext>Mean<\/mtext><mo>=<\/mo><mn>58.4<\/mn><mo>\u2212<\/mo><mn>50.2<\/mn><mo>=<\/mo><mn>8.2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Median} &#8211; \\text{Mean} = 58.4 &#8211; 50.2 = 8.2<\/annotation><\/semantics><\/math><\/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><strong>Which country handed over the BRICS presidency to India for 2026?<\/strong><\/strong><br><br>A. Brazil<br>B. Russia<br>C. China<br>D. South Africa<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>South Africa<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><strong>Which ISRO mission involves uncrewed test flights planned for 2026?<\/strong><\/strong><br><br>A. SAKSHAM<br>B. Gaganyaan<br>C. ANIRUDH<br>D. Aakashyaan<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Gaganyaan<br>\u2705 Answer: 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 23<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong><strong>Which country has developed the &#8220;second living drug&#8221; Qartemi for blood cancer?<\/strong><\/strong><br><br>A. India<br>B. China<br>C. South Korea<br>D. Israel<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\ud83d\udc49 India (approved by CDSCO).<br>\u2705 Answer: 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>Two trains are moving in opposite directions at 72 km\/h and 54 km\/h. They cross each other in 24 seconds. What is the combined length of both trains?<\/strong><br><br>A. 780 m<br>B. 840 m<br>C. 900 m<br>D. 960 m<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Correct answer: B. 840 m<\/strong><br><strong>Solution:<\/strong><br>Relative speed:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>72<\/mn><mo>+<\/mo><mn>54<\/mn><mo>=<\/mo><mn>126<\/mn><mtext>&nbsp;km\/h<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">72+54=126 \\text{ km\/h}<\/annotation><\/semantics><\/math><br>Convert to m\/s: (The factor 5\/18 derived from 1000\/3600)<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>126<\/mn><mo>\u00d7<\/mo><mfrac><mn>5<\/mn><mn>18<\/mn><\/mfrac><mo>=<\/mo><mn>35<\/mn><mtext>&nbsp;m\/s<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">126\\times \\frac{5}{18}=35 \\text{ m\/s}<\/annotation><\/semantics><\/math><br>Distance covered in 24 seconds:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>35<\/mn><mo>\u00d7<\/mo><mn>24<\/mn><mo>=<\/mo><mn>840<\/mn><mtext>&nbsp;m<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">35\\times 24=840 \\text{ m}<\/annotation><\/semantics><\/math><\/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 letter-number cluster will replace the question mark in the series?<br>ADL 5, CFN 8, EHP 11, GJR 14, ?<\/strong><br><br>A. ILT 17<br>B. IMT 17<br>C. ILS 17<br>D. ILT 18<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>The fastest trick:<br>Correct answer: A. ILT 17<\/strong><br><strong>Solution:<\/strong><br>Look at each part separately:<br>First letters: A, C, E, G, <strong>I<\/strong><br>Second letters: D, F, H, J, <strong>L<\/strong><br>Third letters: L, N, P, R, <strong>T<\/strong><br>Numbers: 5, 8, 11, 14, <strong>17<\/strong><br>So the next term is <strong>ILT 17<\/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 (Practice Test 1) \u2013 <strong>Full Test, Quick Tricks, Detailed Solutions<\/strong> (Part 2: Question 26-50)<\/h2>\n\n\n\n<p>This is the mock test of RRB NTPC Exam 1. If you are preparing for RRB NTPC exams, then you are in a right place. You can prepare for any competitive exams here for free. There are no hidden charges. We even give you rewards if you perform well to motivate you in your study. Here you will try to attempt RRB NTPC Graduate CBT 1 exam practice test 1. 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 = 8;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-8\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"8\">\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\">Solution and Explanation of RRB NTPC 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 motorboat covers 30 km downstream in the same time as it covers 18 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 12 km\/h. There is a trick behind it. Check it out.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Aman starts from Point A and moves 14 km east, then 9 km north, then 6 km west, then 9 km south, and finally 2 km east. How far and in which direction should he move to return to Point A?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Always draw simple axes to quickly solve this, visual representation is the key. The correct answer is 10 km to the east.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language, A \u00f7 B means \u2018A is the father of B\u2019 A + B means \u2018A is the mother of B\u2019 A - B means \u2018A is the brother of B\u2019 A \u00d7 B means \u2018A is the sister of B\u2019 Based on the above, how is S related to P if \u2018S \u00f7 K + P\u2019?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is visual representation, so the correct answer is Maternal grandfather.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"From a point on the ground 15 m away from the foot of a tower, the angle of elevation of the top is 60\u00b0. What is the height of the tower?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"We use Tan 60 degree and the correct answer is 26.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"In a code language, BARY is coded as 2746 and VARY is coded as 6749. What is the code for V?\",\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 = 2). The same way in second code the unique is (V =9).\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"Find the mean of the following distribution:\n$$ \\begin{array}{|c|c|} \\hline \\textbf{Marks} & \\textbf{No. of Students} \\\\ \\hline {42} & {3} \\\\ \\hline {56} & {5} \\\\ \\hline {68} & {4} \\\\ \\hline {74} & {2} \\\\ \\hline \\end{array} $$\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 59. Check out how to do it.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which pair of India\u2019s neighbours has a combined land border with India of more than 7,000 km?\",\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 of A so that the 8-digit number 816304A4 is divisible by 4?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 8, check out why only 8 here.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who is deemed as the Father of Artificial Intelligence?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"His name  is John McCarthy.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code, each letter is shifted forward by 1, 2, 3, 4, and 5 respectively. How is PLANT coded?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The question itself gives the hint +1, +2, +3, +4, +5 per letter in the sequence. The correct answer is QNDRY.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Three of the following four letter clusters follow the same rule. Which one does not belong to the group?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"In order to solve this one you need options, check out them first. The correct answer is CZU.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Read the given statements and conclusions carefully.\nStatements: Some jars are bottles. All bottles are cans. Some cans are boxes.\nConclusions: (I) Some jars are cans. (II) Some boxes are bottles.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Only conclusion (I) follows, but how, you should check this out from here.\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which state is building the world's largest data centre?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is Gujrat that will become the largest data centre.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Evaluate: (\u221218) + 7 \u00d7 (\u22124) \u2212 (\u221212) \u00f7 3\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is -42. Check out how to solve it quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who is the Chief of the Army Staff in India as of February 2026?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"He is General Upendra Dwivedi.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Seven people J, K, L, M, N, O, and P are sitting around a circular table facing the centre of the table. M sits second to the right of O. M sits third to the left of J. N sits third to the left of P. K is an immediate neighbour of both O and J. How many people sit between L and K when counted from the left of L?\",\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\": \"A population of deer in a reserve has a carrying capacity of 2,000. The current population is 1,400. What is the most likely trend?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The growth rate will slow and the population will level off near carrying capacity. Check out how.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which element is primarily responsible for the yellow, orange, or red color of the parasitic plant Cuscuta?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is called Stem parasite.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Three friends X, Y and Z start a business by investing money in the ratio 3 : 4 : 5. Z invests \u20b924,000. After 8 months, X withdraws one-third of his capital. If the total annual profit is \u20b949,000, what is the difference between X\u2019s and Y\u2019s profits?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 5600, check the explanation. How to solve it quickly, check out.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"At present, Mira is three times as old as her son, and her daughter is 2 years younger than her son. Three years ago, the sum of their ages was 64 years. What is Mira\u2019s present age?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 45 years, let's learn the trick to find out quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Below are given two sets of numbers. In each set, a certain mathematical operation on the first number results in the second number, then the second to the third, and so on. Which option follows the same set of operations?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The pattern here is the first digit then multiply it by 3, next add 5 then at last double it. That is how we get 5, 15, 20, 40 and 7, 21, 26, 52. Check out the correct answer.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Find the area of a regular hexagon whose side measures 10\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\": \"What is the theme of National Safe Motherhood Day 2026 (April 11)?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"'Equity in Maternal Healthcare: Leaving No Mother Behind'.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"By selling an article at 3\/5 of its actual selling price, Rishi incurs a loss of 25%. If he sells it at 90% 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 12.5%.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If \ud835\udefc and \ud835\udefd are the roots of the equation $4\ud835\udc65^2 \u2212 12\ud835\udc65 + 5 = 0$, find the value of $\ud835\udefc^2 + \ud835\udefd^2$.\",\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 13\/2.\"\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 motorboat covers 30 km downstream in the same time as it covers 18 km upstream. If the speed of the stream is 3 km\/h, what is the speed of the boat in still water?<br><\/strong><br>A. 10 km\/h<br>B. 12 km\/h<br>C. 14 km\/h<br>D. 15 km\/h<\/p>\n\n\n\n<p class=\"is-style-success\">Let the speed of the boat in still water be <strong>b<\/strong> km\/h.<br>Downstream speed = <strong>b + 3<\/strong><br>Upstream speed = <strong>b &#8211; 3<\/strong><br>Given equal time:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>30<\/mn><mrow><mi>b<\/mi><mo>+<\/mo><mn>3<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>18<\/mn><mrow><mi>b<\/mi><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{30}{b+3}=\\frac{18}{b-3}<\/annotation><\/semantics><\/math><br>Cross-multiplying:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>30<\/mn><mo stretchy=\"false\">(<\/mo><mi>b<\/mi><mo>\u2212<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>18<\/mn><mo stretchy=\"false\">(<\/mo><mi>b<\/mi><mo>+<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">30(b-3)=18(b+3)<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>30<\/mn><mi>b<\/mi><mo>\u2212<\/mo><mn>90<\/mn><mo>=<\/mo><mn>18<\/mn><mi>b<\/mi><mo>+<\/mo><mn>54<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">30b-90=18b+54<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>12<\/mn><mi>b<\/mi><mo>=<\/mo><mn>144<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">12b=144<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>b<\/mi><mo>=<\/mo><mn>12<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">b=12<\/annotation><\/semantics><\/math>So, the speed of the boat in still water is <strong>12 km\/h<\/strong>.<br>\u2705 Answer: <strong>B. 12 km\/h<\/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 27<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Aman starts from Point A and moves 14 km east, then 9 km north, then 6 km west, then 9 km south, and finally 2 km east. How far and in which direction should he move to return to Point A?<br><\/strong><br>A. 10 km west<br>B. 10 km east<br>C. 8 km west<br>D. 12 km west<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>B. 10 km <strong>East<\/strong><\/strong><br>Track the movement step by step:<br>Start at A<br>14 km east \u2192 +14 east<br>9 km north<br>6 km west \u2192 net east becomes 8 km<br>9 km south \u2192 north and south cancel out<br>2 km east \u2192 net east becomes <strong>10 km<\/strong><br>So Aman is <strong>10 km east<\/strong> of Point A.<br>To return to Point A, he must move <strong>10 km west<\/strong>.<\/p>\n\n\n\n<p class=\"is-style-error\"><strong>Why others are wrong:<\/strong><br>He is not west of A, so eastward options are incorrect.<br>8 km west and 12 km west do not match the net displacement.<\/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 code language:<br>A \u00f7 B means A is the father of B<br>A + B means A is the mother of B<br>A &#8211; B means A is the brother of B<br>A \u00d7 B means A is the sister of B<br>How is S related to P if S \u00f7 K + P?<\/strong><br><br>A. Maternal grandfather<br>B. Paternal grandmother<br>C. Maternal uncle<br>D. Paternal aunt<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>A. Maternal Grandfather<\/strong><br>Given:<br>S \u00f7 K = S is the <strong>father<\/strong> of K<br>K + P = K is the <strong>mother<\/strong> of P<br>So S is the father of P\u2019s mother. That makes S the <strong>maternal grandfather<\/strong> of P.<\/p>\n\n\n\n<p class=\"is-style-error\"><strong>Why others are wrong:<\/strong><br>Paternal grandmother is female, but S is male.<br>Maternal uncle and paternal aunt do not match the chain of relationships.<\/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>From a point on the ground 15 m away from the foot of a tower, the angle of elevation of the top is 60\u00b0. What is the height of the tower?<br><\/strong><br>A. 24 m<br>B. 26 m<br>C. 28 m<br>D. 30 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 (60\\degree) = \\frac{opposite}{adjacent}\"><semantics><mrow><mi>t<\/mi><mi>a<\/mi><mi>n<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>60<\/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 (60\\degree) = \\frac{opposite}{adjacent}<\/annotation><\/semantics><\/math><br>Using:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>tan<\/mi><mo>\u2061<\/mo><msup><mn>60<\/mn><mo>\u2218<\/mo><\/msup><mo>=<\/mo><mfrac><mtext>height<\/mtext><mn>15<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\tan 60^\\circ = \\frac{\\text{height}}{15}<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msqrt><mn>3<\/mn><\/msqrt><mo>=<\/mo><mfrac><mi>h<\/mi><mn>15<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{3}=\\frac{h}{15}<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>h<\/mi><mo>=<\/mo><mn>15<\/mn><msqrt><mn>3<\/mn><\/msqrt><mo>\u2248<\/mo><mn>25.98<\/mn><mo>\u2248<\/mo><mn>26<\/mn><mtext>&nbsp;m<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">h=15\\sqrt{3}\\approx 25.98 \\approx 26 \\text{ m}<\/annotation><\/semantics><\/math>So, the height of the tower is <strong>26 m<\/strong>.<br>\u2705 Answer: <strong>B. 26 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 code language, BARY is coded as 2746 and VARY is coded as 6749. What is the code for V?<br><\/strong><br>A. 6<br>B. 7<br>C. 4<br>D. 9<\/p>\n\n\n\n<p class=\"is-style-success\">BARY \u2192 2746<br>VARY \u2192 6749<br>Common letter = <strong>V appears in both? No<\/strong><br><strong>Look at A, R and Y<br><\/strong>From first word: A = 7, R = 4, Y = 6<br>From second word: A = 7, R = 4, Y = 9<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>ARY<\/strong> \u2192 2<strong>746<\/strong><br>V<strong>ARY<\/strong> \u2192 <strong>674<\/strong>9<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 = 2). The same way in second code the unique is (V =9).<br>\u2705 Answer: <strong>D. 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>Find the mean of the following distribution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Marks<\/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\">42<\/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\">5<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">68<\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">74<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"is-style-info\">A. 58<br>B. 59<br>C. 60<br>D. 61<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Calculation (Shortcut)<\/strong><br>Compute the weighted mean:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Mean<\/mtext><mo>=<\/mo><mfrac><mrow><mo>\u2211<\/mo><mi>f<\/mi><mi>x<\/mi><\/mrow><mrow><mo>\u2211<\/mo><mi>f<\/mi><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Mean}=\\frac{\\sum fx}{\\sum f}<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>\u2211<\/mo><mi>f<\/mi><mi>x<\/mi><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mn>42<\/mn><mo>\u00d7<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mn>56<\/mn><mo>\u00d7<\/mo><mn>5<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mn>68<\/mn><mo>\u00d7<\/mo><mn>4<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mn>74<\/mn><mo>\u00d7<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">\\sum fx=(42\\times3)+(56\\times5)+(68\\times4)+(74\\times2)<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>126<\/mn><mo>+<\/mo><mn>280<\/mn><mo>+<\/mo><mn>272<\/mn><mo>+<\/mo><mn>148<\/mn><mo>=<\/mo><mn>826<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=126+280+272+148=826<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>\u2211<\/mo><mi>f<\/mi><mo>=<\/mo><mn>3<\/mn><mo>+<\/mo><mn>5<\/mn><mo>+<\/mo><mn>4<\/mn><mo>+<\/mo><mn>2<\/mn><mo>=<\/mo><mn>14<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sum f=3+5+4+2=14<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Mean<\/mtext><mo>=<\/mo><mfrac><mn>826<\/mn><mn>14<\/mn><\/mfrac><mo>=<\/mo><mn>59<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Mean}=\\frac{826}{14}=59<\/annotation><\/semantics><\/math>So, the mean is <strong>59<\/strong>.<br>\u2705 Answer: <strong>B. 59<\/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 pair of India\u2019s neighbours has a combined land border with India of more than 7,000 km?<br><\/strong><br>A. Bangladesh and Pakistan<br>B. Bangladesh and Nepal<br>C. Pakistan and Myanmar<br>D. Nepal and Bhutan<\/p>\n\n\n\n<p class=\"is-style-success\">According to the Ministry of Home Affairs, India shares land borders of about 4,096.70 km with Bangladesh and 3,323 km with Pakistan. Together, they make 7,419.70 km, which is more than 7,000 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 <strong>maximum value of A<\/strong> so that the 8-digit number <strong>816304A4<\/strong> is divisible by 4?<\/strong><br><br>A. 5<br>B. 7<br>C. 8<br>D. 9<\/p>\n\n\n\n<p class=\"is-style-success\">For divisibility by 4, only the <strong>last two digits<\/strong> matter.<br>The number is <strong>816304A4<\/strong>, so the last two digits are <strong>A4<\/strong>.<br>Possible values:<br>04, 24, 44, 64, 84 are divisible by 4<br>So A can be <strong>0, 2, 4, 6, 8<\/strong><br>The <strong>maximum<\/strong> value is <strong>8<\/strong>.<br>\u2705 Answer: <strong>C. 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 34<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong><strong>Who is deemed as the Father of Artificial Intelligence?<\/strong><\/strong><br><br>A. Charles Babbage<br>B. Howard J. Stark<br>C. John McCarthy<br>D. Ruby Fainne<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: C. John McCarthy<\/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 35<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In a certain code, each letter is shifted forward by 1, 2, 3, 4, and 5 respectively. How is PLANT coded?<br><\/strong><br>A. QNDRY<br>B. QNDRZ<br>C. QNERY<br>D. RNDQY<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>The pattern is:<br><\/strong>1st letter +1<br>2nd letter +2<br>3rd letter +3<br>4th letter +4<br>5th letter +5<br>or <strong>PLANT<\/strong>:<br>P \u2192 Q<br>L \u2192 N<br>A \u2192 D<br>N \u2192 R<br>T \u2192 Y<br>So the code is <strong>QNDRY<\/strong>.<br><strong>\u2705 Answer: A. QNDRY<\/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>Three of the following four letter clusters follow the same rule. Which one does <strong>not<\/strong> belong to the group?<\/strong><br><br>A. DXR<br>B. CZU<br>C. BLF<br>D. ASM<\/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 -6 in next letter.<br>A. X (-6) = R<br>B. Z (-5) = U<br>C. L (-6) = F<br>D. S (-6) = M<br>\ud83d\udc49 Only option B is -5, 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 statements and conclusions carefully.<br>Statements:<br>&#8211; Some jars are bottles.<br>&#8211; All bottles are cans.<br>&#8211; Some cans are boxes.<br>Conclusions:<br>(I) Some jars are cans.<br>(II) Some boxes are bottles.<\/strong><br><br>A. Only conclusion (I) follows<br>B. Only conclusion (II) follows<br>C. Both conclusions follow<br>D. Neither conclusion follows<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>From the statements:<br><\/strong>&#8211; Some jars are bottles.<br>&#8211; All bottles are cans.<br>So, the jars that are bottles are also cans. Therefore, <strong>some jars are cans<\/strong> follows.<br>But <strong>some boxes are bottles<\/strong> does not follow, because there is no direct link between boxes and bottles.<br>So only conclusion <strong>(I)<\/strong> follows.<br><strong>\u2705 Answer: A. Only conclusion (I) 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><strong>Which state is building the world&#8217;s largest data centre?<\/strong><\/strong><br><br>A. Karnataka<br>B. Hyderabad<br>C. Gujrat<br>D. Madhya Pradesh<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: C. Gujrat<\/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: (\u221218) + 7 \u00d7 (\u22124) \u2212 (\u221212) \u00f7 3<br><\/strong><br>A. -42<br>B. -38<br>C. -34<br>D. -46<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>18<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mn>7<\/mn><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>4<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>12<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u00f7<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(-18) + 7 \\times (-4) &#8211; (-12) \\div 3<\/annotation><\/semantics><\/math>First do multiplication and division:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>7<\/mn><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>4<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo>\u2212<\/mo><mn>28<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">7 \\times (-4) = -28<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>12<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u00f7<\/mo><mn>3<\/mn><mo>=<\/mo><mo>\u2212<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(-12) \\div 3 = -4<\/annotation><\/semantics><\/math>So,<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>\u2212<\/mo><mn>18<\/mn><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>28<\/mn><mo stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mo>\u2212<\/mo><mn>4<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo>\u2212<\/mo><mn>18<\/mn><mo>\u2212<\/mo><mn>28<\/mn><mo>+<\/mo><mn>4<\/mn><mo>=<\/mo><mo>\u2212<\/mo><mn>42<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">-18 + (-28) &#8211; (-4) = -18 &#8211; 28 + 4 = -42<\/annotation><\/semantics><\/math><br>\u2705 <strong>Correct answer<\/strong>: <strong>A. -42<\/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>Who is the Chief of the Army Staff in India as of February 2026?<\/strong><br><br>A. General Dinesh Tripathi<br>B. General Anil Chauhan<br>C. General Upendra Dwivedi<br>D. General AP Singh<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>C. General Upendra Dwivedi<\/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 J, K, L, M, N, O, and P are sitting around a circular table facing the centre of the table. M sits second to the right of O. M sits third to the left of J. N sits third to the left of P. K is an immediate neighbour of both O and J. How many people sit between L and K when counted from the left of L?<\/strong><br><br>A. One<br>B. Two<br>C. Three<br>D. Zero<\/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: J,K,L,M,N,O,P.<br>&#8211; All we have to do is to fit them in position to solve.<br><br>Let&#8217;s begin.<br>1 = O<br>2 = N<br>3 = M<br>4 = L<br>5 = P<br>6 = J<br>7 = K<br>\u2705 Now Check Conditions (Fast Trick Method):<br>1. M \u2192 O (2nd to right of O)<br><strong>O<\/strong> \u2192 ? \u2192 <strong>M<\/strong> \u2192 ? \u2192 ? \u2192 ? \u2192 ? \u2192 O&#8230; \u2714\ufe0f (The circle starts from O to O)<br><br>2. M \u2192 J (3rd left of J)<br>O \u2192 ? \u2192 <strong>M<\/strong> \u2192 ? \u2192 ? \u2192 <strong>J<\/strong> \u2192 ? \u2192 O&#8230; \u2714\ufe0f<br><br>3. N \u2192 P (Hard to predict right now, so wait for next)<br>O \u2192 ? \u2192 M \u2192 ? \u2192 ? \u2192 J \u2192 ? \u2192 O&#8230; \u2714\ufe0f<br><br>4. K \u2192 O, J (middle of W and F)<br>O \u2192 ? \u2192 M \u2192 ? \u2192 ? \u2192 J \u2192 <strong>K<\/strong> \u2192 O&#8230; \u2714\ufe0f<br><br>3. N \u2192 P (3rd left of P)<br>O \u2192 <strong>N<\/strong> \u2192 M \u2192 ? \u2192 <strong>P<\/strong> \u2192 J \u2192 K \u2192 O&#8230; \u2714\ufe0f<br><br>Now only one left which will be H.<br>O \u2192 N \u2192 M \u2192 <strong>L<\/strong> \u2192 P \u2192 J \u2192 K \u2192 O&#8230; \u2714\ufe0f<br>The question asked:<br>\ud83d\udc49 How many people have sit Between H and G (left of H)<br>O \u2192 N \u2192 M \u2192 <strong>L<\/strong> \u2192 P \u2192 J \u2192 <strong>K<\/strong> \u2192 O&#8230; \u2714\ufe0f<br>Left of H:<br><strong>L<\/strong> \u2192 M \u2192 N \u2192 O \u2192 <strong>K<\/strong> \u2192 J \u2192 P \u2192 L&#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>A population of deer in a reserve has a carrying capacity of 2,000. The current population is 1,400. What is the most likely trend?<br><\/strong><br>A. The population will grow faster and faster without limit.<br>B. The population will decline immediately to zero.<br>C. The growth rate will slow and the population will level off near carrying capacity.<br>D. The population will remain exactly 1,400 forever.<\/p>\n\n\n\n<p class=\"is-style-success\">In <strong>logistic growth<\/strong>, population growth slows as the population approaches the environment\u2019s carrying capacity. Khan Academy states that in logistic growth, the per-capita growth rate gets smaller as the population nears the maximum supported by limited resources.<br>So the deer population will <strong>slow down and level off near carrying capacity<\/strong>.<br><strong>\u2705 Answer: C. The growth rate will slow and the population will level off near 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><strong>Which element is primarily responsible for the yellow, orange, or red color of the parasitic plant Cuscuta (Dodder)?<\/strong><\/strong><br><br>A. Hemiparasites<br>B. Holoparasite<br>C. Root Parasites<br>D. Stem parasite<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: D. Stem parasite<\/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 start a business by investing money in the ratio 3 : 4 : 5. Z invests \u20b924,000. After 8 months, X withdraws one-third of his capital. If the total annual profit is \u20b949,000, what is the difference between X\u2019s and Y\u2019s profits?<br><\/strong><br>A. \u20b94,800<br>B. \u20b95,600<br>C. \u20b96,200<br>D. \u20b97,000<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Investment ratio = 3 : 4 : 5<br>Z invests \u20b924,000, so:<br>X = \u20b914,400<br>Y = \u20b919,200<br>Z = \u20b924,000<br>Now calculate time-weighted investments:<br><strong>X:<br><\/strong>8 months at \u20b914,400<br>4 months at <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>14,400<\/mn><mo>=<\/mo><mn>9,600<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{2}{3}\\times 14{,}400 = 9{,}600<\/annotation><\/semantics><\/math><br>So X\u2019s capital-months:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>14,400<\/mn><mo>\u00d7<\/mo><mn>8<\/mn><mo>+<\/mo><mn>9,600<\/mn><mo>\u00d7<\/mo><mn>4<\/mn><mo>=<\/mo><mn>115,200<\/mn><mo>+<\/mo><mn>38,400<\/mn><mo>=<\/mo><mn>153,600<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">14{,}400 \\times 8 + 9{,}600 \\times 4 = 115{,}200 + 38{,}400 = 153{,}600<\/annotation><\/semantics><\/math><br><strong>Y:<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>19,200<\/mn><mo>\u00d7<\/mo><mn>12<\/mn><mo>=<\/mo><mn>230,400<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">19{,}200 \\times 12 = 230{,}400<\/annotation><\/semantics><\/math><br><strong>Z:<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>24,000<\/mn><mo>\u00d7<\/mo><mn>12<\/mn><mo>=<\/mo><mn>288,000<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">24{,}000 \\times 12 = 288{,}000<\/annotation><\/semantics><\/math><br>Profit ratio:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>153600<\/mn><mo>:<\/mo><mn>230400<\/mn><mo>:<\/mo><mn>288000<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">153600 : 230400 : 288000<\/annotation><\/semantics><\/math>Divide by 9600:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>16<\/mn><mo>:<\/mo><mn>24<\/mn><mo>:<\/mo><mn>30<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">16 : 24 : 30<\/annotation><\/semantics><\/math>Total parts:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>16<\/mn><mo>+<\/mo><mn>24<\/mn><mo>+<\/mo><mn>30<\/mn><mo>=<\/mo><mn>70<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">16+24+30=70<\/annotation><\/semantics><\/math><br>Total profit = \u20b949,000, so one part =<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>49000<\/mn><mo>\u00f7<\/mo><mn>70<\/mn><mo>=<\/mo><mn>700<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">49000 \\div 70 = 700<\/annotation><\/semantics><\/math><br>X\u2019s profit:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>16<\/mn><mo>\u00d7<\/mo><mn>700<\/mn><mo>=<\/mo><mn>11200<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">16 \\times 700 = 11200<\/annotation><\/semantics><\/math><br>Y\u2019s profit:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>24<\/mn><mo>\u00d7<\/mo><mn>700<\/mn><mo>=<\/mo><mn>16800<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">24 \\times 700 = 16800<\/annotation><\/semantics><\/math><br>Difference:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>16800<\/mn><mo>\u2212<\/mo><mn>11200<\/mn><mo>=<\/mo><mn>5600<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">16800 &#8211; 11200 = 5600<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>B. 5,600<\/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, Mira is three times as old as her son, and her daughter is 2 years younger than her son. Three years ago, the sum of their ages was 64 years. What is Mira\u2019s present age?<\/strong><br><br>A. 42 years<br>B. 45 years<br>C. 48 years<br>D. 51 years<\/p>\n\n\n\n<p class=\"is-style-success\">Let son\u2019s present age be <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math>.<br>Then Mira\u2019s present age = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">3x<\/annotation><\/semantics><\/math>.<br>Daughter\u2019s present age = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>\u2212<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x &#8211; 2<\/annotation><\/semantics><\/math>.<br>Three years ago, their ages were:<br>Mira: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><mi>x<\/mi><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3x &#8211; 3<\/annotation><\/semantics><\/math><br>Son: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>\u2212<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x &#8211; 3<\/annotation><\/semantics><\/math><br>Daughter: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>\u2212<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x &#8211; 5<\/annotation><\/semantics><\/math><br>Given:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mi>x<\/mi><mo>\u2212<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>\u2212<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>\u2212<\/mo><mn>5<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>64<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(3x &#8211; 3) + (x &#8211; 3) + (x &#8211; 5) = 64<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>5<\/mn><mi>x<\/mi><mo>\u2212<\/mo><mn>11<\/mn><mo>=<\/mo><mn>64<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5x &#8211; 11 = 64<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>5<\/mn><mi>x<\/mi><mo>=<\/mo><mn>75<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5x = 75<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>15<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x = 15<\/annotation><\/semantics><\/math>So Mira\u2019s present age is 3 times the x, hence we multiply 15 by 3:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>3<\/mn><mi>x<\/mi><mo>=<\/mo><mn>45<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3x = 45<\/annotation><\/semantics><\/math><br><strong>\ud83c\udfaf FINAL ANSWER: B. 45 years\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, a certain mathematical operation on the first number results in the second number, then the second to the third, and so on. Which option follows the same set of operations?<br>5 &#8211; 15 &#8211; 20 &#8211; 40<br>7 &#8211; 21 &#8211; 26 &#8211; 52<\/strong><br><br>A. 9 &#8211; 27 &#8211; 32 &#8211; 64<br>B. 9 &#8211; 28 &#8211; 33 &#8211; 66<br>C. 8 &#8211; 24 &#8211; 29 &#8211; 58<br>D. 6 &#8211; 18 &#8211; 23 &#8211; 46<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pattern:<br><\/strong>\u00d73, +5, \u00d72<br>Let&#8217;s check:<br>5, 15 (5&#215;3), 20 (15+5), 40 (20&#215;2)<br>7, 21 (7&#215;3), 26 (21+5), 52 (26&#215;2)<br>Options A: 9, 27 (9&#215;3), 32 (27+5), 64 (32&#215;2)<br>Check options \u2192 only A fits<br><strong>\u2705 Answer: A. 9 &#8211; 27 &#8211; 32 &#8211; 64<\/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 10\u221a3 cm.<\/strong><br><br>A. 300\u221a3 cm<sup>2<\/sup><br>B. 450\u221a3 cm<sup>2<\/sup><br>C. 500\u221a3 cm<sup>2<\/sup><br>D. 600\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 = 10\\sqrt{3}\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mn>10<\/mn><msqrt><mn>3<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">a = 10\\sqrt{3}<\/annotation><\/semantics><\/math><strong><br><\/strong>Let&#8217;s put in:<br><math data-latex=\"\\frac{3\\sqrt{3}}{2}\\ \\times \\   (10\\sqrt{3})^2 \\\\ \\frac{3\\sqrt{3}}{2}\\ \\times \\   ((10)^2(\\sqrt{3})^2) \\\\ \\frac{3\\sqrt{3}}{2}\\ \\times \\   (100\\times3) \\\\ \\frac{3\\sqrt{3}}{2}\\ \\times \\  300 \\\\ 3\\sqrt{3}\\ \\times \\  150 \\\\ 150\\ \\times \\  3\\sqrt{3} \\\\ 450\\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>10<\/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>10<\/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>100<\/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>300<\/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>150<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>150<\/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>450<\/mn><msqrt><mn>3<\/mn><\/msqrt><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\frac{3\\sqrt{3}}{2}\\ \\times \\   (10\\sqrt{3})^2 \\\\ \\frac{3\\sqrt{3}}{2}\\ \\times \\   ((10)^2(\\sqrt{3})^2) \\\\ \\frac{3\\sqrt{3}}{2}\\ \\times \\   (100\\times3) \\\\ \\frac{3\\sqrt{3}}{2}\\ \\times \\  300 \\\\ 3\\sqrt{3}\\ \\times \\  150 \\\\ 150\\ \\times \\  3\\sqrt{3} \\\\ 450\\sqrt{3}<\/annotation><\/semantics><\/math><strong><br>\u2705 Answer: 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 48<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What is the theme of National Safe Motherhood Day 2026 (April 11)?<\/strong><br><br>A. &#8220;Equity To Maternal: Praise To All Mothers&#8221;<br>B. &#8220;Nurture Maternal Land: Give Soul To Bharat Mata&#8221;<br>C. &#8220;Equality in Safety And Healthcare: Praise All Mothers&#8221;<br>D. &#8220;Equity in Maternal Healthcare: Leaving No Mother Behind&#8221;<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: D. &#8220;Equity in Maternal Healthcare: Leaving No Mother Behind&#8221;<\/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 3\/5 of its actual selling price, Rishi incurs a loss of 25%. If he sells it at 90% of its actual selling price, then the profit percentage is:<\/strong><br><br>A. 10%<br>B. 12.5%<br>C. 15%<br>D. 18%<\/p>\n\n\n\n<p class=\"is-style-success\">Let the actual selling price be <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>S<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">S<\/annotation><\/semantics><\/math>S.<br>Given, selling at <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mn>3<\/mn><mn>5<\/mn><\/mfrac><mi>S<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{3}{5}S<\/annotation><\/semantics><\/math> causes a 25% loss.<br>So cost price:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>C<\/mi><mi>P<\/mi><mo>=<\/mo><mfrac><mn>3<\/mn><mn>5<\/mn><\/mfrac><mi>S<\/mi><mo>\u00f7<\/mo><mn>0.75<\/mn><mo>=<\/mo><mfrac><mn>3<\/mn><mn>5<\/mn><\/mfrac><mi>S<\/mi><mo>\u00d7<\/mo><mfrac><mn>4<\/mn><mn>3<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>4<\/mn><mn>5<\/mn><\/mfrac><mi>S<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">CP = \\frac{3}{5}S \\div 0.75 = \\frac{3}{5}S \\times \\frac{4}{3} = \\frac{4}{5}S<\/annotation><\/semantics><\/math><br>Now if sold at 90% of actual selling price:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>S<\/mi><mi>P<\/mi><mo>=<\/mo><mn>0.9<\/mn><mi>S<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">SP = 0.9S<\/annotation><\/semantics><\/math><br>Profit:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>0.9<\/mn><mi>S<\/mi><mo>\u2212<\/mo><mn>0.8<\/mn><mi>S<\/mi><mo>=<\/mo><mn>0.1<\/mn><mi>S<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">0.9S &#8211; 0.8S = 0.1S<\/annotation><\/semantics><\/math><br>Profit percentage:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mn>0.1<\/mn><mi>S<\/mi><\/mrow><mrow><mn>0.8<\/mn><mi>S<\/mi><\/mrow><\/mfrac><mo>\u00d7<\/mo><mn>100<\/mn><mo>=<\/mo><mn>12.5<\/mn><mi mathvariant=\"normal\">%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{0.1S}{0.8S}\\times 100 = 12.5\\%<\/annotation><\/semantics><\/math><br><strong>\u2705 Answer: B. 12.5%<\/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\">If <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03b1<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha<\/annotation><\/semantics><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03b2<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\beta<\/annotation><\/semantics><\/math> are the roots of the equation<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>4<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>12<\/mn><mi>x<\/mi><mo>+<\/mo><mn>5<\/mn><mo>=<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">4x^2 &#8211; 12x + 5 = 0,<\/annotation><\/semantics><\/math>find the value of <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>\u03b1<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>\u03b2<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha^2 + \\beta^2<\/annotation><\/semantics><\/math>.<br><br>A. 13\/2<br>B. 6<br>C. 7<br>D. 15\/2<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>For the quadratic equation<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>4<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>12<\/mn><mi>x<\/mi><mo>+<\/mo><mn>5<\/mn><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">4x^2 &#8211; 12x + 5 = 0<\/annotation><\/semantics><\/math><br>if <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03b1<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha<\/annotation><\/semantics><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>\u03b2<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\beta<\/annotation><\/semantics><\/math> are roots, then:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>\u03b1<\/mi><mo>+<\/mo><mi>\u03b2<\/mi><mo>=<\/mo><mfrac><mn>12<\/mn><mn>4<\/mn><\/mfrac><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha + \\beta = \\frac{12}{4} = 3<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>\u03b1<\/mi><mi>\u03b2<\/mi><mo>=<\/mo><mfrac><mn>5<\/mn><mn>4<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha\\beta = \\frac{5}{4}<\/annotation><\/semantics><\/math><br>Now,<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mi>\u03b1<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>\u03b2<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mi>\u03b1<\/mi><mo>+<\/mo><mi>\u03b2<\/mi><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>2<\/mn><mi>\u03b1<\/mi><mi>\u03b2<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\alpha^2 + \\beta^2 = (\\alpha+\\beta)^2 &#8211; 2\\alpha\\beta<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>2<\/mn><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>5<\/mn><mn>4<\/mn><\/mfrac><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">= 3^2 &#8211; 2\\left(\\frac{5}{4}\\right)<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>9<\/mn><mo>\u2212<\/mo><mfrac><mn>10<\/mn><mn>4<\/mn><\/mfrac><mo>=<\/mo><mn>9<\/mn><mo>\u2212<\/mo><mfrac><mn>5<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>18<\/mn><mn>2<\/mn><\/mfrac><mo>\u2212<\/mo><mfrac><mn>5<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>13<\/mn><mn>2<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">= 9 &#8211; \\frac{10}{4} = 9 &#8211; \\frac{5}{2} = \\frac{18}{2} &#8211; \\frac{5}{2} = \\frac{13}{2}<\/annotation><\/semantics><\/math><br><strong>\u2705 Answer: A. 13\/2<\/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 (Free Practice Test 1) With Answers And Exam Tricks (Part 3: Question 51-75)<\/h2>\n\n\n\n<p>This is the mock test of RRB NTPC Exam 1 part 3 which contains questions from 51 to 75. You can prepare for any competitive exams here for free. There are no hidden charges. We even give you rewards if you perform well to motivate you in your study. Here you will try to attempt RRB NTPC Graduate CBT 1 exam practice test 1. 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 = 12;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-12\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"12\">\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 \ud835\udc5d : \ud835\udc5e = 3 : 2, then the value of ($4\ud835\udc5d^3 \u2212 \ud835\udc5e^3$) : ($\ud835\udc5d^3 \u2212 2\ud835\udc5e^3$) is____?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 100 : 11, 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 = 132\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 84 degree and learn the real way to solve.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Three machines P, Q and R can complete a job in 10 hours, 15 hours and 30 hours respectively. They work in rotation for one hour each, starting with P. After 6 hours, P stops working, and Q and R continue alternately, starting with Q. How many more hours will Q and R take to finish the job?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 12 hours. Let's learn the trick to solve it in no time.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following activities belongs to the tertiary sector?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Out of all the options, Banking is the right one.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Who appoints the Governor of a State in India?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is President.\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"A cube-shaped wooden block has side 9 m. The maximum number of cylinders of diameter 3 m and height 9 m that can be cut from it is formed. If the entire surface of each cylinder is painted at the rate of \u20b910 per square metre, what is the total painting cost? (\ud835\udf0b = 22\/7)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is  \u20b98,910, let's learn how to solve it quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Among the numbers 842, 617, 953, 726 and 489, what is the product of the first digit of the highest number and the second digit of the lowest number?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 72. Let's learn how to solve it in 3 seconds.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The sum of two numbers is 84. Their difference is one-sixth of their sum. What is their LCM?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 245. Let's learn the trick to solve it in 3 seconds.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a code language, MATH = 4137 and CLAM = 3468. What is the code for HAT?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 137. Let's learn the trick to solve it in 3 seconds.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What is the primary symmetry shown by adult starfish?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Radial symmetry\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which Harappan site is known for its fire altars?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Kalibangan is the right answer to choose.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a code language,\nA @ B means A is the son of B,\nA # B means A is the sister of B,\nA + B means A is the wife of B, and\nA % B means A is the father of B.\nHow is Q related to P if \ud835\udc44%\ud835\udc45@\ud835\udc46#\ud835\udc43?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Brother-in-law, let's learn the simple trick to solve it quickly.\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Evaluate $\\frac{\\sqrt[3]{2197}}{\\sqrt[4]{16}} \\times \\frac{4}{13} \\times 39$\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 84, let's learn the mathematics trick to solve it in no time.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A train 240 m long crosses a pole in 12 seconds. What is its speed?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 72 km\/h.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which gas is released when zinc reacts with dilute hydrochloric acid?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Hydrogen.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which is the smallest unit of an element that retains its chemical properties?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Atom. We have explained it simply for you.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Find the next term in the series:\n3, 8, 15, 24, 35, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 48. let's learn the simple trick to solve and find out why.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following is a metal?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Sodium is the correct answer.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who composed the Ramayana in Tamil?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The original Ramayana was composed by Valmiki, which was in Sanskrit but Kambar composed it later in Tamil in 12th century A.D.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If 5\ud835\udc65 \u2212 3 = 2\ud835\udc65 + 18, what is the value of \ud835\udc65?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 7. Let's learn the way to solve it in 3 second.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The ozone layer is found in the:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Stratosphere is the correct answer.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which country is known as the \u201cLand of the Rising Sun\u201d?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Japan is called the land of the rising sun.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which cell organelle is the site of protein synthesis?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Ribosome.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which part of the human brain controls balance and coordination?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Cerebellum\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which instrument is used to measure atmospheric pressure?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Barometer\"\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=\"p : q = 3 : 2\"><semantics><mrow><mi>p<\/mi><mo lspace=\"0.2222em\" rspace=\"0.2222em\">:<\/mo><mi>q<\/mi><mo>=<\/mo><mn>3<\/mn><mo lspace=\"0.2222em\" rspace=\"0.2222em\">:<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">p : q = 3 : 2<\/annotation><\/semantics><\/math><strong>, then (<\/strong><math data-latex=\"4p^3 - q^3\"><semantics><mrow><mn>4<\/mn><msup><mi>p<\/mi><mn>3<\/mn><\/msup><mo>\u2212<\/mo><msup><mi>q<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">4p^3 &#8211; q^3<\/annotation><\/semantics><\/math><strong>) : (<\/strong><math data-latex=\"p^3 - 2q^3\"><semantics><mrow><msup><mi>p<\/mi><mn>3<\/mn><\/msup><mo>\u2212<\/mo><mn>2<\/mn><msup><mi>q<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">p^3 &#8211; 2q^3<\/annotation><\/semantics><\/math><strong>) is____?<\/strong><br><br>A. 100:11<br>B. 99:11<br>C. 11:100<br>D. 100:13<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Given<\/strong> <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>p<\/mi><mo>:<\/mo><mi>q<\/mi><mo>=<\/mo><mn>3<\/mn><mo>:<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">p:q = 3:2<\/annotation><\/semantics><\/math>, let <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>p<\/mi><mo>=<\/mo><mn>3<\/mn><mi>k<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">p=3k<\/annotation><\/semantics><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>q<\/mi><mo>=<\/mo><mn>2<\/mn><mi>k<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">q=2k<\/annotation><\/semantics><\/math>.<br>Then:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>4<\/mn><msup><mi>p<\/mi><mn>3<\/mn><\/msup><mo>\u2212<\/mo><msup><mi>q<\/mi><mn>3<\/mn><\/msup><mo>=<\/mo><mn>4<\/mn><mo stretchy=\"false\">(<\/mo><mn>27<\/mn><msup><mi>k<\/mi><mn>3<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mn>8<\/mn><msup><mi>k<\/mi><mn>3<\/mn><\/msup><mo>=<\/mo><mn>108<\/mn><msup><mi>k<\/mi><mn>3<\/mn><\/msup><mo>\u2212<\/mo><mn>8<\/mn><msup><mi>k<\/mi><mn>3<\/mn><\/msup><mo>=<\/mo><mn>100<\/mn><msup><mi>k<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">4p^3 &#8211; q^3 = 4(27k^3)-8k^3=108k^3-8k^3=100k^3<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mi>p<\/mi><mn>3<\/mn><\/msup><mo>\u2212<\/mo><mn>2<\/mn><msup><mi>q<\/mi><mn>3<\/mn><\/msup><mo>=<\/mo><mn>27<\/mn><msup><mi>k<\/mi><mn>3<\/mn><\/msup><mo>\u2212<\/mo><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mn>8<\/mn><msup><mi>k<\/mi><mn>3<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>27<\/mn><msup><mi>k<\/mi><mn>3<\/mn><\/msup><mo>\u2212<\/mo><mn>16<\/mn><msup><mi>k<\/mi><mn>3<\/mn><\/msup><mo>=<\/mo><mn>11<\/mn><msup><mi>k<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">p^3 &#8211; 2q^3 = 27k^3 &#8211; 2(8k^3)=27k^3-16k^3=11k^3<\/annotation><\/semantics><\/math>So the ratio is:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>100<\/mn><mo>:<\/mo><mn>11<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">100:11<\/annotation><\/semantics><\/math>\u2705 Answer: <strong>A. 100 : 11<\/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 triangle \ud835\udc43\ud835\udc44\ud835\udc45, \ud835\udc42 is the in-centre and \u2220\ud835\udc44\ud835\udc42\ud835\udc45 = 132\u00b0. What is \u2220\ud835\udc44\ud835\udc43\ud835\udc45?<\/strong><br><br>A. 72\u00b0<br>B. 78\u00b0<br>C. 84\u00b0<br>D. 90\u00b0<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Key Formula:<br><\/strong>For a triangle with in-centre <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>O<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">O<\/annotation><\/semantics><\/math>,<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">\u2220<\/mi><mi>Q<\/mi><mi>O<\/mi><mi>R<\/mi><mo>=<\/mo><msup><mn>90<\/mn><mo>\u2218<\/mo><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi mathvariant=\"normal\">\u2220<\/mi><mi>Q<\/mi><mi>P<\/mi><mi>R<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\angle QOR = 90^\\circ + \\frac{1}{2}\\angle QPR<\/annotation><\/semantics><\/math>Given:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mn>132<\/mn><mo>\u2218<\/mo><\/msup><mo>=<\/mo><msup><mn>90<\/mn><mo>\u2218<\/mo><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi mathvariant=\"normal\">\u2220<\/mi><mi>Q<\/mi><mi>P<\/mi><mi>R<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">132^\\circ = 90^\\circ + \\frac{1}{2}\\angle QPR<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mn>42<\/mn><mo>\u2218<\/mo><\/msup><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mi mathvariant=\"normal\">\u2220<\/mi><mi>Q<\/mi><mi>P<\/mi><mi>R<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">42^\\circ = \\frac{1}{2}\\angle QPR<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">\u2220<\/mi><mi>Q<\/mi><mi>P<\/mi><mi>R<\/mi><mo>=<\/mo><msup><mn>84<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\angle QPR = 84^\\circ<\/annotation><\/semantics><\/math>\u2705 Answer: <strong>C. <strong>84\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 machines P, Q and R can complete a job in 10 hours, 15 hours and 30 hours respectively. They work in rotation for one hour each, starting with P. After 6 hours, P stops working, and Q and R continue alternately, starting with Q. How many more hours will Q and R take to finish the job?<\/strong><br><br>A. 10<br>B. 12<br>C. 14<br>D. 16<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Rates per hour:<\/strong><br>P = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mn>1<\/mn><mn>10<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{10}<\/annotation><\/semantics><\/math><br>Q = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mn>1<\/mn><mn>15<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{15}<\/annotation><\/semantics><\/math><br>R = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mn>1<\/mn><mn>30<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{30}<\/annotation><\/semantics><\/math><br>In 3 hours of the cycle <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo>+<\/mo><mi>Q<\/mi><mo>+<\/mo><mi>R<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">P+Q+R<\/annotation><\/semantics><\/math>, work done is:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>1<\/mn><mn>10<\/mn><\/mfrac><mo>+<\/mo><mfrac><mn>1<\/mn><mn>15<\/mn><\/mfrac><mo>+<\/mo><mfrac><mn>1<\/mn><mn>30<\/mn><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>3<\/mn><mo>+<\/mo><mn>2<\/mn><mo>+<\/mo><mn>1<\/mn><\/mrow><mn>30<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>6<\/mn><mn>30<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>5<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{10}+\\frac{1}{15}+\\frac{1}{30} = \\frac{3+2+1}{30} = \\frac{6}{30} = \\frac{1}{5}<\/annotation><\/semantics><\/math><br>In 6 hours, work done:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><mo>\u00d7<\/mo><mfrac><mn>1<\/mn><mn>5<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>2<\/mn><mn>5<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">2 \\times \\frac{1}{5} = \\frac{2}{5}<\/annotation><\/semantics><\/math>Remaining work:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>1<\/mn><mo>\u2212<\/mo><mfrac><mn>2<\/mn><mn>5<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>3<\/mn><mn>5<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">1-\\frac{2}{5}=\\frac{3}{5}<\/annotation><\/semantics><\/math>Now Q and R work alternately. In 2 hours:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>1<\/mn><mn>15<\/mn><\/mfrac><mo>+<\/mo><mfrac><mn>1<\/mn><mn>30<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>10<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{15}+\\frac{1}{30}=\\frac{1}{10}<\/annotation><\/semantics><\/math>To complete <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mn>3<\/mn><mn>5<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{3}{5}<\/annotation><\/semantics><\/math>\u200b:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>3<\/mn><mn>5<\/mn><\/mfrac><mo>\u00f7<\/mo><mfrac><mn>1<\/mn><mn>10<\/mn><\/mfrac><mo>=<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{3}{5} \\div \\frac{1}{10} = 6<\/annotation><\/semantics><\/math>So they need 6 such 2-hour blocks:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>6<\/mn><mo>\u00d7<\/mo><mn>2<\/mn><mo>=<\/mo><mn>12<\/mn><mtext>&nbsp;hours<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">6 \\times 2 = 12 \\text{ hours}<\/annotation><\/semantics><\/math>\u2705 Answer: <strong>B. 12<\/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 of the following activities belongs to the tertiary sector?<br><\/strong><br>A. Farming<br>B. Banking<br>C. Mining<br>D. Steel production<\/p>\n\n\n\n<p class=\"is-style-success\">The <strong>tertiary sector<\/strong> is the service sector. It includes banking, transport, insurance, communication, education, and similar services.<br>So the correct choice is <strong>Banking<\/strong>.<br>\u2705 Answer: <strong>B. Banking<\/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>Who appoints the Governor of a State in India?<\/strong><br><br>A. Prime Minister<br>B. President<br>C. Chief Justice of India<br>D. Speaker of Lok Sabha<\/p>\n\n\n\n<p class=\"is-style-success\">In India, the <strong>President appoints the Governor of a State<\/strong>.<br><strong>\u2705 Answer: B. President<\/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>A cube-shaped wooden block has side 9 m. The maximum number of cylinders of diameter 3 m and height 9 m that can be cut from it is formed. If the entire surface of each cylinder is painted at the rate of \u20b910 per square metre, what is the total painting cost? (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. \u20b98,820<br>B. \u20b98,910<br>C. \u20b99,000<br>D. \u20b99,180<\/p>\n\n\n\n<p class=\"is-style-success\">For the cube of side <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">9<\/annotation><\/semantics><\/math> m, cylinders of diameter <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3<\/annotation><\/semantics><\/math> m can fit as:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>9<\/mn><mn>3<\/mn><\/mfrac><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9}{3} = 3<\/annotation><\/semantics><\/math>So, on one face, <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><mo>\u00d7<\/mo><mn>3<\/mn><mo>=<\/mo><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3 \\times 3 = 9<\/annotation><\/semantics><\/math> cylinders can be cut.<br>Now find the surface area of one cylinder:<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>r<\/mi><mo>+<\/mo><mi>h<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">2\\pi r(r+h)<\/annotation><\/semantics><\/math>Here,<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>r<\/mi><mo>=<\/mo><mn>1.5<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><mi>h<\/mi><mo>=<\/mo><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">r = 1.5,\\quad h = 9<\/annotation><\/semantics><\/math>So:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>1.5<\/mn><mo>\u00d7<\/mo><mo stretchy=\"false\">(<\/mo><mn>1.5<\/mn><mo>+<\/mo><mn>9<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>1.5<\/mn><mo>\u00d7<\/mo><mn>10.5<\/mn><mo>=<\/mo><mn>99<\/mn><msup><mtext>&nbsp;m<\/mtext><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">2 \\times \\frac{22}{7} \\times 1.5 \\times (1.5+9) = 2 \\times \\frac{22}{7} \\times 1.5 \\times 10.5 = 99 \\text{ m}^2<\/annotation><\/semantics><\/math><br>Cost to paint one cylinder:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>99<\/mn><mo>\u00d7<\/mo><mn>10<\/mn><mo>=<\/mo><mtext>\u20b9<\/mtext><mn>990<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">99 \\times 10 = \u20b9990<\/annotation><\/semantics><\/math><br>Cost for 9 cylinders:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>9<\/mn><mo>\u00d7<\/mo><mn>990<\/mn><mo>=<\/mo><mtext>\u20b9<\/mtext><mn>8910<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">9 \\times 990 = \u20b98910<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>B. \u20b98,910<\/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>Among the numbers 842, 617, 953, 726 and 489, what is the product of the first digit of the highest number and the second digit of the lowest number?<\/strong><br><br>A. 64<br>B. 72<br>C. 81<br>D. 90<\/p>\n\n\n\n<p class=\"is-style-success\">Highest = 953 \u2192 first digit = 9<br>Lowest = 489 \u2192 second digit = 8<br>\ud83d\udc49 9 \u00d7 8 = 72<br>\u2705 Answer: <strong>B. 72<\/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 84. Their difference is one-sixth of their sum. What is their LCM?<br><\/strong><br>A. 210<br>B. 245<br>C. 280<br>D. 315<\/p>\n\n\n\n<p class=\"is-style-success\">Let the two numbers be <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y<\/annotation><\/semantics><\/math>.<br>Given:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>+<\/mo><mi>y<\/mi><mo>=<\/mo><mn>84<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x+y=84<\/annotation><\/semantics><\/math>Their difference is one-sixth of the sum:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>\u2212<\/mo><mi>y<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>6<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>84<\/mn><mo>=<\/mo><mn>14<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x-y=\\frac{1}{6}\\times 84=14<\/annotation><\/semantics><\/math>So:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mfrac><mrow><mn>84<\/mn><mo>+<\/mo><mn>14<\/mn><\/mrow><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>49<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><mi>y<\/mi><mo>=<\/mo><mfrac><mrow><mn>84<\/mn><mo>\u2212<\/mo><mn>14<\/mn><\/mrow><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>35<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x=\\frac{84+14}{2}=49,\\quad y=\\frac{84-14}{2}=35<\/annotation><\/semantics><\/math><br>Now find LCM of 49 and 35:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>49<\/mn><mo>=<\/mo><msup><mn>7<\/mn><mn>2<\/mn><\/msup><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><mn>35<\/mn><mo>=<\/mo><mn>5<\/mn><mo>\u00d7<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">49=7^2,\\quad 35=5 \\times 7<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>LCM<\/mtext><mo>=<\/mo><mn>5<\/mn><mo>\u00d7<\/mo><msup><mn>7<\/mn><mn>2<\/mn><\/msup><mo>=<\/mo><mn>245<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\text{LCM}=5 \\times 7^2=245<\/annotation><\/semantics><\/math><br><strong>Correct answer: B. 245<\/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 code language, MATH = 4137 and CLAM = 3468. What is the code for HAT?<\/strong><br><br>A. 413<br>B. 137<br>C. 346<br>D. 468<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>MA<\/strong>TH = <strong>4<\/strong>1<strong>3<\/strong>7<br>CL<strong>AM<\/strong> = <strong>34<\/strong>68<br>Common letter = <strong>M, A and 3, 4 appears in both<\/strong><br>So position doesn&#8217;t matter. It is hard to find which is M or A out of 3 or 4. But options can make things easy for us.<br>Digit <strong>1<\/strong> and <strong>7<\/strong> are confirmed because of <strong>T<\/strong> and <strong>H<\/strong>. Only confusion is &#8220;which one is <strong>A<\/strong> between 3 or 4?&#8221;<br>Let&#8217;s check: HAT<br><strong>413<\/strong> = There is no 7 and both 4 and 3 are here &#8211; impossible, so incorrect.<br><strong>137<\/strong> = 1 and 7 is here . There is only one between 3 or 4. Seems correct.<br><strong>346<\/strong> = Both 7 and 1 isn&#8217;t here.<br><strong>468<\/strong> = Both 7 and 1 isn&#8217;t here.<br><br>\u2705 Answer: <strong>B. 137<\/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 symmetry shown by adult starfish?<\/strong><br><br>A. Bilateral symmetry<br>B. Radial symmetry<br>C. Asymmetrical body plan<br>D. Spiral symmetry<\/p>\n\n\n\n<p class=\"is-style-success\">Adult starfish show <strong>radial symmetry<\/strong>, more specifically <strong>pentaradial symmetry<\/strong>.<br>\u2705 Answer: <strong>B. Radial symmetry <\/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 site is known for its fire altars?<\/strong><br><br>A. Harappa<br>B. Mohenjodaro<br>C. Kalibangan<br>D. Lothal<\/p>\n\n\n\n<p class=\"is-style-success\">The Harappan site famous for <strong>fire altars<\/strong> is <strong>Kalibangan<\/strong>.<br>\u2705 Answer: <strong>C. Kalibangan<\/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 code language,<br>A @ B means A is the son of B,<br>A # B means A is the sister of B,<br>A + B means A is the wife of B, and<br>A % B means A is the father of B.<br>How is Q related to P if \ud835\udc44%\ud835\udc45@\ud835\udc46#\ud835\udc43?<\/strong><br><br>A. Brother-in-law<br>B. Uncle<br>C. Son<br>D. Cousin<\/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>Q is related to P: <strong>\ud835\udc44%\ud835\udc45@\ud835\udc46#\ud835\udc43<\/strong><br><\/strong>&#8211; Q is father of R.<br>&#8211; R is son of S.<br>&#8211; S is sister of P.<br>So S and P are siblings. Since R is the son of S and Q is the father of R, Q is the spouse of S. Therefore, Q is the <strong>brother-in-law<\/strong> of P.<br>\u2705 Answer: <strong>A. Brother-in-law<\/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]{2197}}{\\sqrt[4]{16}} \\times \\frac{4}{13} \\times 39\"><semantics><mrow><mfrac><mroot><mn>2197<\/mn><mn>3<\/mn><\/mroot><mroot><mn>16<\/mn><mn>4<\/mn><\/mroot><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>4<\/mn><mn>13<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>39<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{\\sqrt[3]{2197}}{\\sqrt[4]{16}} \\times \\frac{4}{13} \\times 39<\/annotation><\/semantics><\/math> = ?<\/strong><br><br>A. 72<br>B. 78<br>C. 84<br>D. 96<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mroot><mn>2197<\/mn><mn>3<\/mn><\/mroot><mo>=<\/mo><mn>13<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt[3]{2197}=13<\/annotation><\/semantics><\/math><br>because <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>13<\/mn><mn>3<\/mn><\/msup><mo>=<\/mo><mn>2197<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">13^3=2197<\/annotation><\/semantics><\/math>.<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mroot><mn>16<\/mn><mn>4<\/mn><\/mroot><mo>=<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt[4]{16}=2<\/annotation><\/semantics><\/math><br>because <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>2<\/mn><mn>4<\/mn><\/msup><mo>=<\/mo><mn>16<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2^4=16<\/annotation><\/semantics><\/math>.<br>Now evaluate:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>13<\/mn><mn>2<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>4<\/mn><mn>13<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>39<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{13}{2}\\times \\frac{4}{13}\\times 39<\/annotation><\/semantics><\/math><br>First simplify:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>13<\/mn><mn>2<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>4<\/mn><mn>13<\/mn><\/mfrac><mo>=<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{13}{2}\\times \\frac{4}{13}=2<\/annotation><\/semantics><\/math><br>Then:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><mo>\u00d7<\/mo><mn>39<\/mn><mo>=<\/mo><mn>78<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2 \\times 39 = 78<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>B. 78<\/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>A train 240 m long crosses a pole in 12 seconds. What is its speed?<\/strong><br><br>A. 60 km\/h<br>B. 72 km\/h<br>C. 80 km\/h<br>D. 84 km\/h<\/p>\n\n\n\n<p class=\"is-style-success\">Speed:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>240<\/mn><mn>12<\/mn><\/mfrac><mo>=<\/mo><mn>20<\/mn><mtext>&nbsp;m\/s<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{240}{12}=20 \\text{ m\/s}<\/annotation><\/semantics><\/math>Convert to km\/h:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>20<\/mn><mo>\u00d7<\/mo><mfrac><mn>18<\/mn><mn>5<\/mn><\/mfrac><mo>=<\/mo><mn>72<\/mn><mtext>&nbsp;km\/h<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">20 \\times \\frac{18}{5}=72 \\text{ km\/h}<\/annotation><\/semantics><\/math>\u2705 Answer: <strong>B. 72 km\/h<\/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>Which gas is released when zinc reacts with dilute hydrochloric acid?<\/strong><br><br>A. Oxygen<br>B. Carbon dioxide<br>C. Hydrogen<br>D. Nitrogen<\/p>\n\n\n\n<p class=\"is-style-success\">Zinc reacts with dilute hydrochloric acid to release <strong>hydrogen gas<\/strong>.<br>\u2705 Answer: <strong>C. Hydrogen<\/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>Which is the smallest unit of an element that retains its chemical properties?<\/strong><br><br>A. Molecule<br>B. Atom<br>C. Ion<br>D. Electron<\/p>\n\n\n\n<p class=\"is-style-success\">The smallest unit of an element that retains its chemical properties is an atom.<br>\u2705 Answer: <strong>B. Atom<\/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>Find the next term in the series:<br>3, 8, 15, 24, 35, ?<\/strong><br><br>A. 45<br>B. 46<br>C. 48<br>D. 50<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Trick:<br><\/strong>The trick here is to square first and then subtract 1 but the digit keeps increasing from left to right.<br>3 = <math data-latex=\"2^2 - 1 = 4 - 1\"><semantics><mrow><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>1<\/mn><mo>=<\/mo><mn>4<\/mn><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2^2 &#8211; 1 = 4 &#8211; 1<\/annotation><\/semantics><\/math><br>8 = <math data-latex=\"3^2 - 1 = 9 - 1\"><semantics><mrow><msup><mn>3<\/mn><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>1<\/mn><mo>=<\/mo><mn>9<\/mn><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3^2 &#8211; 1 = 9 &#8211; 1<\/annotation><\/semantics><\/math><br>15 = <math data-latex=\"4^2 - 1 = 16 - 1\"><semantics><mrow><msup><mn>4<\/mn><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>1<\/mn><mo>=<\/mo><mn>16<\/mn><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">4^2 &#8211; 1 = 16 &#8211; 1<\/annotation><\/semantics><\/math><br>24 = <math data-latex=\"5^2 - 1 = 25 - 1\"><semantics><mrow><msup><mn>5<\/mn><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>1<\/mn><mo>=<\/mo><mn>25<\/mn><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5^2 &#8211; 1 = 25 &#8211; 1<\/annotation><\/semantics><\/math><br>35 = <math data-latex=\"6^2 - 1 = 36 - 1\"><semantics><mrow><msup><mn>6<\/mn><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>1<\/mn><mo>=<\/mo><mn>36<\/mn><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">6^2 &#8211; 1 = 36 &#8211; 1<\/annotation><\/semantics><\/math><br>? = <math data-latex=\"7^2 - 1 = 49 - 1\"><semantics><mrow><msup><mn>7<\/mn><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>1<\/mn><mo>=<\/mo><mn>49<\/mn><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">7^2 &#8211; 1 = 49 &#8211; 1<\/annotation><\/semantics><\/math><br>\ud83d\udc49 <strong>Answer C. 48<\/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 of the following is a metal?<\/strong><br><br>A. Sulphur<br>B. Oxygen<br>C. Sodium<br>D. Chlorine<\/p>\n\n\n\n<p class=\"is-style-success\">Among the options, Sodium is a metal.<br>\u2705 Answer: <strong>C. Sodium<\/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>Who composed the Ramayana in Tamil?<\/strong><br><br>A. Vyasa<br>B. Valmiki<br>C. Kambar<br>D. Kalidasa<\/p>\n\n\n\n<p class=\"is-style-success\">The original Ramayana was composed by Valmiki, which was in Sanskrit but Kambar composed it later in Tamil in 12th century A.D.<br>\u2705 Answer: <strong>C. Kambar<\/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>If 5\ud835\udc65 \u2212 3 = 2\ud835\udc65 + 18, what is the value of \ud835\udc65?<\/strong><br><br>A. 5<br>B. 6<br>C. 7<br>D. 8<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Simple Trick:<br><\/strong><math data-latex=\"5x - 3 = 2x + 18 \\\\ 5x - 2x = 18 + 3 \\\\ 3x = 21 \\\\ x = \\frac{21}{3} \\\\ x = 7\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mn>5<\/mn><mi>x<\/mi><mo>\u2212<\/mo><mn>3<\/mn><mo>=<\/mo><mn>2<\/mn><mi>x<\/mi><mo>+<\/mo><mn>18<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>5<\/mn><mi>x<\/mi><mo>\u2212<\/mo><mn>2<\/mn><mi>x<\/mi><mo>=<\/mo><mn>18<\/mn><mo>+<\/mo><mn>3<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>3<\/mn><mi>x<\/mi><mo>=<\/mo><mn>21<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>x<\/mi><mo>=<\/mo><mfrac><mn>21<\/mn><mn>3<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>x<\/mi><mo>=<\/mo><mn>7<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">5x &#8211; 3 = 2x + 18 \\\\ 5x &#8211; 2x = 18 + 3 \\\\ 3x = 21 \\\\ x = \\frac{21}{3} \\\\ x = 7<\/annotation><\/semantics><\/math><br><strong>\ud83c\udfaf FINAL ANSWER: C. 7\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>The ozone layer is found in the:<\/strong><br><br>A. Troposphere<br>B. Stratosphere<br>C. Mesosphere<br>D. Thermosphere<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: B. Stratosphere<\/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>Which country is known as the \u201cLand of the Rising Sun\u201d?<\/strong><br><br>A. China<br>B. Japan<br>C. Korea<br>D. Thailand<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Japan<\/strong>&nbsp;is known as the &#8220;Land of the Rising Sun&#8221;. This nickname stems from its location to the east of China, making it appear as if the sun rises from Japan, as well as the Japanese name &#8220;Nihon&#8221; or &#8220;Nippon,&#8221; which literally translates to &#8220;origin of the sun&#8221; or &#8220;sun&#8217;s origin&#8221;.<br><strong>\u2705 Answer: B. Japan<\/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>Which cell organelle is the site of protein synthesis?<\/strong><br><br>A. Mitochondria<br>B. Ribosome<br>C. Golgi body<br>D. Vacuole<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>B. Ribosome<\/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>Which part of the human brain controls balance and coordination?<\/strong><br><br>A. Cerebrum<br>B. Cerebellum<br>C. Medulla oblongata<br>D. Pons<\/p>\n\n\n\n<p class=\"is-style-success\">The part of the brain responsible for balance and coordination is the cerebellum.<br>\u2705 Answer: <strong>B. Cerebellum<\/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 instrument is used to measure atmospheric pressure?<\/strong><br><br>A. Hygrometer<br>B. Barometer<br>C. Anemometer<br>D. Altimeter<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: B. Barometer<\/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 (Free Practice Mock test 1) \u2013 <strong>Full Quiz With Smart Hack And Solutions<\/strong> (Part 4: Question 76-100)<\/h2>\n\n\n\n<p>This is the free practice test of RRB NTPC Exam 1 part 4 which keeps questions from 76 to 100. All exams here are totally free. There are no hidden charges. We even give you rewards if you perform well to motivate you in your study. Here you will try to attempt RRB NTPC Graduate CBT 1 exam practice test 1. 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 = 12;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-12\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"12\">\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\">Answer And Tricks of The RRB NTPC 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 statements and conclusions carefully.\nStatements: All cups are plates. Some plates are bowls. All bowls are dishes.\nConclusions:\n(I) Some dishes are plates.\n(II) All bowls are cups.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Only conclusion (I) 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 20% loss. If R paid \u20b94320, then at what price did P purchase the item?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 3600, let's learn how to calculate it simply by saving time.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Five three-digit numbers are given below: 125, 342, 689, 473, 556\nIf all the numbers are arranged in ascending order, how many numbers will remain in the same position?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 2. This is a problem consumes time to answer, so you must learn the trick to solve it quickly.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following is an example of system software?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Operating system\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"If A stands for \u00f7, B stands for \u00d7, C stands for +, and D stands for \u2212, then what will come in place of the question mark?\n36 D 8 A 2 C 3 B 4 = ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 44. 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 a building numbered 1 to 6 from bottom to top.\nOnly two people live below C.\nOnly two people live between B and C.\nA lives above E but below C.\nF 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 in the given sets:\n(6,3,16), (14,8,29)\",\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 7 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 at the same price. He sells X by giving two successive discounts of 50% and 20% and still earns \u20b9100 profit. If he sells Y at a single discount of 60%, then what is the profit percentage on Y?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 20%. 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 pair on the left side of :: is the same as that on the right side?\n# : KMO :: RTV : %\",\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 established a French trade centre in Puducherry in 1674?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"French\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Find the next term in the series: ACE, BDF, CEG, DFH, ?\",\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 leader led the Champaran Satyagraha in 1917?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Mahatma Gandhi\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Find the third proportional to 12 and 18.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 27. let's learn the trick to solve it within 5 second.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What is the width of the broad gauge used in Indian Railways?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is 1676 mm.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following scheduled languages belongs to the Tibeto-Burman branch of the Sino-Tibetan family?\",\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\": \"Teaching in a school\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which Delhi Sultanate ruler introduced token currency?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Muhammad bin Tughlaq\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In the 8-digit number 54231687, if the digits are arranged in ascending order from left to right, how many digits will remain in the same position?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"One stays on the same place from one to eight.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which administrative reform is associated with Alauddin Khalji\u2019s military system?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Dagh and Chehra.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The 86th Amendment to the Constitution inserted which provision to make education a fundamental right for children aged 6 to 14?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Article 21A\"\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\": \"College admission management system designed for ABC institute\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who is the current Railway Minister of India (as of 2026)?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Ashwini Vaishnaw\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which metro line has unveiled India's first indigenously manufactured driverless train?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Bengaluru Metro Yellow Line\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who scored the second highest among five students A, B, C, D and E?\nStatements:\n(I) B scored more than E but less than D.\n(II) C scored more than A but less than B.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Both statements together are sufficient, but neither alone is sufficient. Let's learn why!\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What should come in place of the question mark in the series?\n5, 12, 23, 38, 57, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"There is a pattern here that starts from 5 and growth keeps adding to increase the digits to the point of 80. 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\">Read the statements and conclusions carefully.<br>Statements:<br>All cups are plates.<br>Some plates are bowls.<br>All bowls are dishes.<br>Conclusions:<br>(I) Some dishes are plates.<br>(II) All bowls are cups.<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>From the statements:<br>All cups are plates.<br>Some plates are bowls.<br>All bowls are dishes.<br>Since some plates are bowls, and all bowls are dishes, it follows that <strong>some dishes are plates<\/strong>.<br>But there is no basis to say <strong>all bowls are cups<\/strong>. Cups are only a subset of plates, and bowls are only some plates.<br>So only conclusion <strong>(I)<\/strong> follows.<br>\u2705 Answer: <strong>A. Only conclusion (I) 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 20% loss. If R paid \u20b94320, then at what price did P purchase the item?<\/strong><br><br>A. \u20b93500<br>B. \u20b93600<br>C. \u20b93700<br>D. \u20b93800<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Profit\u2013Loss Chain<\/strong><br>Let P\u2019s cost price be <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math>.<br>P sells to Q at 50% profit:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>S<\/mi><msub><mi>P<\/mi><mn>1<\/mn><\/msub><mo>=<\/mo><mn>1.5<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">SP_1 = 1.5x<\/annotation><\/semantics><\/math><br>Q sells to R at 20% loss:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>S<\/mi><msub><mi>P<\/mi><mn>2<\/mn><\/msub><mo>=<\/mo><mn>0.8<\/mn><mo>\u00d7<\/mo><mn>1.5<\/mn><mi>x<\/mi><mo>=<\/mo><mn>1.2<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">SP_2 = 0.8 \\times 1.5x = 1.2x<\/annotation><\/semantics><\/math><br>Given:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>1.2<\/mn><mi>x<\/mi><mo>=<\/mo><mn>4320<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">1.2x = 4320<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mfrac><mn>4320<\/mn><mn>1.2<\/mn><\/mfrac><mo>=<\/mo><mn>3600<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x = \\frac{4320}{1.2} = 3600<\/annotation><\/semantics><\/math>So P purchased the item for <strong>\u20b93600<\/strong>.<br>\u2705 Answer: <strong>B. \u20b93600<\/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>Five three-digit numbers are given below: 125, 342, 689, 473, 556<br>If all the numbers are arranged in ascending order, how many numbers will remain in the same position?<\/strong><br><br>A. 0<br>B. 1<br>C. 2<br>D. 3<\/p>\n\n\n\n<p class=\"is-style-success\">Arrange the numbers in ascending order:<br><strong>125, 342,<\/strong> 473, 556, 689<br>Compare with the original order:<br><strong>125, 342,<\/strong> 689, 473, 556<br>The first two numbers stay in the same positions. So the number of unchanged positions is 2.<br>\u2705 Answer: <strong>C. 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 79<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which of the following is an example of system software?<br><\/strong><br>A. Spreadsheet software<br>B. Operating system<br>C. Media player<br>D. Photo editor<\/p>\n\n\n\n<p class=\"is-style-success\">An <strong>operating system<\/strong> is system software because it manages hardware resources and provides a platform for other programs.<br>Spreadsheet software, media player, and photo editor are application software.<br>\u2705 Answer: <strong>B. Operating system<\/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 A stands for \u00f7, B stands for \u00d7, C stands for +, and D stands for \u2212, then what will come in place of the question mark?<br>36 D 8 A 2 C 3 B 4 = ?<\/strong><br><br>A. 40<br>B. 44<br>C. 46<br>D. 48<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Given:<br><\/strong>A = \u00f7, B = \u00d7, C = +, D = \u2212<br>Expression:<br>36 \u2212 8 \u00f7 2 + 3 \u00d7 4<br>BODMAS:<br>8 \u00f7 2 = 4<br>3 \u00d7 4 = 12<br>\ud83d\udc49 36 \u2212 4 + 12 = <strong>44<\/strong><br>\ud83d\udc49 <strong>Answer B. 44<\/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 a building numbered 1 to 6 from bottom to top.<br>Only two people live below C.<br>Only two people live between B and C.<br>A lives above E but below C.<br>F does not live above D.<br>Who lives immediately below B?<br><\/strong><br>A. C<br>B. D<br>C. E<br>D. F<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Floor Puzzle<br><\/strong>Only two people live below C\u201d means C is on floor 3.<br>\u201cOnly two people live between B and C\u201d means B is on floor 6.<br>\u201cA lives above E but below C\u201d means A must be on floor 2 and E on floor 1.<br>The remaining floors 4 and 5 go to F and D.<br>\u201cF does not live above D\u201d means F is below D.<br>So:<br>Floor 1: E<br>Floor 2: A<br>Floor 3: C<br>Floor 4: F<br>Floor 5: D<br>Floor 6: B<br>Who lives immediately below B? <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 in the given sets:<br>(6,3,16), (14,8,29)<\/strong><br><br>A. (19,12,38)<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 + 7<br>This is the key trick here.<br><strong>(6, 3, 16)<br><\/strong>16 = 6 + 3 + 7<br>16 = 16<br><br><strong>(14, 8, 29)<br><\/strong>29 = 14 + 8 + 7<br>29 = 29<br><br>Let&#8217;s pick Option A: (19, 12, 38)<br>38 = 19 + 12 + 7<br>38 = 38<br>\u2705 Answer: <strong>A. (19,12,38)<\/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 at the same price. He sells X by giving two successive discounts of 50% and 20% and still earns \u20b9100 profit. If he sells Y at a single discount of 60%, then what is the profit percentage on Y?<\/strong><br><br>A. 20%<br>B. 28%<br>C. 36%<br>D. 40%<\/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 20%<br>Profit = \u20b9100<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&nbsp;Price = <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; 20% = 0.8<br>SP\/FP = MP \u00d7 0.5 \u00d7 0.8 = 0.4x<br><br>Profit:<br>0.4x \u2212 500 = 100<br>\ud83d\udc49 0.4x = 600<br>\ud83d\udc49 x = 1500<br><br>For Y: Same way like above = <math data-latex=\"MP \\times (1 - d_1) = 1500 \\times (1 - 60\\%)\"><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>1500<\/mn><mo>\u00d7<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mn>60<\/mn><mi>%<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">MP \\times (1 &#8211; d_1) = 1500 \\times (1 &#8211; 60\\%)<\/annotation><\/semantics><\/math><br>SP = <strong>40%<\/strong> of 1500 = 600<br>Profit = 600 \u2212 500 = 100<br><math data-latex=\"\\frac{100}{500} \\times 100 = 20\\%\"><semantics><mrow><mfrac><mn>100<\/mn><mn>500<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>100<\/mn><mo>=<\/mo><mn>20<\/mn><mi>%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{100}{500} \\times 100 = 20\\%<\/annotation><\/semantics><\/math><br><br><strong>\u2705 Answer: <strong>A. 20%<\/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 pair on the left side of :: is the same as that on the right side?<br># : KMO :: RTV : %<\/strong><br><br>A. # = GIK; % = VXZ<br>B. # = HJL; % = WYZ<br>C. # = FHK; % = UWY<br>D. # = GJL; % = VXZ<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Trick:<\/strong><br>KMO = <strong>K<\/strong>, L, <strong>M<\/strong>, N, <strong>O<\/strong><br>RTV = <strong>R<\/strong>, S, <strong>T<\/strong>, U, <strong>V<\/strong><br><strong>Let&#8217;s check Option A.<br><\/strong>GIK = <strong>G<\/strong>, H, <strong>I<\/strong>, J, <strong>K<\/strong><br>VXZ = <strong>V<\/strong>, W, <strong>X<\/strong>, Y, <strong>Z<\/strong><br>\u2705 Answer: <strong>A. = GIK; % = VXZ<\/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 established a French trade centre in Puducherry in 1674?<\/strong><br><br>A. Portuguese<br>B. Dutch<br>C. French<br>D. British<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>C. French<\/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>Find the next term in the series: ACE, BDF, CEG, DFH, ?<\/strong><br><br>A. EGI<br>B. FHJ<br>C. GIK<br>D. HJL<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Check pattern (difference): +1 in all<br><\/strong>ACE<br>BDF<br>CEG<br>DFH<br><strong>EGI<\/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 87<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which leader led the Champaran Satyagraha in 1917?<\/strong><br><br>A. Bal Gangadhar Tilak<br>B. Mahatma Gandhi<br>C. Lala Lajpat Rai<br>D. Jawaharlal Nehru<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>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 88<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Find the third proportional to 12 and 18.<\/strong><br><br>A. 24<br>B. 27<br>C. 30<br>D. 36<\/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><br><math data-latex=\"\\frac{18^2}{12} = \\frac{324}{12} = 27\"><semantics><mrow><mfrac><msup><mn>18<\/mn><mn>2<\/mn><\/msup><mn>12<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>324<\/mn><mn>12<\/mn><\/mfrac><mo>=<\/mo><mn>27<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{18^2}{12} = \\frac{324}{12} = 27<\/annotation><\/semantics><\/math><br><strong>\ud83c\udfaf FINAL ANSWER: B. 27<\/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 is the width of the broad gauge used in Indian Railways?<\/strong><br><br>A. 1435 mm<br>B. 1000 mm<br>C. 1676 mm<br>D. 762 mm<\/p>\n\n\n\n<p class=\"is-style-success\">Indian Railways uses 1676 mm as the broad gauge width. The Railway Institute of Civil Engineers document explicitly labels Indian Railways broad gauge as 1676 mm.<br>\u2705 Answer: <strong>C. 1676 mm<\/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 scheduled languages belongs to the Tibeto-Burman branch of the Sino-Tibetan family?<\/strong><br><br>A. Bodo<br>B. Maithili<br>C. Gujarati<br>D. Odia<\/p>\n\n\n\n<p class=\"is-style-success\">Bodo belongs to the Tibeto-Burman branch of the Sino-Tibetan language family. Britannica identifies Bodo as a Tibeto-Burman language, and the Government of India\u2019s language list includes Bodo among the Eighth Schedule languages.<br><br>\u2705 Answer: <strong>A. 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. Mining<br>B. Teaching in a school<br>C. Cotton spinning<br>D. Fishing<\/p>\n\n\n\n<p class=\"is-style-success\">Teaching is a <strong>tertiary activity<\/strong> because it is a service.<br>Mining is primary. Cotton spinning is secondary. Fishing is primary.<br>\u2705 Answer: <strong>B. Teaching in a school<\/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>Which Delhi Sultanate ruler introduced token currency?<\/strong><br><br>A. Iltutmish<br>B. Alauddin Khalji<br>C. Muhammad bin Tughlaq<br>D. Balban<\/p>\n\n\n\n<p class=\"is-style-success\">Muhammad bin Tughlaq introduced token currency. Historical summaries of his reign note that he issued token coins in brass and copper.<br>\ud83d\udc49 <strong>Answer C. Muhammad bin Tughlaq<\/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>In the 8-digit number 54231687, if the digits are arranged in ascending order from left to right, how many digits will remain in the same position?<\/strong><br><br>A. None<br>B. One<br>C. Two<br>D. Three<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Digit Position<\/strong><br>Original: 54231<strong>6<\/strong>87<br>Sorted: 12345<strong>6<\/strong>78<br>\ud83d\udc49 count = <strong>One, only 6 stays inn the same position.<\/strong><br>\u2705 Answer: <strong>B. One<\/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 administrative reform is associated with Alauddin Khalji\u2019s military system?<\/strong><br><br>A. Introduction of mansabdari<br>B. Dagh and Chehra<br>C. Permanent revenue settlement<br>D. Subsidiary alliance<\/p>\n\n\n\n<p class=\"is-style-success\">Alauddin Khalji is associated with the <strong>Dagh and Chehra<\/strong> system. Dagh was the branding of horses, and Chehra was the descriptive record of soldiers.<br>\u2705 Answer: <strong>B. Dagh and Chehra<\/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>The 86th Amendment to the Constitution inserted which provision to make education a fundamental right for children aged 6 to 14?<\/strong><br><br>A. Article 19A<br>B. Article 21A<br>C. Article 24A<br>D. Article 32A<\/p>\n\n\n\n<p class=\"is-style-success\">The 86th Amendment inserted <strong>Article 21A<\/strong>, which provides the right to education for children aged 6 to 14 years. The Constitution text shows Article 21A as the right to education, and the fundamental duties text shows clause <strong>51A(k)<\/strong> was also inserted by the 86th Amendment.<br><strong>\ud83c\udfaf FINAL ANSWER: B. Article 21A<\/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>Which of the following best represents a customized application software?<\/strong><br><br>A. Web browser<br>B. Music player<br>C. College admission management system designed for ABC institute<br>D. Antivirus software<\/p>\n\n\n\n<p class=\"is-style-success\">A college admission management system designed for one institute is customized application software because it is built for a specific organization\u2019s needs.<br><strong>\u2705 Answer: C. College admission management system designed for ABC institute<\/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>Who is the current Railway Minister of India (as of 2026)?<\/strong><br><br>A. Ashwini Vaishnaw<br>B. V. Somanna<br>C. Ravneet Singh<br>D. Piyush Goyal<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: A. Ashwini Vaishnaw<\/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>Which metro line has unveiled India&#8217;s first indigenously manufactured driverless train?<\/strong><br><br>A. Hyderabad Metro Red Line<br>B. Bengaluru Metro Yellow Line<br>C. Mumbai Metro Orange Line<br>D. Kerala Metro Pink Line<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>B. Bengaluru Metro Yellow Line<\/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\">Who scored the second highest among five students A, B, C, D and E?<br>Statements:<br>(I) B scored more than E but less than D.<br>(II) C scored more than A but less than B.<br><br>A. Both statements together are not sufficient<br>B. Statement II alone is sufficient, but Statement I alone is not<br>C. Statement I alone is sufficient, but Statement II alone is not<br>D. Both statements together are sufficient, but neither alone is sufficient<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Data Sufficiency<\/strong><br>(I): D &gt; B &gt; E<br>(II): B &gt; C &gt; A<br>Combine:<br>D &gt; B &gt; C &gt; A,<br>B &gt; E<br>\ud83d\udc49 So D is highest, and B is second highest.<br>Neither statement alone is enough, but together they are sufficient.<br>\u2705 Answer: <strong>D. Both statements together are sufficient, but neither alone is sufficient<\/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 the question mark in the series?<br>5, 12, 23, 38, 57, ?<\/strong><br><br>A. 76<br>B. 78<br>C. 80<br>D. 82<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>The fastest trick:<br><\/strong>Series<br>5, 12, 23, 38, 57, ?<br>Differences:<br>The differences increase by 4 each time, so the next difference is:<br>7, 11, 15, 19, 23, &#8230;<br>Next = +23<br>\ud83d\udc49 57 + 23 = <strong>80<\/strong><br><strong>\u2705 Answer: C. 80<\/strong><\/p>\n<\/div><\/details><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>RRB NTPC Graduate CBT 1 (Free Practice Test 1 With Answer): Try the free practice test of RRB NTPC Graduate CBT 1 competitive exam. Take the quiz and learn from the solutions with a way to get rewards if score well.<\/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":"","footnotes":""},"categories":[7],"tags":[3],"class_list":["post-51","post","type-post","status-publish","format-standard","hentry","category-rrb-ntpc-graduate","tag-rrb-ntpc-graduate-cbt-1"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/posts\/51","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=51"}],"version-history":[{"count":95,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/posts\/51\/revisions"}],"predecessor-version":[{"id":227,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/posts\/51\/revisions\/227"}],"wp:attachment":[{"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/media?parent=51"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/categories?post=51"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/tags?post=51"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}