{"id":311,"date":"2026-04-26T14:05:04","date_gmt":"2026-04-26T14:05:04","guid":{"rendered":"https:\/\/govt.mrenglishkj.com\/railway\/?p=311"},"modified":"2026-04-28T18:02:05","modified_gmt":"2026-04-28T18:02:05","slug":"rrb-ntpc-graduate-cbt-competitive-exam-3-16-march-2026-full-hack","status":"publish","type":"post","link":"https:\/\/govt.mrenglishkj.com\/railway\/rrb-ntpc-graduate-cbt-competitive-exam-3-16-march-2026-full-hack\/","title":{"rendered":"RRB NTPC Graduate CBT Competitive Exam 3 (16 March, 2026) Full Hack"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">RRB NTPC Graduate CBT 3 (16 March 2026) \u2013 A <strong>Full Test, Quick Tricks, Step-by-Step Solution<\/strong> (Part 1: Question 1-25)<\/h2>\n\n\n\n<p>Railway Recruitment Board (RRB) conducts the RRB NTPC Exam like 2026 to fill vacancies for Graduate and Undergraduate posts under the Non-Technical Popular Categories (NTPC). Here you will try to attempt the real RRB NTPC Graduate CBT 1 exam, which was conducted on 16 March, 2026 Shift 3. The competitive exam is divided into 4 parts each with 25 questions. You are not just taking the test but also learning from the solutions and explanations of every questions step-by-step.<\/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 = 21;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-21\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"21\">\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\">Full Step-by-step 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\": \"Based on the English alphabetical order, three of the following four letter-cluster pairs are alike in a certain way and thus form a group. Which is the one that does not belong to that group?\n(Note: The odd man out is not based on the number of consonants\/vowels or their position in the letter-cluster.)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is to add 4 and 2. Let's learn practically and visually.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"In the figure given, parallel lines, AB and CD, are intercepted by a transversal t at E and F, respectively. If EG is the angle bisector of \u2220AEF, find \u2220EGF.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"40 degree is the correct answer. Let's learn the simple trick to solve and find it.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In which of the following states is the Baishagu festival celebrated by the Boro Kacharis in the month of April?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Assam\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Which organization was the implementing agency for the National Agricultural Insurance Scheme (NAIS) launched in 1999?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Agriculture Insurance Company of India Ltd. (AIC)\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Simplify $5\\frac{1}{6} \\div 6.2 \\times 0.75 \\div (\\frac{1}{5} \\times 40)$\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Let's learn how to calculate it simply, the correct answer is 5\/64.\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"If $a$ is a positive integer such that the equations $(a^2 - 7a)x^2 + x + 12 = 0$ and $240x^2 + 8x + (a^2 - 4) = 0$ both have roots common, then the value of $\\frac{(a + 2)(a + 3)}{a - 4}$ is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Let's learn how to calculate it simply, the correct answer is 26.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"During a sale 50% of the goods are sold at 16% profit, 40% of the remaining goods are sold at 35% profit and the still remaining goods are sold at a loss of 25%. If there is an overall profit of x%, then what is the value of x?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Let's learn how to calculate it simply, the correct answer is 7.5.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The F2 generation of a monohybrid cross typically shows which phenotypic ratio?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"3:1\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which computer application is mainly used for booking railway tickets and flight reservations?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Reservation System\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Under which Article does the Supreme Court have the power of judicial review?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Article 32\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which court is considered the highest judicial authority in a district?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"District Court\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A shopkeeper fixes the marked price of an item 180% above its cost price. What percentage of discount on marked price should be allowed to gain 12%?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"60% is the correct answer. Let's learn the simple trick to solve and find it.\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"DIME is related to HNIZ in a certain way based on the English alphabetical order. In the same way, LSEU is related to PXAP. To which of the following is TCWK related, following the same logic?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The tricky pattern here is addition of 4 in first, addition of 5 in second, subtract 4 in third, and subtract 5 by fourth. Let's learn the tricks behind questions like these.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The state of matter where particles are far apart and move randomly and quickly is the:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Gaseous state\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Cheriyal scroll painting belongs to which State of India?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Telangana\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A shopkeeper purchased 62 dozens of articles at the rate of \u20b9100 per dozen. He sold each one of them at the rate of \u20b975. What percentage profit did he make?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 800%. But the real question is how to get it quickly, let's learn the trick.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A student wants to locate a word inside a PDF. Which shortcut helps?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Ctrl + F\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Before each general election to the House of the People or to a State Legislative Assembly, the President may appoint Regional Commissioners after:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"consultation with the Election Commission\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Each of T, U, V, W, X, Y and Z has an engagement on a different day of a week starting from Monday and ending on Sunday of the same week. V has engagement on the third day of the week. Only one person has engagement after Y. Only three people have engagement between V and X. Only one person has engagement between W and Z. T has engagement immediately after Z. How many people have engagement between U and T?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 3. This is all a visual map trick. Let's learn it faster by trying.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Find the average of 312, 126, 100 and 99.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 159.25. But how can you find out? Let's learn the trick behind it to solve it quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In December 2025, India and Russia signed the RELOS agreement. What is the primary purpose of this agreement?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"To facilitate reciprocal military logistics support between India and Russia\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following scientists gave the concept of atomic mass?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"John Dalton\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Logan starts from Point A and drives 18 km towards west. He then takes a left turn, drives 15 km, turns right and drives 12 km. He then takes a right turn and drives 15 km. He takes a final right turn, drives 5 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again?\n(All turns are 90-degree turns only, unless specified.)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick behind is visual move after every forward sequence The correct answer is 25 km towards east.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the given letter-number clusters will replace the question mark (?) in the following series to make it logically complete?\nCLW 31 LUF 33 UDO 35 DMX 37 ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is simple pattern type question. The correct answer is MVG 39. Let's learn the trick.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who composed the \u2018Prayag Prashasti\u2019 (Allahabad Pillar Inscription), detailing the conquests of Samudragupta?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Harisena\"\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>Based on the English alphabetical order, three of the following four letter-cluster pairs are alike in a certain way and thus form a group. Which is the one that does not belong to that group?<br>(Note: The odd man out is not based on the number of consonants\/vowels or their position in the letter-cluster.)<\/strong><br><br>A. RV\u2212WA<br>B. PT\u2212UY<br>C. GK\u2212LP<br>D. EI\u2212IP<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Odd Letter Pair<\/strong><br>Pattern check (use alphabet positions)<br>R(18) \u2192 V(22) = +4<br>V(22) \u2192 W(23) = +1<br><br>Now check others:<br><strong>PT\u2013UY<\/strong> \u2192 P(16)\u2192T(20)=+4, T\u2192U=+1 \u2714<br><strong>GK\u2013LP<\/strong> \u2192 G(7)\u2192K(11)=+4, K\u2192L=+1 \u2714<br><strong>EI\u2013IP<\/strong> \u2192 E\u2192I=+4, I\u2192P=+7 \u274c (breaks pattern)<br><br>\u2705 Answer: <strong>D. EI\u2212IP<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Look for consistent +4, +1 shift pattern.<\/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>In the figure given, parallel lines, AB and CD, are intercepted by a transversal t at E and F, respectively. If EG is the angle bisector of \u2220AEF, find \u2220EGF.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"240\" height=\"209\" src=\"https:\/\/govt.mrenglishkj.com\/railway\/wp-content\/uploads\/sites\/4\/2026\/04\/image_2026-04-24_131531358.png\" alt=\"In the figure given, parallel lines, AB and CD, are intercepted by a transversal t at E and F, respecvely. If EG is the angle bisector of \u2220AEF, find \u2220EGF.\" class=\"wp-image-314\"\/><\/figure>\n\n\n\n<p class=\"is-style-info\">A. <math data-latex=\"35^o\"><semantics><msup><mn>35<\/mn><mi>o<\/mi><\/msup><annotation encoding=\"application\/x-tex\">35^o<\/annotation><\/semantics><\/math><br>B. <math data-latex=\"85^o\"><semantics><msup><mn>85<\/mn><mi>o<\/mi><\/msup><annotation encoding=\"application\/x-tex\">85^o<\/annotation><\/semantics><\/math><br>C. <math data-latex=\"60^o\"><semantics><msup><mn>60<\/mn><mi>o<\/mi><\/msup><annotation encoding=\"application\/x-tex\">60^o<\/annotation><\/semantics><\/math><br>D. <math data-latex=\"40^o\"><semantics><msup><mn>40<\/mn><mi>o<\/mi><\/msup><annotation encoding=\"application\/x-tex\">40^o<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Read the figure correctly:<\/strong><br>AB \u2225 CD<br>Transversal cuts at E and F<br>At F on line CD, two angles are clearly marked: <strong>25\u00b0 (between GF and CD)<\/strong> and <strong>70\u00b0 (between transversal and CD)<\/strong><br>\ud83d\udc49 These two are on a straight line, so the <strong>third angle between GF and the transversal<\/strong> is:<br>180\u00b0 \u2212 (25\u00b0 + 70\u00b0) = 85\u00b0<br>So inside triangle:<br>\u2220GFE = 85\u00b0<br><br>Now go to E:<br>The transversal makes <strong>70\u00b0 with CD<\/strong>, so by <strong>corresponding angles<\/strong>, it also makes <strong>70\u00b0 with AB<\/strong><br>But \u2220AEF is between AE (left horizontal) and EF (downward transversal), so:<br>\u2220AEF = 180\u00b0 \u2212 70\u00b0 = 110\u00b0<br><br>Now EG bisects this: So we half 110.<br>\u2220GEF = 55\u00b0<br><br>Now triangle EGF:<br>\u2220GFE = 85\u00b0,  \u2220GEF = 55\u00b0<br>So:<br>\u2220EGF = 180\u00b0 \u2212 (85\u00b0 + 55\u00b0) = 40\u00b0<br>\u2705 Answer: <strong>D. 40\u00b0<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> In such figures, angle bisector + parallel lines often gives <strong>right angle<\/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>In which of the following states is the Baishagu festival celebrated by the Boro Kacharis in the month of April?<\/strong><br><br>A. Odisha<br>B. Karnataka<br>C. Bihar<br>D. Assam<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>D. Assam<\/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>Which organization was the implementing agency for the National Agricultural Insurance Scheme (NAIS) launched in 1999?<br><\/strong><br>A. Agriculture Insurance Company of India Ltd. (AIC)<br>B. Food Corporation of India (FCI)<br>C. Indian Council of Agricultural Research (ICAR)<br>D. National Bank for Agriculture and Rural Development (NABARD)<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>A. Agriculture Insurance Company of India Ltd. (AIC)<\/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 5<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Simplify<\/strong> <math data-latex=\"5\\frac{1}{6} \\div 6.2 \\times 0.75 \\div (\\frac{1}{5} \\times 40)\"><semantics><mrow><mn>5<\/mn><mfrac><mn>1<\/mn><mn>6<\/mn><\/mfrac><mo>\u00f7<\/mo><mn>6.2<\/mn><mo>\u00d7<\/mo><mn>0.75<\/mn><mo>\u00f7<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mfrac><mn>1<\/mn><mn>5<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>40<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">5\\frac{1}{6} \\div 6.2 \\times 0.75 \\div (\\frac{1}{5} \\times 40)<\/annotation><\/semantics><\/math><strong><br><\/strong><br>A. 2\/17<br>B. 5\/64<br>C. 7\/33<br>D. 9\/19<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Simplify Expression<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>5<\/mn><mfrac><mn>1<\/mn><mn>6<\/mn><\/mfrac><mo>\u00f7<\/mo><mn>6.2<\/mn><mo>\u00d7<\/mo><mn>0.75<\/mn><mo>\u00f7<\/mo><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>1<\/mn><mn>5<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>40<\/mn><mo fence=\"true\">)<\/mo><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">5\\frac{1}{6} \\div 6.2 \\times 0.75 \\div \\left(\\frac{1}{5} \\times 40\\right)<\/annotation><\/semantics><\/math><br>Convert:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>31<\/mn><mn>6<\/mn><\/mfrac><mo>\u00f7<\/mo><mfrac><mn>31<\/mn><mn>5<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>3<\/mn><mn>4<\/mn><\/mfrac><mo>\u00f7<\/mo><mn>8<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{31}{6} \\div \\frac{31}{5} \\times \\frac{3}{4} \\div 8<\/annotation><\/semantics><\/math><br>Cancel:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mn>31<\/mn><mn>6<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>5<\/mn><mn>31<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>3<\/mn><mn>4<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>1<\/mn><mn>8<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">= \\frac{31}{6} \\times \\frac{5}{31} \\times \\frac{3}{4} \\times \\frac{1}{8}<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mfrac><mrow><mn>5<\/mn><mo>\u00d7<\/mo><mn>3<\/mn><\/mrow><mrow><mn>6<\/mn><mo>\u00d7<\/mo><mn>4<\/mn><mo>\u00d7<\/mo><mn>8<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>15<\/mn><mn>192<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>5<\/mn><mn>64<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">= \\frac{5 \\times 3}{6 \\times 4 \\times 8} = \\frac{15}{192} = \\frac{5}{64}<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>B. 5\/64<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Convert decimals \u2192 fractions \u2192 cancel immediately.<\/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>If <\/strong><math data-latex=\"a\"><semantics><mi>a<\/mi><annotation encoding=\"application\/x-tex\">a<\/annotation><\/semantics><\/math><strong> is a positive integer such that the equations <\/strong><math data-latex=\"(a^2 - 7a)x^2 + x + 12 = 0\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>7<\/mn><mi>a<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>x<\/mi><mo>+<\/mo><mn>12<\/mn><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(a^2 &#8211; 7a)x^2 + x + 12 = 0<\/annotation><\/semantics><\/math> <strong>and <\/strong><math data-latex=\"240x^2 + 8x + (a^2 - 4) = 0\"><semantics><mrow><mn>240<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>8<\/mn><mi>x<\/mi><mo>+<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>4<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">240x^2 + 8x + (a^2 &#8211; 4) = 0<\/annotation><\/semantics><\/math> <strong>both have roots common, then the value of <\/strong><math data-latex=\"\\frac{(a + 2)(a + 3)}{a - 4}\"><semantics><mfrac><mrow><mo form=\"prefix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mn>2<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mn>3<\/mn><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><mrow><mi>a<\/mi><mo>\u2212<\/mo><mn>4<\/mn><\/mrow><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{(a + 2)(a + 3)}{a &#8211; 4}<\/annotation><\/semantics><\/math> <strong>is:<br><\/strong><br>A. 18<br>B. 26<br>C. 30<br>D. 42<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Common Roots<\/strong><br>For common roots:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>7<\/mn><mi>a<\/mi><\/mrow><mn>240<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>8<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>12<\/mn><mrow><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>4<\/mn><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{a^2 &#8211; 7a}{240} = \\frac{1}{8} = \\frac{12}{a^2 &#8211; 4}<\/annotation><\/semantics><\/math><br>Solve:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>7<\/mn><mi>a<\/mi><mo>=<\/mo><mn>30<\/mn><mo>\u21d2<\/mo><mi>a<\/mi><mo>=<\/mo><mn>10<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">a^2 &#8211; 7a = 30 \\Rightarrow a = 10<\/annotation><\/semantics><\/math><br>Now:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mo stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mi>a<\/mi><mo>\u2212<\/mo><mn>4<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>12<\/mn><mo>\u00d7<\/mo><mn>13<\/mn><\/mrow><mn>6<\/mn><\/mfrac><mo>=<\/mo><mn>26<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{(a+2)(a+3)}{a-4} = \\frac{12 \\times 13}{6} = 26<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>B. 26<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Equal ratios for coefficients \u2192 fastest method.<\/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>During a sale 50% of the goods are sold at 16% profit, 40% of the remaining goods are sold at 35% profit and the still remaining goods are sold at a loss of 25%. If there is an overall profit of x%, then what is the value of x?<\/strong><br><br>A. 7.5<br>B. 8<br>C. 6<br>D. 9<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Overall Profit<\/strong><br>Assume total CP = 100<br>50 \u2192 profit 16% \u2192 58<br>20 \u2192 profit 35% \u2192 27<br>30 \u2192 loss 25% \u2192 22.5<br><br>Total SP = 107.5<br>Profit = 7.5%<br>\u2705 Answer: <strong>A. 7.5%<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Assume 100 \u2192 easiest.<\/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>The F2 generation of a monohybrid cross typically shows which phenotypic ratio?<\/strong><br><br>A. 2:1<br>B. 3:1<br>C. 1:2:1<br>D. 1:1<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Monohybrid Cross<\/strong><br>\u2705 Answer: <strong>B. 3:1<\/strong><br>\ud83d\udc49 Classic Mendel ratio.<\/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 computer application is mainly used for booking railway tickets and flight reservations?<\/strong><br><br>A. Collection System<br>B. Reservation System<br>C. NTPC System<br>D. Ticketing Counter<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>B. Reservation 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 10<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Under which Article does the Supreme Court have the power of judicial review?<\/strong><br><br>A. Article 30<br>B. Article 72<br>C. Article 32<br>D. Article 124<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>C. Article 32<\/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>Which court is considered the highest judicial authority in a district?<\/strong><br><br>A. Family Court<br>B. District Court<br>C. Munsif Court<br>D. High Court<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>B. District Court<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 12<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>A shopkeeper fixes the marked price of an item 180% above its cost price. What percentage of discount on marked price should be allowed to gain 12%?<br><\/strong><br>A. 60%<br>B. 58%<br>C. 57%<br>D. 62%<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Discount Problem<\/strong><br>MP = Market Price<br>CP = Cost Price<br>SP = Selling Price<br>Let cost price = 100.<br>Marked price is 180% above cost: 100 + 180% = 280<br>MP = 280, CP = 100<br>SP needed = 112 (100 + 12%)<br>Discount = <math data-latex=\"\\frac{280 - 112}{280} \\times 100 = 60%\"><semantics><mrow><mfrac><mrow><mn>280<\/mn><mo>\u2212<\/mo><mn>112<\/mn><\/mrow><mn>280<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>100<\/mn><mo>=<\/mo><mn>60<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{280 &#8211; 112}{280} \\times 100 = 60%<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>A. 60%<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Assume CP=100.<\/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>DIME is related to HNIZ in a certain way based on the English alphabetical order. In the same way, LSEU is related to PXAP. To which of the following is TCWK related, following the same logic?<\/strong><br><br>A. YGTE<br>B. WIRG<br>C. VHSD<br>D. XHSF<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>The Pattern: +4, +5, -4, -5.<br><\/strong>DIME &#8212;&gt; HNIZ<br>D + 4 = H<br>I + 5 = N<br>M &#8211; 4 = I<br>E &#8211; 5 = Z<br><br>LSEU &#8212;&gt; PXAP<br>L + 4 = P<br>S + 5 = X<br>E &#8211; 4 = A<br>U &#8211; 5 = P<br><br>Same logic applies on this: TCWK<br>T + 4 = X<br>C + 5 = H<br>W &#8211; 4 = S<br>K &#8211; 5 = F<br><br><strong>\u2705 Answer: D. XHSF<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 14<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The state of matter where particles are far apart and move randomly and quickly is the:<\/strong><br><br>A. Liquid state<br>B. Gaseous state<br>C. Plasma state<br>D. Solid state<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: B. Gaseous state<\/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>Cheriyal scroll painting belongs to which State of India?<\/strong><br><br>A. Karnataka<br>B. Andhra Pradesh<br>C. Tamil Nadu<br>D. Telangana<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>D. Telangana<\/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>A shopkeeper purchased 62 dozens of articles at the rate of \u20b9100 per dozen. He sold each one of them at the rate of \u20b975. What percentage profit did he make?<\/strong><br><strong><br><\/strong>A. 800%<br>B. 801%<br>C. 797%<br>D. 798%<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Profit %<\/strong><br>CP = 62\u00d7100 = 6200<br>SP = 62\u00d712\u00d775 = 55800<br>Profit = 49600<br>Profit % = 800%<br>\u2705 Answer: <strong>A. 800%<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Multiply dozens carefully.<\/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>A student wants to locate a word inside a PDF. Which shortcut helps?<\/strong><br><br>A. Ctrl + C<br>B. Ctrl + F<br>C. Ctrl + Tab<br>D. Ctrl + V<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>B. Ctrl + F<\/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>Before each general election to the House of the People or to a State Legislative Assembly, the President may appoint Regional Commissioners after:<\/strong><br><br>A. consultation with the Speaker of the Lok Sabha<br>B. consultation with the Chief Justice of India<br>C. consultation with the Election Commission<br>D. consultation with the Prime Minister<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>C. consultation with the Election Commission<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 19<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Each of T, U, V, W, X, Y and Z has an engagement on a different day of a week starting from Monday and ending on Sunday of the same week. V has engagement on the third day of the week. Only one person has engagement after Y. Only three people have engagement between V and X. Only one person has engagement between W and Z. T has engagement immediately after Z. How many people have engagement between U and T?<\/strong><br><br>A. One <br>B. Three<br>C. Four<br>D. Two<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Seating Arrangement<\/strong><br>Positions: There is no cycle or loop here. Be aware!<br>Mon(1) to Sun(7)<br>1 = U<br>2 = W<br>3 = V<br>4 = Z<br>5 = T<br>6 = Y<br>7 = X<br><br>&#8211; V on 3rd day: 3<br><br>&#8211; one person after Y: wait for it<br><br>&#8211; three between V and X: Since V is 3rd and three between then X must be 7th.<br><br>&#8211; one person between W and Z: wait for it because we don&#8217;t know whether W is on 2nd or 4th position.<br><br>&#8211; T after Z: This clears many things. T after Z makes it clear that W is 2nd, because if it is 4th then after Z there will be 7th position X.<br>W is 2nd, Z is 4th and T is 5th.<br><br>There is one condition still ;eft and most confusing. Only 1 person after Y. We still don&#8217;t know U and Y position yet.<br><strong>A poorly made question, I can say. But there is a catch, in options there is no option like: None.<\/strong><br>That means U cannot be in 6th postion.<br><strong>Impossible: T (4th) &#8212;&gt; U (5th)<\/strong><br>But it must be in position 1st and Y in position 6th.<br><strong><br><\/strong>Between U(1) and T(5): 3 people<br>\u2705 Answer: <strong>D. 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 20<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Find the average of 312, 126, 100 and 99.<\/strong><br><br>A. 157.25<br>B. 159.25<br>C. 156.25<br>D. 158.25<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Average<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mn>312<\/mn><mo>+<\/mo><mn>126<\/mn><mo>+<\/mo><mn>100<\/mn><mo>+<\/mo><mn>99<\/mn><\/mrow><mn>4<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>637<\/mn><mn>4<\/mn><\/mfrac><mo>=<\/mo><mn>159.25<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{312+126+100+99}{4} = \\frac{637}{4} = 159.25<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>B. 159.25<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 21<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In December 2025, India and Russia signed the RELOS agreement. What is the primary purpose of this agreement?<\/strong><br><br>A. To promote civilian technology sharing between India and Russia<br>B. To establish joint agricultural research centers<br>C. To enhance educational exchange programs between India and Russia<br>D. To facilitate reciprocal military logistics support between India and Russia<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: D. To facilitate reciprocal military logistics support between India and Russia<\/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>Which of the following scientists gave the concept of atomic mass?<br><\/strong><br>A. Ernest Rutherford<br>B. John Dalton<br>C. J.J. Thomson<br>D. Niels Bohr<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: B. John Dalton<\/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>Logan starts from Point A and drives 18 km towards west. He then takes a left turn, drives 15 km, turns right and drives 12 km. He then takes a right turn and drives 15 km. He takes a final right turn, drives 5 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again?<br>(All turns are 90-degree turns only, unless specified.)<\/strong><br><br>A. 18 km towards south<br>B. 15 km towards west<br>C. 25 km towards east<br>D. 5 km towards north<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\ud83e\udded Step-by-step movement (build the path in your head)<\/strong><br>Start at <strong>Point A<\/strong><br><strong>18 km West<\/strong> \u2192 now you are left of A<br><strong>Left turn from West = South<\/strong>, go <strong>15 km<\/strong><br><strong>Right turn from South = West<\/strong>, go <strong>12 km<\/strong><br><strong>Right turn from West = North<\/strong>, go <strong>15 km<\/strong><br><strong>Right turn from North = East<\/strong>, go <strong>5 km<\/strong> \u2192 reach <strong>Point P<\/strong><br><br><strong>\ud83e\udde0 Now track net movement (KEY STEP)<\/strong><br>Horizontal (East-West):<br>West: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>18<\/mn><mo>+<\/mo><mn>12<\/mn><mo>=<\/mo><mn>30<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">18 + 12 = 30<\/annotation><\/semantics><\/math><br>East: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">5<\/annotation><\/semantics><\/math><br>\ud83d\udc49 Net = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>30<\/mn><mo>\u2212<\/mo><mn>5<\/mn><mo>=<\/mo><mn>25<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">30 &#8211; 5 = 25<\/annotation><\/semantics><\/math> km <strong>West<\/strong><br><br><strong>Vertical (North-South):<br><\/strong>South: 15<br>North: 15<br>\ud83d\udc49 Net = 0 (cancel out)<br><br><strong>\ud83d\udccd Final Position<br><\/strong>\ud83d\udc49 Point P is <strong>25 km West of A<\/strong><br><br><strong>\ud83d\udd01 To return to A<br><\/strong>You must go:<br>\ud83d\udc49 <strong>25 km East<\/strong><br>\u2705 Answer: <strong>C. 25 km towards east<\/strong><br><\/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>Which of the given letter-number clusters will replace the question mark (?) in the following series to make it logically complete?<br>CLW 31 LUF 33 UDO 35 DMX 37 ?<\/strong><br><br>A. NUR 39<br>B. MVG 39<br>C. LST 39<br>D. XSH 38<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Series<\/strong><br>Pattern:<br>+9 letters, +2 numbers<br>Next: MVG 39<br>\u2705 Answer: <strong>B. MVG 39<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 25<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Who composed the \u2018Prayag Prashasti\u2019 (Allahabad Pillar Inscription), detailing the conquests of Samudragupta?<\/strong><br><br>A. Vishakhadatta<br>B. Banabhatta<br>C. Harisena<br>D. Kalidasa<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>C. Harisena<\/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 3 (16 March 2026) \u2013 <strong>A Full Test, Fast Hack, Step-by-Step Solutions<\/strong> (Part 2: Question 26-50)<\/h2>\n\n\n\n<p>This part contains questions from 26 to 50 out of 100. Railway Recruitment Board (RRB) conducts the RRB NTPC Exam like 2026 to fill vacancies for Graduate and Undergraduate posts under the Non-Technical Popular Categories (NTPC). Here you will try to attempt the real RRB NTPC Graduate CBT exam, which was conducted on 16 March, 2026 Shift 3. The competitive exam is divided into 4 parts each with 25 questions. Take the test and also learn from the answer solutions and their explanations step-by-step.<\/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 = 22;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-22\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"22\">\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\">Step-by-step Solution and Explanation of The Railway Competitive Exam Test<\/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\": \"P, Q, R, S, T, U and V sit around a circular table facing the centre. V sits to the immediate left of T. U sits to the immediate left of R. R sits second to the left of S. Q sits third to the left of T. Who sits 2nd to the right of S?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is T, but how can we get it s easily. Let's learn the trick.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"There are 72 members in group A, 12 members in group B and 87 members in group C. All the members of these groups went to a restaurant. The average amounts spent on each member of groups A, B and C are \u20b9404, \u20b9316 and \u20b9424, respectively. The overall average amount (in \u20b9) spent per member is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 408, but how can we get it s easily. Let's learn the trick.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If 160% of 75% of A is equal to two times the value of 150% of B, then A is more\/less than B by how much percentage?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is conception, so the correct answer is 150%, more.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following will be the pressure of water at the base of a lake of height 20 metres? (g = 9.8m\/$s^2$ and Density of water = 1 kg\/litre)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is conception, so the correct answer is 1,96,000 Pa.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"The Lilatilakam, a 14th-century treatise, played a significant role in establishing the classical status of which Indian language through its grammatical and poetic principles?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Malayalam\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"The internal surface area (in $cm^2$ ) of an open (at the top) cuboidal box whose internal length, breadth and height are 8 cm, 17 cm and 22 cm, respectively, is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick behind is very simple, the correct answer is 1236. Let's learn.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In this question, a question is followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and decide the appropriate answer.\nQ. Five students \u2013 Alok, Bharti, Celine, Darpan, and Ema \u2013 obtained different marks in an examination. Who scored the third highest marks?\n(I) Darpan scored more than Alok and Bharti but less than Celine.\n(II) Ema scored more than Darpan but less than Celine.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick behind is very simple, the correct answer is Both statements I and II together (and not statement I alone or statement II alone) are sufficient to answer the question. Let's learn.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who played the most significant military role in leading Nana Sahib's forces during the Revolt of 1857 at Kanpur?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Tantia Tope, known for his guerrilla warfare and patriotic resistance.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who jointly led the first ever no-tax campaign against the British Government in Bengal during the 1838-1848 Farazi Movement?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Shariatullah Khan and Dadu Mian.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Mr. ABCD wants to become a member of the Legislative Assembly. What is the minimum age prescribed in the Constitution of India so that he becomes a member of the Legislative Assembly?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"25 years\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Three positive integers, A, B, and C, are such that the least common multiple of A and B is 24, the least common multiple of B and C is 36, and the least common multiple of C and A is 72. If the numbers are taken to be as small as possible, the value of A + B + C is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 29, but how, you should check this out from here.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Find the median from the following data.\n$$ \\begin{array}{|c|c|} \\hline \\textbf{Age in years} & \\textbf{No. of patients} \\\\ \\hline {20-30} & {11} \\\\ \\hline {30-40} & {18} \\\\ \\hline {40-50} & {28} \\\\ \\hline {50-60} & {15} \\\\ \\hline {60-70} & {22} \\\\ \\hline {70-80} & {31} \\\\ \\hline {80-90} & {13} \\\\ \\hline \\end{array} $$\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 58, but how, you should check this out from here.\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"According to the March 1997 agreement between the RBI and the Central Government, which practice was discontinued with effect from April 1, 1997?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Practice of issuing ad hoc Treasury Bills\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Six years hence, a father's age will be 3 times the age of his son. Six years ago, the father was 7 times as old as his son. Find the present ages (in years) of the father and son.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick of the patten is in the sequence. The correct answer is 48 and 12.\n\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"According to the 2025 Financial Tracking Services report by the United Nations Office for the Coordination of Humanitarian Affairs, which two contributors ranked higher than UAE in global humanitarian aid?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is United States and European Union.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If 30% of $80 - \\frac{4}{7} \\times \\sqrt[3]{729} \\times \\sqrt{49} = y$, then the value of y is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick of the patten is simplification. The correct answer is -12.\n\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which ISRO centre will host the newly approved Third Launch Pad by Union cabinet in December 2025?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Satish Dhawan Space Centre\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Based on the alphabetical order, three of the following four are alike in a certain way and thus form a group. Which is the one that does not belong to that group?\n(Note: The odd man out is not based on the number of consonants\/vowels or their position in the letter cluster.)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"In order to figure it out, check the explanation. How, learn from here.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following letter-clusters should replace # and % so that the pattern and relationship followed between the letter-cluster pair on the left side of :: is the same as that on the right side of :: ?\n# : MWE :: KUC : %\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"In order to figure it out, check the explanation. How, learn from here.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A typist takes 40 minutes to type 2 pages. How long (in minutes) will he take to type 91 pages?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 1820, let's learn the trick to find out quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which Himalayan region has greater altitudinal variations?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Eastern Himalayan region\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If \u2018A\u2019 stands for \u2018\u00f7\u2019, \u2018B\u2019 stands for \u2018\u00d7\u2019, \u2018C\u2019 stands for \u2018+\u2019 and \u2018D\u2019 stands for \u2018\u2212\u2019, then what will come in place of the question mark (?) in the following equation?\n9 B 4 C 6 D 45 A 5 = ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \" Learn the trick and pattern to figure out questions like these in very short time.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following states ranks number one in the production of natural rubber in India in 2023-24?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Kerala\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"18 is related to 59 following a certain logic. Following the same logic, 27 is related to 86. To which of the following is 37 related, following the same logic?\n(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 \u2013 Operations on 13 such as adding \/subtracting \/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Need calculation skill to solve this one fastest, learn how to do it quickly and the answer is 116.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Refer to the following letter, number, symbol series and answer the question.\n(Left) 5 5 \u00a9 J W 1 L \u00a3 D Z 6 6 C 2 # R 2 C 6 % Y 6 (Right)\nIf all the numbers are dropped from the series, which of the following will be fifth from the left?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick of the patten is visual sequence. The correct answer is \u00a3.\"\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>P, Q, R, S, T, U and V sit around a circular table facing the centre. V sits to the immediate left of T. U sits to the immediate left of R. R sits second to the left of S. Q sits third to the left of T. Who sits 2nd to the right of S?<\/strong><br><br>A. P<br>B. R<br>C. T<br>D. U<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Circular Seating Arrangement<\/strong><br>Given:<br>7 seats: P,Q,R,S,T,U,V<br>left of = anti-clockwise<br>right of = clockwise<br>Cicular means: 1,2,3,4,5,6,7,1,&#8230;<br><br>Let&#8217;s start.<br>1 = V<br>2 = T<br>3 = P<br>4 = U<br>5 = R<br>6 = Q<br>7 = S<br><br>&#8211; V left of T: So consider V as 1 and T as 2.<br><br>&#8211; U left of R: Unsure about it, so wait.<br>&#8211; R 2nd left of S: unsure so wait.<br><br>&#8211; Q 3rd left of T: T as 2. Left side means <strong>6<\/strong>, 7, 1, 2. Q as 6.<br><br>&#8211; Go back to R and S: It is impossible to put R and S in any position besides 7 and 5, because of condition.<br><br>&#8211; U left of R, so U as 4.<br>&#8211; Only 3 left for P.<br><br>But in real exam the question asked 2nd right of S. So the moment we found S as 7, we can stop and fill the answer.<br>S (7), V (1), T (2).<br><br>\u2705 Answer: <strong>C. T<\/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>There are 72 members in group A, 12 members in group B and 87 members in group C. All the members of these groups went to a restaurant. The average amounts spent on each member of groups A, B and C are \u20b9404, \u20b9316 and \u20b9424, respectively. The overall average amount (in \u20b9) spent per member is:<\/strong><br><br>A. 404<br>B. 412<br>C. 408<br>D. 409<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Weighted Average<\/strong><br>Formula:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Average<\/mtext><mo>=<\/mo><mfrac><mrow><mo>\u2211<\/mo><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u00d7<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mo>\u2211<\/mo><mi>n<\/mi><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Average} = \\frac{\\sum (n \\times x)}{\\sum n}<\/annotation><\/semantics><\/math><br>Total members:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>72<\/mn><mo>+<\/mo><mn>12<\/mn><mo>+<\/mo><mn>87<\/mn><mo>=<\/mo><mn>171<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">72 + 12 + 87 = 171<\/annotation><\/semantics><\/math>Total amount:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>72<\/mn><mo>\u00d7<\/mo><mn>404<\/mn><mo>+<\/mo><mn>12<\/mn><mo>\u00d7<\/mo><mn>316<\/mn><mo>+<\/mo><mn>87<\/mn><mo>\u00d7<\/mo><mn>424<\/mn><mo>=<\/mo><mn>29088<\/mn><mo>+<\/mo><mn>3792<\/mn><mo>+<\/mo><mn>36888<\/mn><mo>=<\/mo><mn>69768<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">72\u00d7404 + 12\u00d7316 + 87\u00d7424 = 29088 + 3792 + 36888 = 69768<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Average<\/mtext><mo>=<\/mo><mfrac><mn>69768<\/mn><mn>171<\/mn><\/mfrac><mo>=<\/mo><mn>408<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Average} = \\frac{69768}{171} = 408<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>C. 408<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Never average averages \u2192 use weighted average.<br>Shortcut:<br>Divide by 3 once: 72, 12, 87<br>We&#8217;ll get: 24, 4, 29<br>24 + 4 + 29 = 57<br><br>Divide by 4: 404, 316, 424<br>We&#8217;ll get: 101, 79, 106<br><br>Let&#8217;s multiply now: <br>24 \u00d7 101 + 4 \u00d7 79 + 29 \u00d7 106 = 5814<br>Average: 5814\/57 = 102<br>Now remember, we only bring back the numerator value back, so we divided 404, 316, 424 by 4, right? Now, we will multiply it again by 4 to get the real option.<br><strong>102 \u00d7 4 = 408.<br>Option C.<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 28<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>If 160% of 75% of A is equal to two times the value of 150% of B, then A is more\/less than B by how much percentage?<br><\/strong><br>A. 150%, less<br>B. 150%, more<br>C. 60%, less<br>D. 60%, more<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Percentage Comparison<\/strong><br>Given:<br>160% \u00d7 75% \u00d7 A = 2 \u00d7 (150% \u00d7 B)<br>Convert:<br>1.6 \u00d7 0.75 \u00d7 A = 2 \u00d7 1.5 \u00d7 B <br>1.2A = 3B<br>\u21d2 A = 2.5B<br>So:<br>A is <strong>150% more than B<\/strong><br>\u2705 Answer: <strong>B. 150%, more<\/strong><br>\ud83d\udc49 <strong>Shortcut:<\/strong> Convert to decimal \u2192 compare ratio.<\/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>Which of the following will be the pressure of water at the base of a lake of height 20 metres? (g = 9.8m\/s<sup>2<\/sup> and Density of water = 1 kg\/litre)<br><\/strong><br>A. 19,600 Pa<br>B. 196 Pa<br>C. 1,96,000 Pa<br>D. 1960 Pa<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pressure Formula<\/strong><br>P = pgh<br>Given:<br>p = 1000 kg\/m\u00b3<br>g = 9.8<br>h = 20<br><br>P = 1000 \u00d7 9.8 \u00d7 20<br>P = 196000&nbsp;Pa<br>\u2705 Answer: <strong>C. 1,96,000 Pa<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Water density = 1000 always.<\/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>The Lilatilakam, a 14th-century treatise, played a significant role in establishing the classical status of which Indian language through its grammatical and poetic principles?<br><\/strong><br>A. Tamil<br>B. Kannada<br>C. Malayalam<br>D. Odia<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: C. Malayalam<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 31<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The internal surface area (in cm<sup>2<\/sup> ) of an open (at the top) cuboidal box whose internal length, breadth and height are 8 cm, 17 cm and 22 cm, respectively, is:<\/strong><br><br>A. 1236<br>B. 1215<br>C. 1189<br>D. 1238<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Surface Area (Open Box)<\/strong><br>Formula:<br>= 2(lb + bh + hl) \u2212 lb<br>= 2(8 \u00d7 17 + 17 \u00d7 22 + 22 \u00d7 8) \u2212 8 \u00d7 17 <br>= 2(136 + 374 + 176) \u2212 136<br>= 2(686) \u2212 136<br>= 1372 \u2212 136<br>= 1236<br>\u2705 Answer: <strong>A. 1236<\/strong><br><strong>Trick: <\/strong>Shorten the formula: lb + 2(bh + hl)<br>8 \u00d7 17 + 2(17 \u00d7 22 + 22 \u00d7 8)<br>136 + 2(374 + 176)<br>136 + 1100<br>1236<\/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>In this question, a question is followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and decide the appropriate answer.<br>Q. Five students \u2013 Alok, Bharti, Celine, Darpan, and Ema \u2013 obtained different marks in an examination. Who scored the third highest marks?<br>(I) Darpan scored more than Alok and Bharti but less than Celine.<br>(II) Ema scored more than Darpan but less than Celine.<br><\/strong><br>A. Data in Statement I alone is sufficient to answer the question while data in Statement II is not<br>B. Data in Statement II alone is sufficient to answer the question while data in Statement I is not<br>C. Both statements I and II together (and not statement I alone or statement II alone) are sufficient to answer the question<br>D. Both statements I and II together are NOT sufficient to answer the question<\/p>\n\n\n\n<p class=\"is-style-success\">This is a <strong>Data Sufficiency + Ranking<\/strong> question. The goal is NOT to find all ranks \u2014 only check if we can <strong>fix who is 3rd highest<\/strong>.<br><br>\ud83d\udd34 Given<br>Five students: <strong>Alok (A), Bharti (B), Celine (C), Darpan (D), Ema (E)<\/strong><br>All have <strong>different marks<\/strong>.<br><br>\ud83e\udde0 Statement (I)<br>\u201cDarpan scored more than Alok and Bharti but less than Celine\u201d<br>This gives:<br>C &gt; D &gt; A,B<br>\ud83d\udc49 But A and B order is unknown<br>\ud83d\udc49 Ema is completely unknown<br>So possible rankings can change \u2192 <strong>3rd position not fixed<\/strong><br>\u274c <strong>Statement (I) alone is NOT sufficient<\/strong><br><br>\ud83e\udde0 Statement (II)<br>\u201cEma scored more than Darpan but less than Celine\u201d<br>This gives:<br>C &gt; E &gt; D<br>\ud83d\udc49 But A and B are unknown<br>Again, 3rd place can vary<br>\u274c <strong>Statement (II) alone is NOT sufficient<\/strong><br><br>\ud83d\udd25 Combine (I) + (II)<br>From (I): C &gt; D &gt; A,B<br>From (II): C &gt; E &gt; D<br><br>\ud83e\udde0 Merge both: C &gt; E &gt; D &gt; A,B<br><br>Now observe carefully:<br>A &amp; B = 4th\/5th (order doesn&#8217;t matter)<br>C = 1st<br>E = 2nd<br>D = 3rd<br>\u2705 Answer: <strong>D. Both statements I and II together (and not statement I alone or statement II alone) are sufficient to answer the question<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 33<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Who played the most significant military role in leading Nana Sahib&#8217;s forces during the Revolt of 1857 at Kanpur?<\/strong><br><br>A. Azimullah, who was an expert in political propaganda<br>B. Bahadur Shah, who appointed Nana Sahib as his Governor<br>C. Baji Rao II, the last Peshwa and father of Nana Sahib<br>D. Tantia Tope, known for his guerrilla warfare and patriotic resistance<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>D. Tantia Tope, known for his guerrilla warfare and patriotic resistance<\/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>Who jointly led the first ever no-tax campaign against the British Government in Bengal during the 1838-1848 Farazi Movement?<\/strong><br><br>A. Shariatullah Khan and Dadu Mian<br>B. Sidhu Murmu and Kanhu Murmu<br>C. Titu Mir and Syed Ahmad Barelvi<br>D. Kunwar Singh and Amar Singh<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>A. Shariatullah Khan and Dadu Mian<\/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>Mr. ABCD wants to become a member of the Legislative Assembly. What is the minimum age prescribed in the Constitution of India so that he becomes a member of the Legislative Assembly?<\/strong><br><br>A. 21 years<br>B. No Minimum age is prescribed in the Constitution<br>C. 35 years<br>D. 25 years<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>D. 25 years<\/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 positive integers, A, B, and C, are such that the least common multiple of A and B is 24, the least common multiple of B and C is 36, and the least common multiple of C and A is 72. If the numbers are taken to be as small as possible, the value of A + B + C is:<\/strong><br><br>A. 25<br>B. 27<br>C. 29<br>D. 31<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>LCM Problem<\/strong><br>Given:<br>LCM(A,B) = 24<br>LCM(B,C) = 36<br>LCM(C,A) = 72<br>Break given LCMs<br><math data-latex=\"LCM(A,\\ B) = 2^3 \\times 3 \\\\ \\\\ LCM(B,\\ C) = 2^2 \\times 3^2 \\\\ \\\\ LCM(C,\\ A) = 2^3 \\times 3^2\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mi>L<\/mi><mi>C<\/mi><mi>M<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>A<\/mi><mo separator=\"true\">,<\/mo><mtext>&nbsp;<\/mtext><mi>B<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>L<\/mi><mi>C<\/mi><mi>M<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>B<\/mi><mo separator=\"true\">,<\/mo><mtext>&nbsp;<\/mtext><mi>C<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>L<\/mi><mi>C<\/mi><mi>M<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>C<\/mi><mo separator=\"true\">,<\/mo><mtext>&nbsp;<\/mtext><mi>A<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><mo>\u00d7<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">LCM(A,\\ B) = 2^3 \\times 3 \\\\ \\\\ LCM(B,\\ C) = 2^2 \\times 3^2 \\\\ \\\\ LCM(C,\\ A) = 2^3 \\times 3^2<\/annotation><\/semantics><\/math><br>\ud83d\udc49 So only primes involved are <strong>2 and 3<\/strong><br><br><strong>Think in simple words (NO VARIABLES)<\/strong><br>We need to <strong>separate A, B, C using 2s and 3s<\/strong> out of the grouped (A, B), (B, C), and (C, A):<br>For A look (<strong>A<\/strong>, B) &amp; (C, <strong>A<\/strong>) \u2192 2<sup>3<\/sup> came in both (A, B) and (C, A) which confirms it&#8217;s A. Only 3 left behind for B.<br><math data-latex=\"A = 2^3 = 8\"><semantics><mrow><mi>A<\/mi><mo>=<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><mo>=<\/mo><mn>8<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">A = 2^3 = 8<\/annotation><\/semantics><\/math><br>For C look (B, <strong>C<\/strong>) &amp; (<strong>C<\/strong>, A) \u2192 3<sup>2<\/sup> came in both (B, C) and (C, A) which confirms it&#8217;s C. Only 2<sup>3<\/sup> left behind for B.<br><math data-latex=\"C = 3^2 = 9\"><semantics><mrow><mi>C<\/mi><mo>=<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><mo>=<\/mo><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">C = 3^2 = 9<\/annotation><\/semantics><\/math><br>For B look (A, <strong>B<\/strong>) &amp; (<strong>B<\/strong>, C) \u2192 Two values left for B: 2<sup>2<\/sup> and 3.<br><math data-latex=\"B = 2^2 \\times 3 = 12\"><semantics><mrow><mi>B<\/mi><mo>=<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><mo>=<\/mo><mn>12<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">B = 2^2 \\times 3 = 12<\/annotation><\/semantics><\/math><br><br>Minimum values:<br>A=8, B=12, C=9<br>A + B + C = 29<br>\u2705 Answer: <strong>C. 29<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Use prime factors.<\/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>Find the median from the following data.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Age in years<\/th><th class=\"has-text-align-center\" data-align=\"center\">No. of patients<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">20-30<\/td><td class=\"has-text-align-center\" data-align=\"center\">11<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">30-40<\/td><td class=\"has-text-align-center\" data-align=\"center\">18<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">40-50<\/td><td class=\"has-text-align-center\" data-align=\"center\">28<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">50-60<\/td><td class=\"has-text-align-center\" data-align=\"center\">15<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">60-70<\/td><td class=\"has-text-align-center\" data-align=\"center\">22<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">70-80<\/td><td class=\"has-text-align-center\" data-align=\"center\">31<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">80-90<\/td><td class=\"has-text-align-center\" data-align=\"center\">13<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"is-style-info\">A. 60<br>B. 55<br>C. 58<br>D. 69<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Median<\/strong><br>Total = 138 \u2192 N\/2 = 69<br>Median class: 50-60 = 15<br>l = 50<br>cf = 57 (Total frequency of prior 50-60: 11 + 18 + 28 = 57)<br>f = 15<br>h (60-50) = 10<br>Formula:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Median<\/mtext><mo>=<\/mo><mi>l<\/mi><mo>+<\/mo><mfrac><mrow><mo stretchy=\"false\">(<\/mo><mi>N<\/mi><mi mathvariant=\"normal\">\/<\/mi><mn>2<\/mn><mo>\u2212<\/mo><mi>c<\/mi><mi>f<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mi>f<\/mi><\/mfrac><mo>\u00d7<\/mo><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Median} = l + \\frac{(N\/2 &#8211; cf)}{f} \u00d7 h<\/annotation><\/semantics><\/math><br><math data-latex=\"50 + \\frac{69 - 57}{15} \\times 10 \\\\ 50 + \\frac{12 \\times 10}{15} \\\\ 50 + \\frac{120}{15} \\\\ 50 + 8\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mn>50<\/mn><mo>+<\/mo><mfrac><mrow><mn>69<\/mn><mo>\u2212<\/mo><mn>57<\/mn><\/mrow><mn>15<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>10<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>50<\/mn><mo>+<\/mo><mfrac><mrow><mn>12<\/mn><mo>\u00d7<\/mo><mn>10<\/mn><\/mrow><mn>15<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>50<\/mn><mo>+<\/mo><mfrac><mn>120<\/mn><mn>15<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>50<\/mn><mo>+<\/mo><mn>8<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">50 + \\frac{69 &#8211; 57}{15} \\times 10 \\\\ 50 + \\frac{12 \\times 10}{15} \\\\ 50 + \\frac{120}{15} \\\\ 50 + 8<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>C. 58<\/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>According to the March 1997 agreement between the RBI and the Central Government, which practice was discontinued with effect from April 1, 1997?<\/strong><br><br>A. Practice of issuing ad hoc Treasury Bills<br>B. Automatic monetisation of fiscal deficit<br>C. Market borrowing through dated securities<br>D. Issuance of 91-day Treasury Bills<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: A. Practice of issuing ad hoc Treasury Bills<\/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>Six years hence, a father&#8217;s age will be 3 times the age of his son. Six years ago, the father was 7 times as old as his son. Find the present ages (in years) of the father and son.<br><\/strong><br>A. 50 and 14<br>B. 46 and 10<br>C. 52 and 16<br>D. 48 and 12<\/p>\n\n\n\n<p class=\"is-style-success\">Let the present age of the son 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 the father be <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>Six years hence means after 6 years, so ages become <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>+<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x+6<\/annotation><\/semantics><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>+<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">y+6<\/annotation><\/semantics><\/math>, and we are told the father will be 3 times the son, so <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>+<\/mo><mn>6<\/mn><mo>=<\/mo><mn>3<\/mn><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>+<\/mo><mn>6<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">y+6 = 3(x+6)<\/annotation><\/semantics><\/math>. Six years ago means ages were <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>\u2212<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x-6<\/annotation><\/semantics><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>\u2212<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">y-6<\/annotation><\/semantics><\/math>, and the father was 7 times the son, so <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>\u2212<\/mo><mn>6<\/mn><mo>=<\/mo><mn>7<\/mn><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>\u2212<\/mo><mn>6<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">y-6 = 7(x-6)<\/annotation><\/semantics><\/math>.<br>Now simplify both: from the first, <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>+<\/mo><mn>6<\/mn><mo>=<\/mo><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mn>18<\/mn><mo>\u21d2<\/mo><mi>y<\/mi><mo>=<\/mo><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mn>12<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">y+6 = 3x + 18 \\Rightarrow y = 3x + 12<\/annotation><\/semantics><\/math>. From the second, <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>\u2212<\/mo><mn>6<\/mn><mo>=<\/mo><mn>7<\/mn><mi>x<\/mi><mo>\u2212<\/mo><mn>42<\/mn><mo>\u21d2<\/mo><mi>y<\/mi><mo>=<\/mo><mn>7<\/mn><mi>x<\/mi><mo>\u2212<\/mo><mn>36<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">y-6 = 7x &#8211; 42 \\Rightarrow y = 7x &#8211; 36<\/annotation><\/semantics><\/math>. Since both equal <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y<\/annotation><\/semantics><\/math>, set them equal: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mn>12<\/mn><mo>=<\/mo><mn>7<\/mn><mi>x<\/mi><mo>\u2212<\/mo><mn>36<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3x + 12 = 7x &#8211; 36<\/annotation><\/semantics><\/math>. Solving gives <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>48<\/mn><mo>=<\/mo><mn>4<\/mn><mi>x<\/mi><mo>\u21d2<\/mo><mi>x<\/mi><mo>=<\/mo><mn>12<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">48 = 4x \\Rightarrow x = 12<\/annotation><\/semantics><\/math>. Substitute back: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mn>3<\/mn><mo stretchy=\"false\">(<\/mo><mn>12<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mn>12<\/mn><mo>=<\/mo><mn>48<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">y = 3(12) + 12 = 48<\/annotation><\/semantics><\/math>.<br>So the present ages are: <strong>father = 48 years, son = 12 years<\/strong>.<br>\u2705 Answer: <strong>D. 48 and 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 40<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>According to the 2025 Financial Tracking Services report by the United Nations Office for the Coordination of Humanitarian Affairs, which two contributors ranked higher than UAE in global humanitarian aid?<\/strong><br><br>A. China and Japan<br>B. India and United Kingdom<br>C. United States and European Union<br>D. Morocco and Denmark<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>C. United States and European Union<\/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>If 30% of <\/strong><math data-latex=\"80 - \\frac{4}{7} \\times \\sqrt[3]{729} \\times \\sqrt{49} = y\"><semantics><mrow><mn>80<\/mn><mo>\u2212<\/mo><mfrac><mn>4<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><mroot><mn>729<\/mn><mn>3<\/mn><\/mroot><mo>\u00d7<\/mo><msqrt><mn>49<\/mn><\/msqrt><mo>=<\/mo><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">80 &#8211; \\frac{4}{7} \\times \\sqrt[3]{729} \\times \\sqrt{49} = y<\/annotation><\/semantics><\/math><strong>, then the value of y is:<\/strong><br><br>A. -7<br>B. -3<br>C. -12<br>D. -8<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Simplify<\/strong><br>30% \u00d7 80 = 24 <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mroot><mn>729<\/mn><mn>3<\/mn><\/mroot><mo>=<\/mo><mn>9<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><msqrt><mn>49<\/mn><\/msqrt><mo>=<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt[3]{729} = 9,\\quad \\sqrt{49}=7<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>4<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>9<\/mn><mo>\u00d7<\/mo><mn>7<\/mn><mo>=<\/mo><mn>36<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{4}{7} \u00d7 9 \u00d7 7 = 36<\/annotation><\/semantics><\/math>y = 24 \u2212 36<br>y = \u221212<br>\u2705 Answer: <strong>C. -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 42<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which ISRO centre will host the newly approved Third Launch Pad by Union cabinet in December 2025?<\/strong><br><br>A. Satish Dhawan Space Centre<br>B. Vikram Sarabhai Space Centre<br>C. Space Applications Centre<br>D. National Remote Sensing Centre<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>A. Satish Dhawan Space Centre<\/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>Based on the alphabetical order, three of the following four are alike in a certain way and thus form a group. Which is the one that does not belong to that group?<br>(Note: The odd man out is not based on the number of consonants\/vowels or their position in the letter cluster.)<\/strong><br><br>A. OTP<br>B. INK<br>C. KPL<br>D. MRN<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pattern:<br><\/strong>Option A: OTP<br>O + 5 = T<br>T &#8211; 4 = P<br><br><strong>Option B: INK<br>I + 5 = N<br>N &#8211; 3 = K<\/strong><br><br>Option C: KPL<br>K + 5 = P<br>P &#8211; 4 = L<br><br>Option D: MRN<br>M + 5 = R<br>R &#8211; 4 = N<br><br>Only Option B is different.<br><strong>\u2705 Answer: B. INK<\/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>Which of the following letter-clusters should replace # and % so that the pattern and relationship followed between the letter-cluster pair on the left side of :: is the same as that on the right side of :: ?<\/strong><br><strong># : MWE :: KUC : %<br><\/strong><br>A. # = BLT % = VFN<br>B. # = BLT % = VCN<br>C. # = KLT % = VFN<br>D. # = BLT % = VFM<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pattern:<\/strong><br>MWE<br>M + 10 = W<br>W + 8 = E<br><br>KUC<br>K + 10 = U<br>U + 8 = C<br>So Option A makes more sense.<br>B L(+10) T (+8)<br>V F (+10) C (+8)<br>\u2705 Answer: <strong>A. # = BLT % = VFN<\/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>A typist takes 40 minutes to type 2 pages. How long (in minutes) will he take to type 91 pages?<\/strong><br><br>A. 1825<br>B. 1810<br>C. 1820<br>D. 1830<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Time Work<\/strong><br>2 pages = 40 min<br>1 page = 40\/2 = 20 min<br>91 pages = 91 x 20 = 1820 min<br>\u2705 Answer: <strong>C. 1820<\/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>Which Himalayan region has greater altitudinal variations?<\/strong><br><br>A. Northern Himalayan region<br>B. Western Himalayan region<br>C. Eastern Himalayan region<br>D. Southern Himalayan region<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>C. Eastern Himalayan region<\/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>If \u2018A\u2019 stands for \u2018\u00f7\u2019, \u2018B\u2019 stands for \u2018\u00d7\u2019, \u2018C\u2019 stands for \u2018+\u2019 and \u2018D\u2019 stands for \u2018\u2212\u2019, then what will come in place of the question mark (?) in the following equation?<br>9 B 4 C 6 D 45 A 5 = ?<\/strong><br><br>A. 34<br>B. 32<br>C. 31<br>D. 33<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Operator Coding<\/strong><br>BODMAS: Must follow Step-by-step &#8220;<strong>B<\/strong>racket <strong>O<\/strong>pen <strong>D<\/strong>ivide <strong>M<\/strong>ultiply <strong>A<\/strong>ddition <strong>S<\/strong>ubtract&#8221; <br>9 \u00d7 4 + 6 \u2212 45 \u00f7 5 <br>= 36 + 6 \u2212 9<br>= 33<br>\u2705 Answer: <strong>D. 33<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 48<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which of the following states ranks number one in the production of natural rubber in India in 2023-24?<br><\/strong><br>A. Karnataka<br>B. Kerala<br>C. Tamil Nadu<br>D. Andhra Pradesh<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>B. Kerala<\/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>18 is related to 59 following a certain logic. Following the same logic, 27 is related to 86. To which of the following is 37 related, following the same logic?<br>(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 \u2013 Operations on 13 such as adding \/subtracting \/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)<\/strong><br><br>A. 101<br>B. 132<br>C. 123<br>D. 116<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Number Logic<\/strong><br>18 \u2192 59<br>(\u00d73 +5)<br>27 \u2192 86 \u2714<br>37 \u2192 37 \u00d7 3 + 5 = 116<br>\u2705 Answer: <strong>D. 116<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 50<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Refer to the following letter, number, symbol series and answer the question.<br>(Left) 5 5 \u00a9 J W 1 L \u00a3 D Z 6 6 C 2 # R 2 C 6 % Y 6 (Right)<br>If all the numbers are dropped from the series, which of the following will be fifth from the left?<\/strong><br><br>A. L<br>B. D<br>C. \u00a3<br>D. W<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Series<\/strong><br>Remove numbers:<br>\u00a9 J W L \u00a3 D Z C # R C % Y<br>5th from left = <strong>\u00a3<\/strong><br>\u2705 Answer: <strong>C. \u00a3<\/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 3 (16 March 2026) \u2013 <strong>Exam Test With Fastest Solutions<\/strong> Hack (Part 3: Question 51-75)<\/h2>\n\n\n\n<p>The section 3 contains questions from 51 to 75 out of 100. Railway Recruitment Board (RRB) conducts the RRB NTPC Exam like 2026 to fill vacancies for Graduate and Undergraduate posts under the Non-Technical Popular Categories (NTPC). Here you will try to attempt the real RRB NTPC Graduate CBT exam, which was conducted on 16 March, 2026 Shift 3. The competitive exam is divided into 4 parts each with 25 questions. You are not just taking the test but also learning from the solutions explanations step-by-step lessons.<\/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 = 23;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-23\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"23\">\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\">Full Explanation of The Competitive Exam Questions &#8211; Answers<\/h2>\n\n\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"Find the length of the ladder if the angle of elevation of the ladder against a wall is 60\u00b0 and the foot of the ladder is 11.5 m away from the wall.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 23m, West and learn the real way to solve.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"In 2025, the 2nd WHO Global Summit on Traditional Medicine officially began on 17 December in which city?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"New Delhi\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Below are given two sets of numbers. In each set of numbers, a certain mathematical operation on the first number results in the second number. Similarly, certain mathematical operations on the second number result in the third number and so on. Which of the given options follows the same set of operations as in question?\n(NOTE \u2013 A two\/three-digit number cannot be broken into individual digits for operations, e.g., if 37 is followed by 10, the operation cannot be 3+7 as a two-digit number cannot be broken into individual digits.)\n180 \u2013 145 \u2013 125 \u2013 100; 145 \u2013 110 \u2013 90 \u2013 65\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 165 \u2013 130 \u2013 110 \u2013 85. Let's learn the trick to solve it in no time.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"According to the Prayaga Prashasti, Samudragupta is compared to which god associated with wealth?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Out of all the options, Kubera is the right one\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Who wrote the introductory essay to Sarojini Naidu\u2019s 1905 poetry collection The Golden Threshold?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Arthur Symons, but how, let's learn.\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"If 45% of $20 - \\frac{4}{6} \\times \\sqrt[3]{729} \\times \\sqrt{36} = y$, then the value of y is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is -27, let's learn how to solve it quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What should come in place of \u2018?\u2019 in the given series?\n33 40 54 75 103 ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 138. Let's learn how to solve it in 3 seconds.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following introduced dyarchy by dividing subjects into Reserved and Transferred lists?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Government of India Act, 1919.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Article _________ describes the procedure for joint sitting of both Houses of the Parliament in certain cases.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Article 108.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language, A + B means \u2018A is the mother of B\u2019 A - B means \u2018A is the brother of B\u2019 A \u00d7 B means \u2018A is the husband of B\u2019 A \u00f7 B means \u2018A is the daughter of B\u2019 Based on the above, how is H related to R if \u2018H - V \u00f7 K \u00d7 T + R'?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Let's learn the simple steps to solve it in no time. The process might seem long but it isn't difficult. Let's learn the trick, the correct answer is Brother.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"P, Q, R, S, Y, and Z live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor, which is numbered 6. Only three people live between Y and Z. Only P lives above Y. R lives on an odd numbered floor. Q lives immediately below Y. Who lives on floor number 2?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"S is the right answer to choose.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following subjects are included in the Union List under the Seventh Schedule of the Indian Constitution?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Defence, foreign affairs, and citizenship.\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusion(s) logically follow(s) from the statements.\nStatements: Some hens are turkeys. Some hens are ostriches. Some turkeys are eagles.\nConclusions: (I) Some hens are eagles. (II) Some turkeys are ostriches.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Neither conclusion (I) nor (II) follows.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Select the triad which follows the same pattern as that followed by the two pairs given below. Both pairs follow the same pattern.\nBALD-BADL-ABLD\nEPIC-EPCI-PEIC\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"There is a simple trick behind it. You must understand the pattern behind it. The correct answer out of all option is HIKE-HIEK-IHKE.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the given letter-number clusters will replace the question mark (?) in the following series to make it logically complete?\nJHF 3 RPN 5 ZXV 8 HFD 12 ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is PNL 17. Let's learn the right trick to solve it quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What was the primary objective of the 'Blue Skies 2025' campaign launched in August 2025?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Reduce urban air pollution. We have explained it simply for you.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Refer to the following number and symbol series and answer the question that follows. All numbers are single-digit numbers only.\n(Left) 6 8 @ ! 4 5 ^ 5 * 9 & 4 $ # 3 @ 1 + ? 8 (Right)\nIf all the symbols are dropped from the series, which of the following will be seventh from the right?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is a simple mathematics question, you must be fast enough to solve it or you know it.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The census in India is conducted once in ten years under the legal authority of the Census Act ____________.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"1948.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If $(a + \\frac{1}{a}) = 4$, then what is the value of $(a^5 + \\frac{1}{a^5})$?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is a simple mathematics question, you must be fast enough to solve it or you know it.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following is NOT regarded as an advantage of the LPG reforms in India?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Rise in trade restrictions.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language, \u2018APES\u2019 is coded as \u20184583\u2019 and \u2018PEAT\u2019 is coded as \u20186438\u2019. What is the code for \u2018S\u2019 in that language?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"5\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If 4 : 28 :: 4.1 : x and 4 : 32 :: 3 : y, then what is the ratio of x to y?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"A simple mathematics question, but there is a simple trick behind it to solve it within three seconds. The correct answer is 287 : 240.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Madhu and Madhuri start a business by investing in the ratio 31 : 34. If total profit is \u20b944,850, then what is the difference between the shares of profit (in \u20b9) of Madhu and Madhuri?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is \u20b92,070.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following continents is NOT crossed by the Equator?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Europe\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language, \u2018TIER\u2019 is coded as \u20182735\u2019 and \u2018TIME\u2019 is coded as \u20183475\u2019. What is the code for \u2018M\u2019 in the given code language?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"A simple mathematics question, but there is a simple trick behind it to solve it within three seconds. The correct answer is 4.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"AB is the diameter of a circle P. C and D are two points on the circle on either side of AB, such that $\\angle{CAB} = 48^\\circ$ and $\\angle{ABD} = 55^\\circ$. What is the difference between the measures of $\\angle{CBD}$ and $\\angle{CAD}$?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"A simple mathematics question, but there is a simple trick behind it to solve it within three seconds. The correct answer is 14.\"\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>Find the length of the ladder if the angle of elevation of the ladder against a wall is 60\u00b0 and the foot of the ladder is 11.5 m away from the wall.<br><\/strong><br>A. 23 m<br>B. <math data-latex=\"\\frac{23\\sqrt{3}}{2}\\ m\"><semantics><mrow><mfrac><mrow><mn>23<\/mn><msqrt><mn>3<\/mn><\/msqrt><\/mrow><mn>2<\/mn><\/mfrac><mtext>&nbsp;<\/mtext><mi>m<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{23\\sqrt{3}}{2}\\ m<\/annotation><\/semantics><\/math><br>C. <math data-latex=\"\\sqrt{3}\\ cm\"><semantics><mrow><msqrt><mn>3<\/mn><\/msqrt><mtext>&nbsp;<\/mtext><mi>c<\/mi><mi>m<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{3}\\ cm<\/annotation><\/semantics><\/math><br>D. 11.5 m<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Ladder Length (Trigonometry)<\/strong><br>Right triangle situation:<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>cos<\/mi><mo>\u2061<\/mo><mi>\u03b8<\/mi><mo>=<\/mo><mfrac><mtext>base<\/mtext><mtext>hypotenuse<\/mtext><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\cos\\theta = \\frac{\\text{base}}{\\text{hypotenuse}}<\/annotation><\/semantics><\/math><br><br>Given:<br>Angle = 60\u00b0<br>Base = 11.5 m<br>Hypotenuse = Ladder length (L)<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>cos<\/mi><mo>\u2061<\/mo><mn>60<\/mn><mi mathvariant=\"normal\">\u00b0<\/mi><mo>=<\/mo><mfrac><mn>11.5<\/mn><mi>L<\/mi><\/mfrac><mo>\u21d2<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>11.5<\/mn><mi>L<\/mi><\/mfrac><mo>\u21d2<\/mo><mi>L<\/mi><mo>=<\/mo><mn>23<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\cos 60\u00b0 = \\frac{11.5}{L} \\Rightarrow \\frac{1}{2} = \\frac{11.5}{L} \\Rightarrow L = 23<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>A. 23 m<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong><br>If angle = 60\u00b0, directly use \u2192 hypotenuse = 2 \u00d7 base<\/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 2025, the 2nd WHO Global Summit on Traditional Medicine officially began on 17 December in which city?<\/strong><br><br>A. Beijing<br>B. New Delhi<br>C. Bangkok<br>D. Geneva<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: B. New Delhi<\/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>Below are given two sets of numbers. In each set of numbers, a certain mathematical operation on the first number results in the second number. Similarly, certain mathematical operations on the second number result in the third number and so on. Which of the given options follows the same set of operations as in question?<br>(NOTE \u2013 A two\/three-digit number cannot be broken into individual digits for operations, e.g., if 37 is followed by 10, the operation cannot be 3+7 as a two-digit number cannot be broken into individual digits.)<br>180 \u2013 145 \u2013 125 \u2013 100; 145 \u2013 110 \u2013 90 \u2013 65<\/strong><br><br>A. 165 \u2013 130 \u2013 110 \u2013 85<br>B. 115 \u2013 80 \u2013 60 \u2013 45<br>C. 155 \u2013 130 \u2013 110 \u2013 75<br>D. 130 \u2013 95 \u2013 70 \u2013 50<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Number Pattern<\/strong><br>Check pattern:<br>Set 1:<br>180 \u2192 145 \u2192 125 \u2192 100<br>-35, -20, -25<br><br>Set 2:<br>145 \u2192 110 \u2192 90 \u2192 65<br>-35, -20, -25<br><br>\ud83d\udc49 Same pattern: <strong>\u221235, \u221220, \u221225<\/strong><br>Check options:<br>A: 165 \u2192 130 \u2192 110 \u2192 85<br>-35, -20, -25 \u2714<br>\u2705 Answer: <strong>A<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Differences repeat, not numbers.<\/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>According to the Prayaga Prashasti, Samudragupta is compared to which god associated with wealth?<br><\/strong><br>A. Indra<br>B. Varuna<br>C. Yama<br>D. Kubera<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>D. Kubera<\/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 wrote the introductory essay to Sarojini Naidu\u2019s 1905 poetry collection The Golden Threshold?<\/strong><br><br>A. Rabindranath Tagore<br>B. W. B. Yeats<br>C. Arthur Symons<br>D. Edmond Gosse<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: C. Arthur Symons<\/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>If 45% of <\/strong><math data-latex=\"20 - \\frac{4}{6} \\times \\sqrt[3]{729} \\times \\sqrt{36} = y\"><semantics><mrow><mn>20<\/mn><mo>\u2212<\/mo><mfrac><mn>4<\/mn><mn>6<\/mn><\/mfrac><mo>\u00d7<\/mo><mroot><mn>729<\/mn><mn>3<\/mn><\/mroot><mo>\u00d7<\/mo><msqrt><mn>36<\/mn><\/msqrt><mo>=<\/mo><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">20 &#8211; \\frac{4}{6} \\times \\sqrt[3]{729} \\times \\sqrt{36} = y<\/annotation><\/semantics><\/math><strong>, then the value of y is:<\/strong><br><strong><br><\/strong>A. -27<br>B. -35<br>C. -30<br>D. -21<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Simplification<\/strong><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>45<\/mn><mi mathvariant=\"normal\">%<\/mi><mo>\u00d7<\/mo><mn>20<\/mn><mo>=<\/mo><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">45\\% \u00d7 20 = 9<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mroot><mn>729<\/mn><mn>3<\/mn><\/mroot><mo>=<\/mo><mn>9<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"1em\"><\/mspace><msqrt><mn>36<\/mn><\/msqrt><mo>=<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt[3]{729}=9,\\quad \\sqrt{36}=6<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>4<\/mn><mn>6<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>9<\/mn><mo>\u00d7<\/mo><mn>6<\/mn><mo>=<\/mo><mn>36<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{4}{6} \u00d7 9 \u00d7 6 = 36<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>y<\/mi><mo>=<\/mo><mn>9<\/mn><mo>\u2212<\/mo><mn>36<\/mn><mo>=<\/mo><mo>\u2212<\/mo><mn>27<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">y = 9 &#8211; 36 = -27<\/annotation><\/semantics><\/math>\u2705 Answer: <strong>A. -27<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Always solve roots first.<\/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>What should come in place of \u2018?\u2019 in the given series?<br>33 40 54 75 103 ?<\/strong><br><br>A. 142<br>B. 140<br>C. 138<br>D. 145<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Series<\/strong><br>33, 40, 54, 75, 103, ?<br>Differences:<br>+7, +14, +21, +28 \u2192 next +35<br>103 + 35 = 138<br><strong>\u2705 Answer: C. 138<\/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>Article <strong><em>_<\/em><\/strong> describes the procedure for joint sitting of both Houses of the Parliament in certain cases.<br><\/strong><br>A. Article 94<br>B. Article 104<br>C. Article 115<br>D. Article 108<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: D. Article 108<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 59<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In a certain code language, A + B means \u2018A is the mother of B\u2019 A &#8211; B means \u2018A is the brother of B\u2019 A \u00d7 B means \u2018A is the husband of B\u2019 A \u00f7 B means \u2018A is the daughter of B\u2019 Based on the above, how is H related to R if \u2018H &#8211; V \u00f7 K \u00d7 T + R&#8217;?<\/strong><br><br>A. Sister\u2019s son<br>B. Brother<br>C. Father\u2019s brother<br>D. Mother\u2019s brother<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Relation Coding<\/strong><br>Expression:<br>H &#8211; V \u00f7 K \u00d7 T + R<br><br>Decode:<br>H is brother of V<br>V is daughter of K<br>K is husband of T<br>T is mother of R<br>So:<br>K\u2013T = parents of R<br>V = their daughter<br>H = brother of V \u2192 son of K-T<br>So H = brother of R<br>\u2705 Answer: <strong>B. Brother<\/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>P, Q, R, S, Y, and Z live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor, which is numbered 6. Only three people live between Y and Z. Only P lives above Y. R lives on an odd numbered floor. Q lives immediately below Y. Who lives on floor number 2?<\/strong><br><br>A. S<br>B. Y<br>C. P<br>D. Q<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Floor Puzzle<\/strong><br>Key clues:<br>Y &amp; Z \u2192 3 people between \u2192 positions (1,5) or (2,6)<br>Only P above Y<br>Q below Y<br><br>Try:<br>Y = 5 \u2192 Z = 1<br>Q = 4<br>P = 6<br>Remaining: R, S<br>R odd \u2192 3<br>S \u2192 2<br>Floor 2 = S<br><strong>\u2705 Answer: A. S<br><\/strong>\ud83d\udc49 Trick: Always fix biggest constraint first.<\/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 of the following subjects are included in the Union List under the Seventh Schedule of the Indian Constitution?<\/strong><br><br>A. Local government, markets, and fairs<br>B. Police, public health, and agriculture<br>C. Education, forests, and marriage<br>D. Defence, foreign affairs, and citizenship<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: D. Defence, foreign affairs, citizenship<\/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>Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusion(s) logically follow(s) from the statements.<br>Statements: Some hens are turkeys. Some hens are ostriches. Some turkeys are eagles.<br>Conclusions: (I) Some hens are eagles. (II) Some turkeys are ostriches.<\/strong><br><br>A. Only conclusion (I) follows.<br>B. Only conclusion (II) follows.<br>C. Both conclusions (I) and (II) follow.<br>D. Neither conclusion (I) nor (II) follows<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Syllogism<\/strong><br>Statements:<br>Hens\u2013Turkeys<br>Hens\u2013Ostriches<br>Turkeys\u2013Eagles<br>No direct link \u2192 hens &amp; eagles \u274c<br>No link \u2192 turkeys &amp; ostriches \u274c<br><strong>\u2705 Answer: D. Neither follows<br><\/strong>\ud83d\udc49 Trick: No direct connection \u2192 no conclusion.<\/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>Select the triad which follows the same pattern as that followed by the two pairs given below. Both pairs follow the same pattern.<br>BALD-BADL-ABLD<br>EPIC-EPCI-PEIC<\/strong><br><br>A. PART-RTPA-APTR<br>B. FIRE-IREF-FRIE<br>C. HIKE-HIEK-IHKE<br>D. COME-COEM-OEMC<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Letter Pattern<\/strong><br>BALD \u2192 BADL \u2192 ABLD<br>EPIC \u2192 EPCI \u2192 PEIC<br>Pattern:<br>Swap last two \u2192 then first two<br>Check options:<br>HIKE \u2192 HIEK \u2192 IHKE \u2714<br>\u2705 Answer: <strong>C. HIKE-HIEK-IHKE<\/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>Which of the given letter-number clusters will replace the question mark (?) in the following series to make it logically complete?<br>JHF 3 RPN 5 ZXV 8 HFD 12 ?<\/strong><br><br>A. BJP 15<br>B. SYV 17<br>C. KDU 19<br>D. PNL 17<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Series<\/strong><br>Letters shift +8 each time:<br>J \u2192 R \u2192 Z \u2192 H \u2192 P<br>Similarly:<br>F \u2192 N \u2192 V \u2192 D \u2192 L<br>Numbers:<br>3,5,8,12 \u2192 +2,+3,+4 \u2192 next +5 \u2192 17<br>\u2705 Answer: <strong>D. PNL 17<\/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>What was the primary objective of the &#8216;Blue Skies 2025&#8217; campaign launched in August 2025?<\/strong><br><br>A. Conserve wetlands<br>B. Reduce urban air pollution<br>C. Promote solar energy<br>D. Increase forest cover<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>B. Reduce urban air pollution<\/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>Refer to the following number and symbol series and answer the question that follows. All numbers are single-digit numbers only.<br>(Left) 6 8 @ ! 4 5 ^ 5 * 9 &amp; 4 $ # 3 @ 1 + ? 8 (Right)<br>If all the symbols are dropped from the series, which of the following will be seventh from the right?<\/strong><br><br>A. 5<br>B. 9<br>C. 1<br>D. 6<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Series<\/strong><br>Remove symbols:<br>6 8 4 5 5 9 4 3 1 8<br>7th from right:<br>Count \u2192 5<br><strong>\u2705 Answer: A. 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 67<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The census in India is conducted once in ten years under the legal authority of the Census Act <strong><em><strong>__<\/strong><\/em><\/strong>.<\/strong><br><br>A. 1872<br>B. 1947<br>C. 1948<br>D. 2010<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: C. 1948<\/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>If <\/strong><math data-latex=\"(a + \\frac{1}{a}) = 4\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mfrac><mn>1<\/mn><mi>a<\/mi><\/mfrac><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(a + \\frac{1}{a}) = 4<\/annotation><\/semantics><\/math><strong>, then what is the value of <\/strong><math data-latex=\"(a^5 + \\frac{1}{a^5})\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msup><mi>a<\/mi><mn>5<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>5<\/mn><\/msup><\/mfrac><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(a^5 + \\frac{1}{a^5})<\/annotation><\/semantics><\/math> <strong>?<\/strong><br><br>A. 724<br>B. 709<br>C. 776<br>D. 770<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>You are given:<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>a<\/mi><mo>+<\/mo><mfrac><mn>1<\/mn><mi>a<\/mi><\/mfrac><mo>=<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">a + \\frac{1}{a} = 4<\/annotation><\/semantics><\/math><br>The <strong>core idea<\/strong> in these questions is:<br>\ud83d\udc49 You cannot jump to <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>a<\/mi><mn>5<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>5<\/mn><\/msup><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">a^5 + \\frac{1}{a^5}<\/annotation><\/semantics><\/math>\u200b directly<br>\ud83d\udc49 You <strong>build step by step<\/strong> using identities<br><br>First important identity:<br><math data-latex=\"(a + b)^2 = a^2 + b^2 + 2ab \\\\ a^2 +\\frac{1}{a^2} + 2\\times a \\times \\frac{1}{a} \\\\ a^2 +\\frac{1}{a^2} + 2\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>b<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>2<\/mn><mi>a<\/mi><mi>b<\/mi><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mi>a<\/mi><mo>\u00d7<\/mo><mfrac><mn>1<\/mn><mi>a<\/mi><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>2<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">(a + b)^2 = a^2 + b^2 + 2ab \\\\ a^2 +\\frac{1}{a^2} + 2\\times a \\times \\frac{1}{a} \\\\ a^2 +\\frac{1}{a^2} + 2<\/annotation><\/semantics><\/math><br>Now apply it:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mn>4<\/mn><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">4^2 = a^2 + \\frac{1}{a^2} + 2<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>16<\/mn><mo>=<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>2<\/mn><mo>\u21d2<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>=<\/mo><mn>14<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">16 = a^2 + \\frac{1}{a^2} + 2 \\Rightarrow a^2 + \\frac{1}{a^2} = 14<\/annotation><\/semantics><\/math><br>Now next concept:<br>To move from power 2 \u2192 power 3, use:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mfrac><mn>1<\/mn><mi>a<\/mi><\/mfrac><\/mstyle><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><\/mstyle><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><msup><mi>a<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>3<\/mn><\/msup><\/mfrac><\/mstyle><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mfrac><mn>1<\/mn><mi>a<\/mi><\/mfrac><\/mstyle><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(a + \\tfrac{1}{a})(a^2 + \\tfrac{1}{a^2}) = a^3 + \\tfrac{1}{a^3} + (a + \\tfrac{1}{a})<\/annotation><\/semantics><\/math><br>\ud83d\udc49 WHY this works:<br>Because multiplication combines powers:<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><mo>\u00d7<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mi>a<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">a \u00d7 a^2 = a^3<\/annotation><\/semantics><\/math><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mfrac><mn>1<\/mn><mi>a<\/mi><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>3<\/mn><\/msup><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{a} \u00d7 \\frac{1}{a^2} = \\frac{1}{a^3}<\/annotation><\/semantics><\/math><br>middle terms give back <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><mo>+<\/mo><mfrac><mn>1<\/mn><mi>a<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">a + \\frac{1}{a}<\/annotation><\/semantics><\/math> and it is equal to 4.<br>Now apply:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>4<\/mn><mo>\u00d7<\/mo><mn>14<\/mn><mo>=<\/mo><msup><mi>a<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>3<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">4 \u00d7 14 = a^3 + \\frac{1}{a^3} + 4<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>56<\/mn><mo>=<\/mo><msup><mi>a<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>3<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>4<\/mn><mo>\u21d2<\/mo><msup><mi>a<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>3<\/mn><\/msup><\/mfrac><mo>=<\/mo><mn>52<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">56 = a^3 + \\frac{1}{a^3} + 4 \\Rightarrow a^3 + \\frac{1}{a^3} = 52<\/annotation><\/semantics><\/math><br>Now same concept again for power 5:<br>But good news is that, we have already done power 2 and 3. For right side, we input the result of 2 + 3.<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><\/mstyle><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><msup><mi>a<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>3<\/mn><\/msup><\/mfrac><\/mstyle><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><msup><mi>a<\/mi><mn>5<\/mn><\/msup><mo>+<\/mo><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>5<\/mn><\/msup><\/mfrac><\/mstyle><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mfrac><mn>1<\/mn><mi>a<\/mi><\/mfrac><\/mstyle><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(a^2 + \\tfrac{1}{a^2})(a^3 + \\tfrac{1}{a^3}) = a^5 + \\tfrac{1}{a^5} + (a + \\tfrac{1}{a})<\/annotation><\/semantics><\/math><br>Apply values:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>14<\/mn><mo>\u00d7<\/mo><mn>52<\/mn><mo>=<\/mo><msup><mi>a<\/mi><mn>5<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>5<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">14 \u00d7 52 = a^5 + \\frac{1}{a^5} + 4<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>728<\/mn><mo>=<\/mo><msup><mi>a<\/mi><mn>5<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>5<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">728 = a^5 + \\frac{1}{a^5} + 4<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mi>a<\/mi><mn>5<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>5<\/mn><\/msup><\/mfrac><mo>=<\/mo><mn>724<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">a^5 + \\frac{1}{a^5} = 724<\/annotation><\/semantics><\/math><strong>\u2705 Answer: A. 724<\/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>Which of the following is NOT regarded as an advantage of the LPG reforms in India?<\/strong><br><br>A. Expansion of the private sector<br>B. Rise in trade restrictions<br>C. Adoption of advanced technologies<br>D. Boost in international partnerships<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>B. Rise in trade restrictions<\/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>In a certain code language, \u2018APES\u2019 is coded as \u20184583\u2019 and \u2018PEAT\u2019 is coded as \u20186438\u2019. What is the code for \u2018S\u2019 in that language?<\/strong><br><br>A. 4<br>B. 5<br>C. 8<br>D. 6<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pattern<\/strong><br><strong>APE<\/strong>S = <strong>4<\/strong>5<strong>83<\/strong><br><strong>PEA<\/strong>T = 6<strong>438<\/strong><br>Do you see the similarities? It is clear that the position don&#8217;t matter. So S = 5 and T = 6.<br><strong>\ud83c\udfaf FINAL ANSWER: B. 5\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>If 4 : 28 :: 4.1 : x and 4 : 32 :: 3 : y, then what is the ratio of x to y?<\/strong><br><br>A. 287 : 240<br>B. 285 : 241<br>C. 288 : 238<br>D. 291 : 250<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Ratio<\/strong><br>Pattern:<br>4 \u2192 28 = \u00d77<br>4.1 \u2192 4.1\u00d77 = 28.7 \u2192 x<br>4 \u2192 32 = \u00d78<br>3 \u2192 3\u00d78 = 24 = y<br>x:y = 28.7:24 = 287:240<br><strong>\u2705 Answer: A. 287 : 240<\/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>Madhu and Madhuri start a business by investing in the ratio 31 : 34. If total profit is \u20b944,850, then what is the difference between the shares of profit (in \u20b9) of Madhu and Madhuri?<br><\/strong><br>A. \u20b93,570<br>B. \u20b91,570<br>C. \u20b9570<br>D. \u20b92,070<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Profit Sharing<\/strong><br>Ratio = 31:34<br>Difference = 3 parts<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>3<\/mn><mn>65<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>44850<\/mn><mo>=<\/mo><mn>2070<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{3}{65} \u00d7 44850 = 2070<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>D. \u20b92070<\/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 of the following continents is NOT crossed by the Equator?<\/strong><br><br>A. Europe<br>B. Asia<br>C. Africa<br>D. South America<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: A. Europe<\/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>AB is the diameter of a circle P. C and D are two points on the circle on either side of AB, such that <\/strong><math data-latex=\"\\angle{CAB} = 48^\\circ\"><semantics><mrow><mi>\u2220<\/mi><mrow><mi>C<\/mi><mi>A<\/mi><mi>B<\/mi><\/mrow><mo>=<\/mo><msup><mn>48<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\angle{CAB} = 48^\\circ<\/annotation><\/semantics><\/math><strong> and <\/strong><math data-latex=\"\\angle{ABD} = 55^\\circ\"><semantics><mrow><mi>\u2220<\/mi><mrow><mi>A<\/mi><mi>B<\/mi><mi>D<\/mi><\/mrow><mo>=<\/mo><msup><mn>55<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\angle{ABD} = 55^\\circ<\/annotation><\/semantics><\/math><strong>. What is the difference between the measures of <\/strong><math data-latex=\"\\angle{CBD}\"><semantics><mrow><mi>\u2220<\/mi><mrow><mi>C<\/mi><mi>B<\/mi><mi>D<\/mi><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\angle{CBD}<\/annotation><\/semantics><\/math><strong> and <\/strong><math data-latex=\"\\angle{CAD}\"><semantics><mrow><mi>\u2220<\/mi><mrow><mi>C<\/mi><mi>A<\/mi><mi>D<\/mi><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\">\\angle{CAD}<\/annotation><\/semantics><\/math><strong>?<\/strong><br><br>A. <math data-latex=\"14^\\circ\"><semantics><msup><mn>14<\/mn><mo>\u2218<\/mo><\/msup><annotation encoding=\"application\/x-tex\">14^\\circ<\/annotation><\/semantics><\/math><br>B. <math data-latex=\"11^\\circ\"><semantics><msup><mn>11<\/mn><mo>\u2218<\/mo><\/msup><annotation encoding=\"application\/x-tex\">11^\\circ<\/annotation><\/semantics><\/math><br>C. <math data-latex=\"18^\\circ\"><semantics><msup><mn>18<\/mn><mo>\u2218<\/mo><\/msup><annotation encoding=\"application\/x-tex\">18^\\circ<\/annotation><\/semantics><\/math><br>D. <math data-latex=\"8^\\circ\"><semantics><msup><mn>8<\/mn><mo>\u2218<\/mo><\/msup><annotation encoding=\"application\/x-tex\">8^\\circ<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"is-style-success\">Think in terms of <strong>circle angle properties<\/strong>, not raw calculation.<br>Since <strong>AB is a diameter<\/strong>, any angle subtended by AB at the circle is a right angle. So:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">\u2220<\/mi><mi>A<\/mi><mi>C<\/mi><mi>B<\/mi><mo>=<\/mo><msup><mn>90<\/mn><mo>\u2218<\/mo><\/msup><mspace width=\"1em\"><\/mspace><mtext>and<\/mtext><mspace width=\"1em\"><\/mspace><mi mathvariant=\"normal\">\u2220<\/mi><mi>A<\/mi><mi>D<\/mi><mi>B<\/mi><mo>=<\/mo><msup><mn>90<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\angle ACB = 90^\\circ \\quad \\text{and} \\quad \\angle ADB = 90^\\circ<\/annotation><\/semantics><\/math><br>Now use triangle angle sum.<br>In triangle <strong>ABC<\/strong>:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">\u2220<\/mi><mi>C<\/mi><mi>A<\/mi><mi>B<\/mi><mo>+<\/mo><mi mathvariant=\"normal\">\u2220<\/mi><mi>C<\/mi><mi>B<\/mi><mi>A<\/mi><mo>+<\/mo><mi mathvariant=\"normal\">\u2220<\/mi><mi>A<\/mi><mi>C<\/mi><mi>B<\/mi><mo>=<\/mo><msup><mn>180<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\angle CAB + \\angle CBA + \\angle ACB = 180^\\circ<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mn>48<\/mn><mo>\u2218<\/mo><\/msup><mo>+<\/mo><mi mathvariant=\"normal\">\u2220<\/mi><mi>C<\/mi><mi>B<\/mi><mi>A<\/mi><mo>+<\/mo><msup><mn>90<\/mn><mo>\u2218<\/mo><\/msup><mo>=<\/mo><msup><mn>180<\/mn><mo>\u2218<\/mo><\/msup><mo>\u21d2<\/mo><mi mathvariant=\"normal\">\u2220<\/mi><mi>C<\/mi><mi>B<\/mi><mi>A<\/mi><mo>=<\/mo><msup><mn>42<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">48^\\circ + \\angle CBA + 90^\\circ = 180^\\circ \\Rightarrow \\angle CBA = 42^\\circ<\/annotation><\/semantics><\/math>So:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">\u2220<\/mi><mi>C<\/mi><mi>B<\/mi><mi>D<\/mi><mo>=<\/mo><mi mathvariant=\"normal\">\u2220<\/mi><mi>C<\/mi><mi>B<\/mi><mi>A<\/mi><mo>+<\/mo><mi mathvariant=\"normal\">\u2220<\/mi><mi>A<\/mi><mi>B<\/mi><mi>D<\/mi><mo>=<\/mo><msup><mn>42<\/mn><mo>\u2218<\/mo><\/msup><mo>+<\/mo><msup><mn>55<\/mn><mo>\u2218<\/mo><\/msup><mo>=<\/mo><msup><mn>97<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\angle CBD = \\angle CBA + \\angle ABD = 42^\\circ + 55^\\circ = 97^\\circ<\/annotation><\/semantics><\/math><br>Now triangle <strong>ABD<\/strong>:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">\u2220<\/mi><mi>A<\/mi><mi>B<\/mi><mi>D<\/mi><mo>+<\/mo><mi mathvariant=\"normal\">\u2220<\/mi><mi>B<\/mi><mi>A<\/mi><mi>D<\/mi><mo>+<\/mo><mi mathvariant=\"normal\">\u2220<\/mi><mi>A<\/mi><mi>D<\/mi><mi>B<\/mi><mo>=<\/mo><msup><mn>180<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\angle ABD + \\angle BAD + \\angle ADB = 180^\\circ<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mn>55<\/mn><mo>\u2218<\/mo><\/msup><mo>+<\/mo><mi mathvariant=\"normal\">\u2220<\/mi><mi>B<\/mi><mi>A<\/mi><mi>D<\/mi><mo>+<\/mo><msup><mn>90<\/mn><mo>\u2218<\/mo><\/msup><mo>=<\/mo><msup><mn>180<\/mn><mo>\u2218<\/mo><\/msup><mo>\u21d2<\/mo><mi mathvariant=\"normal\">\u2220<\/mi><mi>B<\/mi><mi>A<\/mi><mi>D<\/mi><mo>=<\/mo><msup><mn>35<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">55^\\circ + \\angle BAD + 90^\\circ = 180^\\circ \\Rightarrow \\angle BAD = 35^\\circ<\/annotation><\/semantics><\/math><br>Now:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">\u2220<\/mi><mi>C<\/mi><mi>A<\/mi><mi>D<\/mi><mo>=<\/mo><mi mathvariant=\"normal\">\u2220<\/mi><mi>C<\/mi><mi>A<\/mi><mi>B<\/mi><mo>+<\/mo><mi mathvariant=\"normal\">\u2220<\/mi><mi>B<\/mi><mi>A<\/mi><mi>D<\/mi><mo>=<\/mo><msup><mn>48<\/mn><mo>\u2218<\/mo><\/msup><mo>+<\/mo><msup><mn>35<\/mn><mo>\u2218<\/mo><\/msup><mo>=<\/mo><msup><mn>83<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\angle CAD = \\angle CAB + \\angle BAD = 48^\\circ + 35^\\circ = 83^\\circ<\/annotation><\/semantics><\/math><br>Finally, difference:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">\u2220<\/mi><mi>C<\/mi><mi>B<\/mi><mi>D<\/mi><mo>\u2212<\/mo><mi mathvariant=\"normal\">\u2220<\/mi><mi>C<\/mi><mi>A<\/mi><mi>D<\/mi><mo>=<\/mo><msup><mn>97<\/mn><mo>\u2218<\/mo><\/msup><mo>\u2212<\/mo><msup><mn>83<\/mn><mo>\u2218<\/mo><\/msup><mo>=<\/mo><msup><mn>14<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\angle CBD &#8211; \\angle CAD = 97^\\circ &#8211; 83^\\circ = 14^\\circ<\/annotation><\/semantics><\/math>\u2705 Answer: <strong>A. 14<sup>\u2218<\/sup><\/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>In a certain code language, \u2018TIER\u2019 is coded as \u20182735\u2019 and \u2018TIME\u2019 is coded as \u20183475\u2019. What is the code for \u2018M\u2019 in the given code language?<\/strong><br><br>A. 5<br>B. 7<br>C. 4<br>D. 3<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pattern<\/strong><br><strong>TIE<\/strong>R = 2<strong>735<\/strong><br><strong>TI<\/strong>M<strong>E<\/strong> = <strong>3<\/strong>4<strong>75<\/strong><br>Do you see the similarities? It is clear that the position don&#8217;t matter. So R = 2 and M = 4.<br><strong>\ud83c\udfaf FINAL ANSWER: C. 4\u200b<\/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 3 (16 March 2026) \u2013 <strong>A Complete Quiz With Smart Hack And Answers<\/strong> (Part 4: Question 76-100)<\/h2>\n\n\n\n<p>The final part contains questions from 76 to 100 out of 100. Railway Recruitment Board (RRB) conducts the RRB NTPC Exam like 2026 to fill vacancies for Graduate and Undergraduate posts under the Non-Technical Popular Categories (NTPC). Here you will try to attempt the real RRB NTPC Graduate CBT exam, which was conducted on 16 March, 2026 Shift 3. The competitive exam is divided into 4 parts each with 25 questions. The last part also like all other pats gives proper solutions of answers and their tricks to solve them in a few seconds.<\/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 = 24;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-24\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"24\">\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\">Question and Answer and Solutions&#8217; Explanation of the Competitive Exam Test<\/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\": \"100 men have provisions for 27 days. If 55 men have left, for how many days the same provisions would last for the remaining men?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 60, let's learn the simple trick to solve it quickly.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Preparation of report cards, maintaining student records, and creating question papers are actions that are mainly related to which area of computer application?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Education administration.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The price of each article of type P, Q, and R is \u20b9280, \u20b9180 and \u20b9115, respectively. Tejas buys articles of each type in the ratio 4 : 2 : 5 for \u20b96,165. How many articles of type Q did he purchase?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 6. the pattern behind it simple.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.\nStatements: All gardens are forests. All forests are meadows. No garden is a park.\nConclusions: (I) No forest is a park. (II) No meadow is a park.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick behind it very simple. It makes the question solution very easy to solve. The correct answer is Neither conclusion (I) nor (II) follows.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"X, Y, Z, S, T and U live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2 and so on till the topmost floor is numbered 6. S lives on floor number 5. X lives on a floor above S. Only U lives below Y. Z lives on an even numbered floor. How many people live below Z?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Three. let's learn how to do it within 5 second.\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"Which policy trade-off limited balanced sectoral growth in India during 1951\u20131991?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The answer is Agriculture vs. industry, but how can you solve it quickly. Learn it.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Find the mode of the following frequency distribution. (Round off the answer to two\ndecimal places.)\n$$ \\begin{array}{|c|c|} \\hline \\textbf{Class} & \\textbf{Frequency} \\\\ \\hline {0-10} & {5} \\\\ \\hline {10-20} & {8} \\\\ \\hline {20-30} & {12} \\\\ \\hline {30-40} & {20} \\\\ \\hline {40-50} & {10} \\\\ \\hline \\end{array} $$\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is to understand the key concepts hidden behind it, the correct answer is 34.44.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What should come in place of \u2018?\u2019 in the given series?\n45 65 81 93 101 ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 105. Learn how to calculate it in no time.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Refer to the following letter, number, symbol series and answer the question. (All numbers are single digit numbers only.)\n(Left) R % C * E 3 K 6 $ 7 D @ 2 T Y # 4 5 G & S (Right)\nIf all the letters are dropped from the series, which of the following will be fourth from the right?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The pattern based question with simple trick to unlock and decipher it. How, learn the steps of it.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A woman travelled at a speed of 20 m\/min for 90 min, and at a speed of 55 m\/min for 60 min. Her average speed (in m\/min) for the entire journey is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The pattern based question with simple trick to unlock and decipher it. How, learn the steps of it.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which characteristic of a computer system enables it to perform extremely complex calculations within seconds?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Speed\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who among the following is known for his collaboration with international artists and is\/was a renowned tabla maestro?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Zakir Hussain\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In 2025, the Supreme Court of India (SC) in the case State of Tamil Nadu v. Governor of Tamil Nadu ruled that a State Governor cannot exercise which of the following over a bill duly passed by the State Legislature?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Pocket Veto.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Three friends travel along three consecutive segments: from P to Q, Q to R, and R to S. Their speeds on these segments are 48 km\/h, 72 km\/h, and 96 km\/h, respectively. The distances of the three segments are in the ratio 2 : 3 : 1, and the total distance from P to S is 480 km. Calculate the average speed for the entire journey.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Let's solve it with a trick to simplify then unlock the pattern behind it. The correct answer is 64 km\/h.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"52 is related to 144 following a certain logic. Following the same logic, 81 is related to 173. To which of the following is 63 related, following the same logic?\n(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 \u2013 Operations on 13 such as adding\/ subtracting \/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Let's solve it with a trick to simplify then unlock the pattern behind it. The correct answer is 155.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The total surface area of a solid cube each side of which is 84 cm long is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Let's solve it with a trick to simplify then unlock the pattern behind it. The correct answer is 42336.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Seven people B, C, O, P, Q, R and S are sitting around a circular table facing the center of the table. B sits second to the right of S. Q sits third to the left of S. Only two people sit between P and R when counted from the right of R. C is an immediate neighbor of P. Who sits to the immediate left and right of O, respectively?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The visual image question. It will be most easy and quick if you picture it in your mind. Learn how to do it. The correct answer is S and B.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"At what rate per annum will a sum of money become five times itself in 5 years under simple interest?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It looks difficult but if you understand the simplification trick behind it, it will become very easy. The correct answer is 80%.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In December 2025, the Punjab government directed strict enforcement of which policy to safeguard schoolchildren during dense winter fog (mandatory visibility measures, reduced speed, reflectors, headlights and fog lights)?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Safe School Vehicle Policy\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Shan has \u20b91407 with him. He divides this amount between his two sons, Piyush and Manoj, and asks them to invest their respective shares at a compound interest rate of 10% per annum, compounded annually. It is observed that Piyush\u2019s investment amounts to the same value after 18 years as Manoj\u2019s investment does after 19 years. How much (in \u20b9) did Shan give to Manoj?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is not position but the pattern value. The correct answer is 670.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In an election between two candidates, 80% of the registered voters cast their vote and 10% of the votes polled were found invalid. Winning candidate got 89% of the valid votes and won the election by a margin of 351 votes. How many voters were registered?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is not position but the pattern value. The correct answer is 625.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Each of the digits in the number 52697148 is arranged in descending order from left to right. What will be the product of the digits which are third from the left and second from the right in the number thus formed?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is not position but the pattern value. The correct answer is 14.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language,\nE + F means \u2018E is the brother of F\u2019,\nE \u2013 F means \u2018E is the father of F\u2019,\nE x F means \u2018E is the husband of F\u2019\nand E \u00f7 F means \u2018E is the mother of F\u2019.\nHow is P related to T if \u2018P + Q \u2013 R x S \u00f7 T\u2019?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The visual image question. It will be most easy and quick if you picture it in your mind. Learn how to do it. The correct answer is  Father's Father's Brother.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which island country, along with Sri Lanka, is identified as India\u2019s southern neighbour across the Indian Ocean?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Maldives\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which Ministry was primarily responsible for implementing online child safety initiatives as of December 2025?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Ministry of Electronics and Information Technology (MeitY)\"\n    }\n  }\n  }\n}\n<\/script>\n\n\n\n<div class=\"wp-block-coblocks-accordion\">\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 76<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>100 men have provisions for 27 days. If 55 men have left, for how many days the same provisions would last for the remaining men?<\/strong><br><br>A. 60<br>B. 64<br>C. 62<br>D. 58<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Men &amp; Days (Work Concept)<\/strong><br>\ud83d\udc49 Total work = Men \u00d7 Days (constant)<br>Initial:<br>100 \u00d7 27 = <strong>2700 man-days<\/strong><br>Remaining men = 100 \u2212 55 = 45<br>Days:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>2700<\/mn><mn>45<\/mn><\/mfrac><mo>=<\/mo><mn>60<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{2700}{45} = 60<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>A. 60<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Always convert to <em>man-days<\/em> \u2192 divide by new men.<\/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>Preparation of report cards, maintaining student records, and creating question papers are actions that are mainly related to which area of computer application?<\/strong><br><br>A. Space research<br>B. Education administration<br>C. Business marketing<br>D. Automobile control<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>B. Education administration<\/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>The price of each article of type P, Q, and R is \u20b9280, \u20b9180 and \u20b9115, respectively. Tejas buys articles of each type in the ratio 4 : 2 : 5 for \u20b96,165. How many articles of type Q did he purchase?<\/strong><br><br>A. 14<br>B. 6<br>C. 3<br>D. 12<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Ratio Purchase<\/strong><br>Ratio = 4 : 2 : 5 \u2192 total = 11 units<br>Cost per unit:<br>4 \u00d7 280 + 2 \u00d7 180 + 5 \u00d7 115<br>= 1120 + 360 + 575<br>= 2055<br>Given total = 6165<br><br>6165\/2055 = 3<br>So Q articles:<br>2 \u00d7 3 = 6<br><strong>\u2705 Answer: B. 6<\/strong><br>\ud83d\udc49 Trick: Find cost of one ratio block.<\/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>Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.<br>Statements: All gardens are forests. All forests are meadows. No garden is a park.<br>Conclusions: (I) No forest is a park. (II) No meadow is a park.<br><\/strong><br>A. Neither conclusion (I) nor (II) follows<br>B. Only conclusion (I) follows<br>C. Both conclusions (I) and (II) follow<br>D. Only conclusion (II) follows<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Syllogism<\/strong><br>Statements:<br>Garden \u2282 Forest \u2282 Meadow<br>No Garden = Park<br>Conclusion I:<br>Forest \u2192 may include non-garden \u2192 \u274c<br>Conclusion II:<br>Meadow \u2192 may include park \u2192 \u274c<br><strong>\u2705 Answer: A. Neither conclusion (I) nor (II) follows<br><\/strong>\ud83d\udc49 Trick: \u201cAll\u201d doesn\u2019t reverse.<\/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>X, Y, Z, S, T and U live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2 and so on till the topmost floor is numbered 6. S lives on floor number 5. X lives on a floor above S. Only U lives below Y. Z lives on an even numbered floor. How many people live below Z?<\/strong><br><br>A. Three<br>B. Four<br>C. Two<br>D. One<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Floor Puzzle<\/strong><br>Given:<br>S = 5<br>X above S \u2192 6<br>Only U below Y \u2192 Y = 2, U = 1<br>Z even \u2192 4<br>So below Z (4): floors 1,2,3 \u2192 3 people<br><strong>\u2705 Answer: A. 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 81<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which policy trade-off limited balanced sectoral growth in India during 1951\u20131991?<br><\/strong><br>A. Private vs. public sector<br>B. Imports vs. exports<br>C. Agriculture vs. industry<br>D. Services vs. manufacturing<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>C. Agriculture vs. industry<\/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>Find the mode of the following frequency distribution. (Round off the answer to two decimal places.)<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Class<\/th><th class=\"has-text-align-center\" data-align=\"center\">Frequency<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">0-10<\/td><td class=\"has-text-align-center\" data-align=\"center\">5<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">10-20<\/td><td class=\"has-text-align-center\" data-align=\"center\">8<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">20-30<\/td><td class=\"has-text-align-center\" data-align=\"center\">12<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">30-40<\/td><td class=\"has-text-align-center\" data-align=\"center\">20<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">40-50<\/td><td class=\"has-text-align-center\" data-align=\"center\">10<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"is-style-info\">A. 32.25<br>B. 31.51<br>C. 33.35<br>D. 34.44<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Mode (Grouped Data)<\/strong><br>Formula:<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mtext>Mode<\/mtext><mo>=<\/mo><mi>l<\/mi><mo>+<\/mo><mfrac><mrow><msub><mi>f<\/mi><mn>1<\/mn><\/msub><mo>\u2212<\/mo><msub><mi>f<\/mi><mn>0<\/mn><\/msub><\/mrow><mrow><mn>2<\/mn><msub><mi>f<\/mi><mn>1<\/mn><\/msub><mo>\u2212<\/mo><msub><mi>f<\/mi><mn>0<\/mn><\/msub><mo>\u2212<\/mo><msub><mi>f<\/mi><mn>2<\/mn><\/msub><\/mrow><\/mfrac><mo>\u00d7<\/mo><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Mode} = l + \\frac{f_1 &#8211; f_0}{2f_1 &#8211; f_0 &#8211; f_2} \\times h<\/annotation><\/semantics><\/math><br><br>Modal class = 30\u201340<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>l<\/mi><mo>=<\/mo><mn>30<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">l = 30<\/annotation><\/semantics><\/math><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>f<\/mi><mn>1<\/mn><\/msub><mo>=<\/mo><mn>20<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">f_1 = 20<\/annotation><\/semantics><\/math><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>f<\/mi><mn>0<\/mn><\/msub><mo>=<\/mo><mn>12<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">f_0 = 12<\/annotation><\/semantics><\/math><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>f<\/mi><mn>2<\/mn><\/msub><mo>=<\/mo><mn>10<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">f_2 = 10<\/annotation><\/semantics><\/math><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>h<\/mi><mo>=<\/mo><mn>10<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">h = 10<\/annotation><\/semantics><\/math><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>30<\/mn><mo>+<\/mo><mfrac><mrow><mn>20<\/mn><mo>\u2212<\/mo><mn>12<\/mn><\/mrow><mrow><mn>40<\/mn><mo>\u2212<\/mo><mn>12<\/mn><mo>\u2212<\/mo><mn>10<\/mn><\/mrow><\/mfrac><mo>\u00d7<\/mo><mn>10<\/mn><mo>=<\/mo><mn>30<\/mn><mo>+<\/mo><mfrac><mn>8<\/mn><mn>18<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>10<\/mn><mo>=<\/mo><mn>30<\/mn><mo>+<\/mo><mn>4.44<\/mn><mo>=<\/mo><mn>34.44<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">= 30 + \\frac{20-12}{40-12-10} \u00d7 10 = 30 + \\frac{8}{18}\u00d710 = 30 + 4.44 = 34.44<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>D. 34.44<\/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 83<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What should come in place of \u2018?\u2019 in the given series?<br>45 65 81 93 101 ?<\/strong><br><br>A. 105<br>B. 103<br>C. 106<br>D. 104<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Series<\/strong><br>45, 65, 81, 93, 101<br>Differences:<br>+20, +16, +12, +8 \u2192 next +4<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>101<\/mn><mo>+<\/mo><mn>4<\/mn><mo>=<\/mo><mn>105<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">101 + 4 = 105<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>A. 105<\/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>Refer to the following letter, number, symbol series and answer the question. (All numbers are single digit numbers only.)<br>(Left) R % C * E 3 K 6 $ 7 D @ 2 T Y # 4 5 G &amp; S (Right)<br>If all the letters are dropped from the series, which of the following will be fourth from the right?<\/strong><br><br>A. @<br>B. 4<br>C. #<br>D. 2<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Series<\/strong><br>Remove letters:<br>% * 3 6 $ 7 @ 2 # 4 5 &amp;<br>4th from right:<br>&amp; (1), 5 (2), 4 (3), # (4)<br>\u2705 Answer: <strong>C. #<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 85<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>A woman travelled at a speed of 20 m\/min for 90 min, and at a speed of 55 m\/min for 60 min. Her average speed (in m\/min) for the entire journey is:<\/strong><br><br>A. 27<br>B. 40<br>C. 38<br>D. 34<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Average Speed<\/strong><br>Distance:<br>20 \u00d7 90 = 1800,<br>55 \u00d7 60 = 3300<br>Total = 5100<br>Time = 150<br><br>5100\/150 = 34<br><strong>\u2705 Answer: D. 34<\/strong><br>\ud83d\udc49 Trick: Avg speed = total distance \/ total time.<\/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>Which characteristic of a computer system enables it to perform extremely complex calculations within seconds?<\/strong><br><br>A. Versatility<br>B. Automation<br>C. Accuracy<br>D. Speed<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: D. Speed<\/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>Who among the following is known for his collaboration with international artists and is\/was a renowned tabla maestro?<\/strong><br><br>A. Hari Prasad Chaurasia<br>B. Sajjad Hussain<br>C. Zakir Hussain<br>D. EM Subramaniam<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: C. Zakir Hussain<\/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>In 2025, the Supreme Court of India (SC) in the case State of Tamil Nadu v. Governor of Tamil Nadu ruled that a State Governor cannot exercise which of the following over a bill duly passed by the State Legislature?<\/strong><br><br>A. Line-item veto<br>B. Pocket Veto<br>C. Veto only on financial bills<br>D. Conditional assent<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>B. Pocket veto<\/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>Three friends travel along three consecutive segments: from P to Q, Q to R, and R to S. Their speeds on these segments are 48 km\/h, 72 km\/h, and 96 km\/h, respectively. The distances of the three segments are in the ratio 2 : 3 : 1, and the total distance from P to S is 480 km. Calculate the average speed for the entire journey.<\/strong><br><br>A. 58 km\/h<br>B. 64 km\/h<br>C. 65 km\/h<br>D. 68 km\/h<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Average Speed (Weighted)<\/strong><br>Ratio distance = 2:3:1 \u2192 total = 6<br>Distances:<br>160, 240, 80<br>Time:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>160<\/mn><mn>48<\/mn><\/mfrac><mo>+<\/mo><mfrac><mn>240<\/mn><mn>72<\/mn><\/mfrac><mo>+<\/mo><mfrac><mn>80<\/mn><mn>96<\/mn><\/mfrac><mo>=<\/mo><mn>3.33<\/mn><mo>+<\/mo><mn>3.33<\/mn><mo>+<\/mo><mn>0.83<\/mn><mo>=<\/mo><mn>7.5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{160}{48} + \\frac{240}{72} + \\frac{80}{96} = 3.33 + 3.33 + 0.83 = 7.5<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>480<\/mn><mn>7.5<\/mn><\/mfrac><mo>=<\/mo><mn>64<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{480}{7.5} = 64<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>B. 64 km\/h<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Use weighted harmonic average.<\/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>52 is related to 144 following a certain logic. Following the same logic, 81 is related to 173. To which of the following is 63 related, following the same logic?<br>(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 \u2013 Operations on 13 such as adding\/ subtracting \/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)<\/strong><br><br>A. 165<br>B. 175<br>C. 145<br>D. 155<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Number Logic<\/strong><br>52 \u2192 144<br>81 \u2192 173<br>Pattern:<br>\u00d7 2 + 40<br>Check:<br>52 \u00d7 2 + 40 = 144<br>81 \u00d7 2 + 11 = 173 \u274c<br><br>Better:<br>\u00d7 2 + (number \u2212 something)<br>Correct:<br>52 \u00d7 2 + 40 = 14481 \u00d7 2 + 11 = 173<br>Difference reduces by 29 \u2192 next +?<br><br>Try:<br>63 \u00d7 2 + 29 = 155<br>\u2705 Answer: <strong>D. 155<\/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>The total surface area of a solid cube each side of which is 84 cm long is:<\/strong><br><br>A. 42365 cm<sup>2<\/sup><br>B. 42292 cm<sup>2<\/sup><br>C. 42359 cm<sup>2<\/sup><br>D. 42336 cm<sup>2<\/sup><\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Surface Area Cube<\/strong><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mtext>Surface&nbsp;Area<\/mtext><mo>=<\/mo><mn>6<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Surface Area} = 6a^2<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>6<\/mn><mo>\u00d7<\/mo><msup><mn>84<\/mn><mn>2<\/mn><\/msup><mo>=<\/mo><mn>6<\/mn><mo>\u00d7<\/mo><mn>7056<\/mn><mo>=<\/mo><mn>42336<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">6\u00d784^2 = 6\u00d77056 = 42336<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>D. 42336<\/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>Seven people B, C, O, P, Q, R and S are sitting around a circular table facing the center of the table. B sits second to the right of S. Q sits third to the left of S. Only two people sit between P and R when counted from the right of R. C is an immediate neighbor of P. Who sits to the immediate left and right of O, respectively?<br><\/strong><br>A. S and B<br>B. C and B<br>C. S and P<br>D. C and S<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>The Pattern Trick:<br><\/strong>right of = clockwise<br>left of = anti-clockwise<br>7 people = B,C,O,P,Q,R,S<br>circular = 1,2,3,4,5,6,7,1&#8230;<br><br>1 = S<br>2 = O<br>3 = B<br>4 = R<br>5 = Q<br>6 = C<br>7 = P<br><br>&#8211; B 2nd right of S: We start from S and in B will be 3.<br><br>&#8211; Q 3rd left of S: Since S is 1, so Q will be 5 anti-clockwise.<br><br>&#8211; Two between P and R: Starting from R to P there are two between them. This is confusing, because R could be in place of 4 or 6. Let&#8217;s check others to confirm.<br><br>&#8211; C immediate of P means it can be left of right any place. It clears the above issue as well. Because if R is in 6, then there is no room left for C.<br>So for R = 4, P = 7, C = 6.<br>Only place left is O = 2.<br><br>The question asks: left and right of O<br>S = 1, O = 2, B = 3.<br>\ud83d\udc49 <strong>Answer A. = S and 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 93<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>At what rate per annum will a sum of money become five times itself in 5 years under simple interest?<br><\/strong><br>A. 82%<br>B. 160%<br>C. 80%<br>D. 78%<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Simple Interest<\/strong><br>Amount = 5P \u2192 SI = 4P<br>We start putting interest after the end of 1 year, so 5 becomes 4.<br><math data-latex=\"SI = \\frac{P \\times R \\times T}{100} \\\\ 4P = \\frac{P \\times R \\times 5}{100} \\\\ \\frac{4}{R} = \\frac{P \\times 5}{100 \\times P} \\\\ \\frac{1}{R} = \\frac{5}{100 \\times 4} \\\\ R = \\frac{400}{5}\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mi>S<\/mi><mi>I<\/mi><mo>=<\/mo><mfrac><mrow><mi>P<\/mi><mo>\u00d7<\/mo><mi>R<\/mi><mo>\u00d7<\/mo><mi>T<\/mi><\/mrow><mn>100<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>4<\/mn><mi>P<\/mi><mo>=<\/mo><mfrac><mrow><mi>P<\/mi><mo>\u00d7<\/mo><mi>R<\/mi><mo>\u00d7<\/mo><mn>5<\/mn><\/mrow><mn>100<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mn>4<\/mn><mi>R<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>P<\/mi><mo>\u00d7<\/mo><mn>5<\/mn><\/mrow><mrow><mn>100<\/mn><mo>\u00d7<\/mo><mi>P<\/mi><\/mrow><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mn>1<\/mn><mi>R<\/mi><\/mfrac><mo>=<\/mo><mfrac><mn>5<\/mn><mrow><mn>100<\/mn><mo>\u00d7<\/mo><mn>4<\/mn><\/mrow><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>R<\/mi><mo>=<\/mo><mfrac><mn>400<\/mn><mn>5<\/mn><\/mfrac><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">SI = \\frac{P \\times R \\times T}{100} \\\\ 4P = \\frac{P \\times R \\times 5}{100} \\\\ \\frac{4}{R} = \\frac{P \\times 5}{100 \\times P} \\\\ \\frac{1}{R} = \\frac{5}{100 \\times 4} \\\\ R = \\frac{400}{5}<\/annotation><\/semantics><\/math><br>\u21d2 R = 80%<br><strong>\u2705 Answer: C. 80%<\/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>In December 2025, the Punjab government directed strict enforcement of which policy to safeguard schoolchildren during dense winter fog (mandatory visibility measures, reduced speed, reflectors, headlights and fog lights)?<\/strong><br><br>A. Motor Vehicles Safety Compliance Programme<br>B. Safe School Vehicle Policy<br>C. National Road Safety Policy<br>D. National School Safety and Security Guidelines<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>B. Safe School Vehicle Policy<\/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>Shan has \u20b91407 with him. He divides this amount between his two sons, Piyush and Manoj, and asks them to invest their respective shares at a compound interest rate of 10% per annum, compounded annually. It is observed that Piyush\u2019s investment amounts to the same value after 18 years as Manoj\u2019s investment does after 19 years. How much (in \u20b9) did Shan give to Manoj?<\/strong><br><br>A. 670<br>B. 837<br>C. 737<br>D. 520<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>I Investment<\/strong><br>Given:<br>Piyush (18 yrs) = Manoj (19 yrs)<br>P(1.1)<sup>18<\/sup> = M(1.1)<sup>19<\/sup><br>\u21d2 P = M(1.1)<sup>1<\/sup><br>\u21d2 P = 1.1M<br>Total:<br>1.1M + M = 1407<br>\u21d2 2.1M = 1407<br>\u21d2 M = 1407\/2.1<br>\u21d2 M = 670<br><strong>\u2705 Answer: A. 670<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 96<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In an election between two candidates, 80% of the registered voters cast their vote and 10% of the votes polled were found invalid. Winning candidate got 89% of the valid votes and won the election by a margin of 351 votes. How many voters were registered?<\/strong><br><br>A. 625<br>B. 650<br>C. 600<br>D. 675<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Election<\/strong><br>Let voters = x<br>Votes cast = 0.8x<br>Valid = 0.9\u00d70.8x = 0.72x<br>Winner gets 89%<br>Loser = 11%<br><br>Margin:<br>0.78 \u00d7 0.72x = 351<br>\u21d2 0.5616x = 351<br>\u21d2 x = 351\/0.5616<br>\u21d2 x = 625<br>\u2705 Answer: <strong>A. 625<\/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>Each of the digits in the number 52697148 is arranged in descending order from left to right. What will be the product of the digits which are third from the left and second from the right in the number thus formed?<\/strong><br><br>A. 14<br>B. 12<br>C. 16<br>D. 28<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Digits<\/strong><br>Descending:<br>9 8 7 6 5 4 2 1<br>3rd left = 7<br>2nd right = 2<br>7 \u00d7 2 = 14<br>\u2705 Answer: <strong>A. 14<\/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>In a certain code language,<br>E + F means \u2018E is the brother of F\u2019,<br>E \u2013 F means \u2018E is the father of F\u2019,<br>E x F means \u2018E is the husband of F\u2019<br>and E \u00f7 F means \u2018E is the mother of F\u2019.<br>How is P related to T if \u2018P + Q \u2013 R x S \u00f7 T\u2019?<\/strong><br><br>A. Father&#8217;s Father&#8217;s Brother<br>B. Father&#8217;s Brother<br>C. Father<br>D. Brother<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Relation<\/strong><br>P + Q \u2192 brother<br>Q \u2013 R \u2192 father<br>R \u00d7 S \u2192 husband<br>S \u00f7 T \u2192 mother<br>So:<br>R is father of T.<br>Q is father of R.<br>P is brother of Q.<br><strong>\u2705 Answer: A. Father&#8217;s Father&#8217;s Brother<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 99<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which island country, along with Sri Lanka, is identified as India\u2019s southern neighbour across the Indian Ocean?<\/strong><br><br>A. Indonesia<br>B. Bhutan<br>C. Maldives<br>D. Thailand<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>C. Maldives<\/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>Which Ministry was primarily responsible for implementing online child safety initiatives as of December 2025?<\/strong><br><br>A. Ministry of Social Justice<br>B. Ministry of Electronics and Information Technology (MeitY)<br>C. Ministry of Home Affairs<br>D. Ministry of Education<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: B. Ministry of Electronics and Information Technology (MeitY)<\/strong><\/p>\n<\/div><\/details><\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>RRB NTPC Graduate CBT Competitive Exam 3 (16 Mar, 2026): Try another Test of RRB NTPC Graduate CBT 3 exam, which was conducted on 16 March, 2026. Take the tests and also learn from answer solutions and tricks hack.<\/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":[5,6,7],"tags":[3],"class_list":["post-311","post","type-post","status-publish","format-standard","hentry","category-railway","category-rrb-ntpc","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\/311","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=311"}],"version-history":[{"count":21,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/posts\/311\/revisions"}],"predecessor-version":[{"id":363,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/posts\/311\/revisions\/363"}],"wp:attachment":[{"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/media?parent=311"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/categories?post=311"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/tags?post=311"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}