{"id":281,"date":"2026-04-23T15:51:34","date_gmt":"2026-04-23T15:51:34","guid":{"rendered":"https:\/\/govt.mrenglishkj.com\/railway\/?p=281"},"modified":"2026-04-23T15:51:38","modified_gmt":"2026-04-23T15:51:38","slug":"rrb-ntpc-graduate-cbt-2-competitive-exam-1-quick-hack","status":"publish","type":"post","link":"https:\/\/govt.mrenglishkj.com\/railway\/rrb-ntpc-graduate-cbt-2-competitive-exam-1-quick-hack\/","title":{"rendered":"RRB NTPC Graduate CBT 2 Competitive Exam 1: Quick Hack"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">RRB NTPC Graduate CBT 2 (Free Practice Quiz 1) \u2013 <strong>Question, Tricks, Solutions<\/strong> (Part 1: Question 1-25)<\/h2>\n\n\n\n<p>How is your RRB NTPC exam preparation going? You are in a right place to prepare for any competitive exams. Everything here is for free. There are no hidden charges. We even give you rewards if you perform well to motivate you in your study. Here you will try to attempt RRB NTPC Graduate CBT 2 exam practice test 1. The competitive exam is divided into 4 parts each with 25 questions. You are not just taking the exercise but also learning from the answers, explanations, and hack.<\/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 = 17;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-17\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"17\">\n            <div class=\"kq-loading\">Loading quiz...<\/div>\n        <\/div>\n        \n    <div id=\"kq-auth-modal\" class=\"kq-auth-modal\" style=\"display:none;\">\n      <div class=\"kq-auth-modal-inner\">\n        <button id=\"kq-auth-close\" class=\"kq-auth-close\" aria-label=\"Close\">\u2716<\/button>\n\n        <!-- TAB NAV -->\n        <div class=\"kq-auth-tabs\" role=\"tablist\">\n          <button class=\"kq-tab active\" data-tab=\"register\" type=\"button\" role=\"tab\" aria-selected=\"true\">Register<\/button>\n          <button class=\"kq-tab\" data-tab=\"login\" type=\"button\" role=\"tab\" aria-selected=\"false\">Login<\/button>\n          <button class=\"kq-tab\" data-tab=\"forgot\" type=\"button\" role=\"tab\" aria-selected=\"false\">Forgot<\/button>\n        <\/div>\n\n        <!-- PANELS -->\n        <div class=\"kq-auth-panel-wrap\">\n\n          <!-- REGISTER -->\n          <div class=\"kq-auth-panel\" data-panel=\"register\" style=\"display:block\">\n            <div class=\"kq-auth-card\">\n              <h3>Register<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-username\" placeholder=\"Username\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-email\" placeholder=\"Email\" type=\"email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-signup-btn\" class=\"button kq-btn-small\">Register<\/button>\n              <small style=\"display:block;margin-top:8px;\">Already registered? Use Login tab.<\/small>\n            <\/div>\n          <\/div>\n\n          <!-- LOGIN -->\n          <div class=\"kq-auth-panel\" data-panel=\"login\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Login<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-login-btn\" class=\"button kq-btn-small\">Login<\/button>\n            <\/div>\n          <\/div>\n\n          <!-- FORGOT -->\n          <div class=\"kq-auth-panel\" data-panel=\"forgot\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Forgot Password<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-newpass\" placeholder=\"New Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-forgot-btn\" class=\"button kq-btn-small\">Update Password<\/button>\n            <\/div>\n          <\/div>\n\n        <\/div>\n\n      <\/div>\n    <\/div>\n    \n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Answers of The RRB NTPC Competitive Exam Questions<\/h2>\n\n\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"Select the set in which the numbers are related in the same way as the following sets:\n(8,9,28), (5,7,20)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is to get 3rd value by multiplying 1st value with 2 then addition it with 2nd value, later add 3. Let's learn practically.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Where did the first passenger train run in India?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Between Bori Bunder and Thane is the correct answer. Let's check others.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Six people A, B, C, D, E and F live on six different floors of a building numbered 1 to 6 from bottom to top.\nOnly one person lives below C.\nB lives immediately above C.\nA lives above B but below E.\nF lives below D.\nWho lives on floor number 5?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is D that lives there, let's learn the simple visual trick to solve it within three seconds.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Which shortcut is used to transfer all the content in the folder to another folder?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Ctrl+X\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"In this question, a question is followed by two statements numbered (I) and (II). Decide whether the data are sufficient to answer the question.\nFour friends A, B, C and D are of different ages. Who is the second oldest?\n(I) B is older than C but younger than A.\n(II) D is older than B but younger than A.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Both statements together are sufficient, but neither alone is sufficient. Let's learn why.\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"On which date did the first passenger train run in India?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"April 16, 1853\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Among the numbers 684, 529, 791, 436 and 857, what is the sum of the second digit of the highest number and the second digit of the lowest number?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Let's learn the trick to solve this in five seconds and find out the correct answer. Check out how.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language:\nA + B means A is the son of B\nA - B means A is the mother of B\nA \u00d7 B means A is the daughter of B\nA \u00f7 B means A is the father of B\nHow is S related to B if B \u00f7 T + S?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Wife is the correct answer.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What is the name of the first electric train in India?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Deccan Queen\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If a number is increased by 20% and becomes equal to another number, which is 25% less than a third number, then the ratio of the first number to the third number is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Let's learn how to calculate ration simply, the correct answer is 5:8.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which is the highest railway station in India?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"he correct answer is Ghum Railway Station.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A right triangle with sides 3 cm, 4 cm and 5 cm is revolved about the side 4 cm. Find the volume of the solid formed. Use $\\pi = \\frac{22}{7}$.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"37.71 cm\u00b3 is the correct answer. Let's learn the simple trick to solve and find it.\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What is the official mascot of Indian Railways?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Bholu, the Guard Elephant\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What should come in place of the question mark?\n14, 17, 22, 29, 38, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 49. 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 which year was the Railway Budget merged with the Union Budget?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"2017\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If $x^2 \u2212 6x + 9 = 0$ and $x^2 \u2212 4x + t = 0$ have one common root, then the value of t is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 3. But the real question is how to get it quickly, let's learn the trick.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who was the first Railway Minister of Independent India?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"John Mathai is the correct answer. Let's learn more.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What is the name of the indigenously developed anti-collision system in Railway?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Kavach\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A shopkeeper pretends to sell goods at a 40% loss, but by using a false balance he actually gains 75%. The actual weight used for 1 kg is approximately:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 342.9 g. The trick behind is very simple. Let's learn it in 5 seconds.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language:\nA - B means A is the mother of B\nA + B means A is the wife of B\nA \u00d7 B means A is the sister of B\nA \u00f7 B means A is the father of B\nHow is G related to P if G - R + P?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Mother-in-law\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"How many letters are there in the following series, each of which is immediately preceded by a symbol and immediately followed by a symbol?\nA * B # C $ D @ E % F & G\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"There are only 5 like that. Let's learn the visual ways.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If 15% of $160 \u2212 \\frac{1}{2} \u00d7 \\sqrt[3]{64} \u00d7 \\sqrt{16} = y$, then the value of y is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick is simple and the correct answer is 16.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which letter-number cluster completes the series?\nBDF 7, EGI 10, HJL Which letter-number cluster completes the series?\nBDF 7, EGI 10, HJL 13, KMO 16, ?13, KMO 16, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick behind is addition of 2 in each letter and number after every forward sequence The correct answer is NPR 19.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Three of the following four letter clusters are alike in a certain way and form a group. Which one does not belong to the group?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is simple skimming type question. The correct answer is GJM. Let's learn the trick.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What should come next in the series?\n4, 10, 18, 28, 40, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 54. This is all a visual map trick. Let's learn it faster by trying.\"\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>Select the set in which the numbers are related in the same way as the following sets:<br>(8,9,28), (5,7,20)<\/strong><br><br>A. (11, 8, 33)<br>B. (12, 6, 31)<br>C. (10, 5, 26)<br>D. (9, 4, 24)<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Given:<br><\/strong>Solution<br>For the given sets:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mn>8<\/mn><mo separator=\"true\">,<\/mo><mn>9<\/mn><mo separator=\"true\">,<\/mo><mn>28<\/mn><mo stretchy=\"false\">)<\/mo><mo separator=\"true\">,<\/mo><mtext>&nbsp;<\/mtext><mo stretchy=\"false\">(<\/mo><mn>5<\/mn><mo separator=\"true\">,<\/mo><mn>7<\/mn><mo separator=\"true\">,<\/mo><mn>20<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(8, 9, 28),\\ (5, 7, 20)<\/annotation><\/semantics><\/math>Check the pattern:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><mo>\u00d7<\/mo><mn>8<\/mn><mo>+<\/mo><mn>9<\/mn><mo>+<\/mo><mn>3<\/mn><mo>=<\/mo><mn>28<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2 \\times 8 + 9 + 3 = 28<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><mo>\u00d7<\/mo><mn>5<\/mn><mo>+<\/mo><mn>7<\/mn><mo>+<\/mo><mn>3<\/mn><mo>=<\/mo><mn>20<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2 \\times 5 + 7 + 3 = 20<\/annotation><\/semantics><\/math>So the rule is:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>third&nbsp;number<\/mtext><mo>=<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mtext>first<\/mtext><mo>+<\/mo><mtext>second<\/mtext><mo>+<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\text{third number} = 2 \\times \\text{first} + \\text{second} + 3<\/annotation><\/semantics><\/math><br>Now test the options:<br>A: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>2<\/mn><mo>\u00d7<\/mo><mn>11<\/mn><mo>+<\/mo><mn>8<\/mn><mo>+<\/mo><mn>3<\/mn><mo>=<\/mo><mn>33<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2 \\times 11 + 8 + 3 = 33<\/annotation><\/semantics><\/math> \u2713<br>B: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>2<\/mn><mo>\u00d7<\/mo><mn>12<\/mn><mo>+<\/mo><mn>6<\/mn><mo>+<\/mo><mn>3<\/mn><mo>=<\/mo><mn>33<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2 \\times 12 + 6 + 3 = 33<\/annotation><\/semantics><\/math> \u2717<br>C: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>2<\/mn><mo>\u00d7<\/mo><mn>10<\/mn><mo>+<\/mo><mn>5<\/mn><mo>+<\/mo><mn>3<\/mn><mo>=<\/mo><mn>28<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2 \\times 10 + 5 + 3 = 28<\/annotation><\/semantics><\/math> \u2717<br>D: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>2<\/mn><mo>\u00d7<\/mo><mn>9<\/mn><mo>+<\/mo><mn>4<\/mn><mo>+<\/mo><mn>3<\/mn><mo>=<\/mo><mn>25<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2 \\times 9 + 4 + 3 = 25<\/annotation><\/semantics><\/math> \u2717<br>\u2705 Answer: <strong>A. (11, 8, 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 2<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Where did the first passenger train run in India?<\/strong><br><br>A. between Byculla and Thane<br>B. between Bori Bunder and Thane<br>C. between Howrah Junction and Royapuram Railway Station<br>D. between Byculla and Bori Bunder<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>B. between Bori Bunder and Thane<\/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>Six people A, B, C, D, E and F live on six different floors of a building numbered 1 to 6 from bottom to top.<br>Only one person lives below C.<br>B lives immediately above C.<br>A lives above B but below E.<br>F lives below D.<br>Who lives on floor number 5?<\/strong><br><br>A. A<br>B. B<br>C. C<br>D. D<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Let\u2019s place the floors carefully.<br>Only one person lives below C, so C is on floor 2.<br>B lives immediately above C, so B is on floor 3.<br>A lives above B but below E. That means A must be on floor 4 and E on floor 6.<br>F lives below D, so the remaining floors 1 and 5 go to F and D respectively.<br>So the arrangement is:<br>1. F<br>2. C<br>3. B<br>4. A<br>5. D<br>6. E<br>Therefore, the person on floor 5 is <strong>D<\/strong>.<br>\u2705 Answer: <strong>D. D<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 4<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which shortcut is used to transfer all the content in the folder to another folder?<br><\/strong><br>A. Ctrl+P<br>B. Ctrl+S<br>C. Ctrl+X<br>D. Ctrl+A<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>C. Ctrl+X<\/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>In this question, a question is followed by two statements numbered (I) and (II). Decide whether the data are sufficient to answer the question.<br>Four friends A, B, C and D are of different ages. Who is the second oldest?<br>(I) B is older than C but younger than A.<br>(II) D is older than B but younger than A.<br><\/strong><br>A. Data in Statement I alone is sufficient, but Statement II alone is not<br>B. Data in Statement II alone is sufficient, but Statement I alone is not<br>C. Both statements together are sufficient, but neither alone is sufficient<br>D. Both statements together are not sufficient<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Statement I:<br>B &gt; C<br>A &gt; B<br>So A &gt; B &gt; C, but D is not placed. Not sufficient.<br><br>Statement II:<br>D &gt; B<br>A &gt; D<br>So A &gt; D &gt; B, but C is not placed. Not sufficient.<br><br>Together:<br>From I: A &gt; B &gt; C<br>From II: A &gt; D &gt; B<br>Combine them:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>A<\/mi><mo>&gt;<\/mo><mi>D<\/mi><mo>&gt;<\/mo><mi>B<\/mi><mo>&gt;<\/mo><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A &gt; D &gt; B &gt; C<\/annotation><\/semantics><\/math><br>So the second oldest is <strong>D<\/strong>. Together the statements are sufficient, but neither alone is sufficient.<br>\ud83d\udc49 <strong>Answer C: Both statements together are sufficient, but neither alone is sufficient<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 6<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>National Waterway 57 (NW-57) is developed on which river?<br><\/strong><br>A. June 18, 1848<br>B. March 22, 1896<br>C. April 16, 1853<br>D. August 18, 1901<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>C. April 16, 1853<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 7<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In a certain code language:<br>A + B means A is the son of B<br>A &#8211; B means A is the mother of B<br>A \u00d7 B means A is the daughter of B<br>A \u00f7 B means A is the father of B<br>How is S related to B if B \u00f7 T + S?<\/strong><br><br>A. Mother-in-law<br>B. Sister<br>C. Daughter<br>D. Wife<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Given:<br>B \u00f7 T means B is the father of T.<br>T + S means T is the son of S.<br>That makes B the wife of B.<br>\u2705 Answer: <strong>D. Wife<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 8<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What is the name of the first electric train in India?<\/strong><br><br>A. Lord Dalhousie<br>B. Kathiawar<br>C. GIPR No. 1<br>D. Deccan Queen<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>The correct answer is D: Deccan Queen<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 9<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>If a number is increased by 20% and becomes equal to another number, which is 25% less than a third number, then the ratio of the first number to the third number is:<\/strong><br><br>A. 5:8<br>B. 8:5<br>C. 16:25<br>D. 25:16<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Let the first number be <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math>.<br>After a 20% increase, it becomes <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>1.2<\/mn><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">1.2x<\/annotation><\/semantics><\/math>.<br>This is equal to a number that is 25% less than a third number <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>z<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">z<\/annotation><\/semantics><\/math>, so:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>1.2<\/mn><mi>x<\/mi><mo>=<\/mo><mn>0.75<\/mn><mi>z<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">1.2x = 0.75z<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mi>x<\/mi><mi>z<\/mi><\/mfrac><mo>=<\/mo><mfrac><mn>0.75<\/mn><mn>1.2<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>75<\/mn><mn>120<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>5<\/mn><mn>8<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{x}{z} = \\frac{0.75}{1.2} = \\frac{75}{120} = \\frac{5}{8}<\/annotation><\/semantics><\/math><br>So the ratio of the first number to the third number is <strong>5:8<\/strong>.<br>\u2705 Answer: <strong>A. 5:8<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 10<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which is the highest railway station in India?<\/strong><br><br>A. Hubli Railway Station<br>B. Ghum Railway Station<br>C. Gorakhpur Railway Station<br>D. Siddharoodha Swamiji Hubballi Junction<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>B. Ghum Railway Station<\/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>A right triangle with sides 3 cm, 4 cm and 5 cm is revolved about the side 4 cm. Find the volume of the solid formed. Use <\/strong><math data-latex=\"\\pi = \\frac{22}{7}\"><semantics><mrow><mi>\u03c0<\/mi><mo>=<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\pi = \\frac{22}{7}<\/annotation><\/semantics><\/math><strong>.<\/strong><br><br>A. 35.71 cm\u00b3<br>B. 36.71 cm\u00b3<br>C. 37.71 cm\u00b3<br>D. 38.71 cm\u00b3<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>A 3-4-5 triangle is a right triangle. Revolving it about the side 4 cm forms a cone with:<br>radius = 3 cm<br>height = 4 cm<br>Volume of cone:<br><math data-latex=\"V = \\frac13\u200b\u03c0r^2h \\\\ V = \\frac{1}{3} \\times \\frac{22}{7} r^2h \\\\ V = \\frac{1}{3} \\times \\frac{22}{7} \\times 3^2 \\times 4 \\\\ V = \\frac{22}{7} \\times 3 \\times 4 \\\\ V = \\frac{22}{7} \\times 12 \\\\ V = \\frac{264}{7}\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mtext>\u200b<\/mtext><mi>\u03c0<\/mi><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mi>h<\/mi><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><msup><mi>r<\/mi><mn>2<\/mn><\/msup><mi>h<\/mi><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><mn>4<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><mn>4<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mn>22<\/mn><mn>7<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>12<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>V<\/mi><mo>=<\/mo><mfrac><mn>264<\/mn><mn>7<\/mn><\/mfrac><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">V = \\frac13\u200b\u03c0r^2h \\\\ V = \\frac{1}{3} \\times \\frac{22}{7} r^2h \\\\ V = \\frac{1}{3} \\times \\frac{22}{7} \\times 3^2 \\times 4 \\\\ V = \\frac{22}{7} \\times 3 \\times 4 \\\\ V = \\frac{22}{7} \\times 12 \\\\ V = \\frac{264}{7}<\/annotation><\/semantics><\/math><br>V = 37.71&nbsp;cm<sup>3<\/sup>&nbsp;(approx.)<br>\u2705 Answer: <strong>C. 37.71 cm\u00b3<\/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 triangle ABC with sides 3 cm, 4 cm and 5 cm is revolved about the side 3 cm. Find the volume of the solid so obtained. (Use <\/strong><math data-latex=\"\\pi = 3.14\"><semantics><mrow><mi>\u03c0<\/mi><mo>=<\/mo><mn>3.14<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\pi = 3.14<\/annotation><\/semantics><\/math><strong>)<\/strong><br><br>A. Bholu, the Guard Ox<br>B. Bholu, the Guard Elephant<br>C. Garud, the Flying Eagle<br>D. Garud, the Flying Kite<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>B. Bholu, the Guard Elephant<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 13<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What should come in place of the question mark?<br>14, 17, 22, 29, 38, ?<\/strong><br><br>A. 47<br>B. 49<br>C. 50<br>D. 51<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Look at the differences:<br>17 \u2212 14 = 3,<br>22 \u2212 17 = 5,<br>29 \u2212 22 = 7,<br>38 \u2212 29 = 9<br>The differences are increasing by 2 each time. So the next difference is:<br>11<br>38 + 11 = 49<br><strong>\u2705 Answer: B. 49<\/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>In which year was the Railway Budget merged with the Union Budget?<\/strong><br><br>A. 2010<br>B. 2014<br>C. 2017<br>D. 2020<\/p>\n\n\n\n<p class=\"is-style-success\">2017: Ending a 92-year-old tradition<br>\u2705 Answer: <strong>C. 2017<\/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>If <\/strong><math data-latex=\"x^2 \u2212 6x + 9 = 0\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>6<\/mn><mi>x<\/mi><mo>+<\/mo><mn>9<\/mn><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x^2 \u2212 6x + 9 = 0<\/annotation><\/semantics><\/math><strong> and <\/strong><math data-latex=\"x^2 \u2212 4x + t = 0\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>4<\/mn><mi>x<\/mi><mo>+<\/mo><mi>t<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x^2 \u2212 4x + t = 0<\/annotation><\/semantics><\/math><strong> have one common root, then the value of <\/strong><math data-latex=\"t\"><semantics><mi>t<\/mi><annotation encoding=\"application\/x-tex\">t<\/annotation><\/semantics><\/math><strong> is:<\/strong><br><br>A. 1<br>B. 2<br>C. 3<br>D. 4<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>The first equation is:<br>x<sup>2<\/sup> \u2212 6x + 9 = 0<br>This is: (x\u22123)<sup>2<\/sup> = 0<br>So its equal root is 3.<br>Since the second equation shares one common root, that root must also be 3.<br>Substitute x = 3 into the second equation:<br>3<sup>2<\/sup> \u2212 4(3) + t = 0<br>9 \u2212 12 + t = 0<br>t = 3<br>\u2705 Answer: <strong>C. 3<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 16<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Who was the first Railway Minister of Independent India?<br><\/strong><br>A. Ram Krishna Gopal<br>B. John Mathai<br>C. Jay Mithai<br>D. Krishna Gopal Ram<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>B. John Mathai<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 17<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What is the name of the indigenously developed anti-collision system in Railway?<\/strong><br><br>A. Kavach<br>B. Breaker<br>C. Guard 2.0<br>D. Surakhsha (ACD)<\/p>\n\n\n\n<p class=\"is-style-success\">\ud83d\udc49 <strong>Answer A: Kavach<\/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>A shopkeeper pretends to sell goods at a 40% loss, but by using a false balance he actually gains 75%. The actual weight used for 1 kg is approximately:<\/strong><br><br>A. 328.6 g<br>B. 342.9 g<br>C. 350.0 g<br>D. 360.0 g<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Let the cost price of 1 kg be <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">C<\/annotation><\/semantics><\/math>.<br>He claims a 40% loss, so he charges only 60% of the cost price:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>S<\/mi><mi>P<\/mi><mo>=<\/mo><mn>0.6<\/mn><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">SP = 0.6C<\/annotation><\/semantics><\/math><br>But he actually gains 75%, which means:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>S<\/mi><mi>P<\/mi><mo>=<\/mo><mn>1.75<\/mn><mo>\u00d7<\/mo><mtext>actual&nbsp;cost&nbsp;of&nbsp;goods&nbsp;given<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">SP = 1.75 \\times \\text{actual cost of goods given}<\/annotation><\/semantics><\/math><br>If the actual weight given is <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>w<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">w<\/annotation><\/semantics><\/math> kg, then cost to him is <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>w<\/mi><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">wC<\/annotation><\/semantics><\/math>. So:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>0.6<\/mn><mi>C<\/mi><mo>=<\/mo><mn>1.75<\/mn><mi>w<\/mi><mi>C<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">0.6C = 1.75wC<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>w<\/mi><mo>=<\/mo><mfrac><mn>0.6<\/mn><mn>1.75<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>12<\/mn><mn>35<\/mn><\/mfrac><mtext>&nbsp;kg<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">w = \\frac{0.6}{1.75} = \\frac{12}{35} \\text{ kg}<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>12<\/mn><mn>35<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>1000<\/mn><mo>=<\/mo><mn>342.857<\/mn><mtext>&nbsp;g<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{12}{35}\\times 1000 = 342.857\\text{ g}<\/annotation><\/semantics><\/math><br>Rounded: <strong>342.9 g<\/strong><br>\u2705 Answer: <strong>B. 342.9 g<\/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>In a certain code language:<br>A &#8211; B means A is the mother of B<br>A + B means A is the wife of B<br>A \u00d7 B means A is the sister of B<br>A \u00f7 B means A is the father of B<br>How is G related to P if G &#8211; R + P?<\/strong><br><br>A. Mother-in-law<br>B. Sister<br>C. Daughter<br>D. Aunt<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Given:<br>G\u2212R means G is the mother of R.<br>R+P means R is the wife of P.<br>So G is the mother of R, and R is the wife of P. Therefore, G is the mother-in-law of P.<br>\u2705 Answer: <strong>A. Mother-in-law<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 20<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>How many letters are there in the following series, each of which is immediately preceded by a symbol and immediately followed by a symbol?<br>A * B # C $ D @ E % F &amp; G<\/strong><br><br>A. 3<br>B. 4<br>C. 5<br>D. 6<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>We need letters that are immediately preceded and immediately followed by symbols.<br>Series:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>A<\/mi><mo>\u2217<\/mo><mi>B<\/mi><mi mathvariant=\"normal\">#<\/mi><mi>C<\/mi><mi mathvariant=\"normal\">$<\/mi><mi>D<\/mi><mi mathvariant=\"normal\">@<\/mi><mi>E<\/mi><mi mathvariant=\"normal\">%<\/mi><mi>F<\/mi><mi mathvariant=\"normal\">&amp;<\/mi><mi>G<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">A * B \\# C \\$ D @ E \\% F \\&amp; G<\/annotation><\/semantics><\/math><br>Check each letter:<br><strong>B<\/strong> is between * and # \u2192 yes<br><strong>C<\/strong> is between # and $ \u2192 yes<br><strong>D<\/strong> is between $ and @ \u2192 yes<br><strong>E<\/strong> is between @ and % \u2192 yes<br><strong>F<\/strong> is between % and &amp; \u2192 yes<br>So there are <strong>5<\/strong> such letters.<br><strong>\ud83c\udfaf FINAL ANSWER: C. 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 21<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>If 15% of <\/strong><math data-latex=\"160 \u2212 \\frac{1}{2} \u00d7 \\sqrt[3]{64} \u00d7 \\sqrt{16} = y\"><semantics><mrow><mn>160<\/mn><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>\u00d7<\/mo><mroot><mn>64<\/mn><mn>3<\/mn><\/mroot><mo>\u00d7<\/mo><msqrt><mn>16<\/mn><\/msqrt><mo>=<\/mo><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">160 \u2212 \\frac{1}{2} \u00d7 \\sqrt[3]{64} \u00d7 \\sqrt{16} = y<\/annotation><\/semantics><\/math><strong>, then the value of y is:<\/strong><br><br>A. 12<br>B. 14<br>C. 16<br>D. 18<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<br><\/strong>15% of 160=24<br><math data-latex=\"\\sqrt[3]{64} = 4,\\ \\ \\sqrt{16} = 4\"><semantics><mrow><mroot><mn>64<\/mn><mn>3<\/mn><\/mroot><mo>=<\/mo><mn>4<\/mn><mo separator=\"true\">,<\/mo><mtext>&nbsp;<\/mtext><mtext>&nbsp;<\/mtext><msqrt><mn>16<\/mn><\/msqrt><mo>=<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt[3]{64} = 4,\\ \\ \\sqrt{16} = 4<\/annotation><\/semantics><\/math><br>Then:<br><math data-latex=\"\\frac{1}{2} \\times 2 \\times 2 = 8\"><semantics><mrow><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mn>2<\/mn><mo>=<\/mo><mn>8<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{2} \\times 2 \\times 2 = 8<\/annotation><\/semantics><\/math><br>So:<br>y = 24 \u2212 8 = 16<br><strong>\u2705 Answer: C. 16<\/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 letter-number cluster completes the series?<br>BDF 7, EGI 10, HJL Which letter-number cluster completes the series?<br>BDF 7, EGI 10, HJL 13, KMO 16, ?13, KMO 16, ?<\/strong><br><br>A. NPR 19<br>B. NPS 19<br>C. OPR 20<br>D. NPR 18<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Look at the pattern:<br>BDF \u2192 letters increase by 2 each step, number 7<br>EGI \u2192 +3 from BDF in each letter, number 10<br>HJL \u2192 +3 again, number 13<br>KMO \u2192 +3 again, number 16<br><br>So the next cluster is:<br>N P R<br>number 19<br><strong>\u2705 Answer: A. NPR 19<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 23<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Three of the following four letter clusters are alike in a certain way and form a group. Which one does not belong to the group?<\/strong><br><br>A. BDF<br>B. CEG<br>C. FHJ<br>D. GJM<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Check the letter gaps:<br>BDF \u2192 +2, +2<br>CEG \u2192 +2, +2<br>FHJ \u2192 +2, +2<br>GJM \u2192 +3, +3<br>Three clusters follow the same +2 pattern. <strong>GJM<\/strong> does not.<br>\u2705 Answer: <strong>D. GJM<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 24<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What should come next in the series?<br>4, 10, 18, 28, 40, ?<\/strong><br><br>A. 50<br>B. 52<br>C. 54<br>D. 56<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Series:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>4<\/mn><mo separator=\"true\">,<\/mo><mn>10<\/mn><mo separator=\"true\">,<\/mo><mn>18<\/mn><mo separator=\"true\">,<\/mo><mn>28<\/mn><mo separator=\"true\">,<\/mo><mn>40<\/mn><mo separator=\"true\">,<\/mo><mo stretchy=\"false\">?<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">4, 10, 18, 28, 40, ?<\/annotation><\/semantics><\/math>Differences are:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>6<\/mn><mo separator=\"true\">,<\/mo><mn>8<\/mn><mo separator=\"true\">,<\/mo><mn>10<\/mn><mo separator=\"true\">,<\/mo><mn>12<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">6, 8, 10, 12<\/annotation><\/semantics><\/math>Next difference:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>14<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">14<\/annotation><\/semantics><\/math>So:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>40<\/mn><mo>+<\/mo><mn>14<\/mn><mo>=<\/mo><mn>54<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">40 + 14 = 54<\/annotation><\/semantics><\/math>\ud83d\udc49 <strong>Answer C: 54<\/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>Among the numbers 684, 529, 791, 436 and 857, what is the sum of the second digit of the highest number and the second digit of the lowest number?<\/strong><br><br>A. 8<br>B. 9<br>C. 10<br>D. 11<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>The fastest trick:<br><\/strong>Numbers:<br>436, 529, 684, 791, 857<br>Highest = 857 \u2192 2nd digit = 5<br>Lowest = 436 \u2192 2nd digit = 3<br>\ud83d\udc49 5 + 3 = 8<br><strong>\u2705 Answer: A. 8<\/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 2 (Practice Quiz 1) \u2013 <strong>Full Exercise, Quick Tricks, Step-by-step Solutions<\/strong> (Part 2: Question 26-50)<\/h2>\n\n\n\n<p>This is the mock test of RRB NTPC Exam 1 of CBT Shift 2. Are you a pioneer who is preparing for any competitive exams? If yes then all exams here are completely free. There are no hidden charges. We even give you rewards if you perform well to motivate you in your study. Here you will try to attempt RRB NTPC Graduate CBT 2 exam practice test 1. 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, and tricks.<\/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 = 18;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-18\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"18\">\n            <div class=\"kq-loading\">Loading quiz...<\/div>\n        <\/div>\n        \n    <div id=\"kq-auth-modal\" class=\"kq-auth-modal\" style=\"display:none;\">\n      <div class=\"kq-auth-modal-inner\">\n        <button id=\"kq-auth-close\" class=\"kq-auth-close\" aria-label=\"Close\">\u2716<\/button>\n\n        <!-- TAB NAV -->\n        <div class=\"kq-auth-tabs\" role=\"tablist\">\n          <button class=\"kq-tab active\" data-tab=\"register\" type=\"button\" role=\"tab\" aria-selected=\"true\">Register<\/button>\n          <button class=\"kq-tab\" data-tab=\"login\" type=\"button\" role=\"tab\" aria-selected=\"false\">Login<\/button>\n          <button class=\"kq-tab\" data-tab=\"forgot\" type=\"button\" role=\"tab\" aria-selected=\"false\">Forgot<\/button>\n        <\/div>\n\n        <!-- PANELS -->\n        <div class=\"kq-auth-panel-wrap\">\n\n          <!-- REGISTER -->\n          <div class=\"kq-auth-panel\" data-panel=\"register\" style=\"display:block\">\n            <div class=\"kq-auth-card\">\n              <h3>Register<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-username\" placeholder=\"Username\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-email\" placeholder=\"Email\" type=\"email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-signup-btn\" class=\"button kq-btn-small\">Register<\/button>\n              <small style=\"display:block;margin-top:8px;\">Already registered? Use Login tab.<\/small>\n            <\/div>\n          <\/div>\n\n          <!-- LOGIN -->\n          <div class=\"kq-auth-panel\" data-panel=\"login\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Login<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-login-btn\" class=\"button kq-btn-small\">Login<\/button>\n            <\/div>\n          <\/div>\n\n          <!-- FORGOT -->\n          <div class=\"kq-auth-panel\" data-panel=\"forgot\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Forgot Password<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-newpass\" placeholder=\"New Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-forgot-btn\" class=\"button kq-btn-small\">Update Password<\/button>\n            <\/div>\n          <\/div>\n\n        <\/div>\n\n      <\/div>\n    <\/div>\n    \n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Solution and Explanation of RRB NTPC Competitive Exam<\/h2>\n\n\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"Select the set in which the numbers are related in the same way as the following sets:\n(8,9,26), (5,7,19)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is (11, 8, 27). Let's learn the simple trick to solve it within 3 seconds correctly.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"In cyclic quadrilateral ABCD, $\u2220A = 4x + 12^\u2218$  and $\u2220C = 2x + 48^\u2218$. What is the value of x?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 20. Let's learn the simple trick to solve it within 3 seconds correctly.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Where is the National Academy of Indian Railways (formerly Railway Staff College) located?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Vadodara (Baroda), Gujarat\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"A, B, C, D, E, F and G live on seven different floors of a building numbered 1 to 7 from bottom to top.\nOnly one person lives above C.\nD lives immediately below C.\nA lives above D but below G.\nOnly two people live below E.\nF lives below B.\nWho lives on floor number 3?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick is simple and the correct answer is E.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Which station is the headquarters of the East Coast Railway?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Bhubaneswar.\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"Riya, Sia and Tara invest \u20b9900, \u20b91200 and \u20b91500 respectively in a business. If the annual profit is \u20b91800, what is Tara\u2019s share?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is \u20b9750.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The LCM of two numbers is 1008 and their HCF is 24. If one of the numbers is 168, the other number is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick behind is very simple, the correct answer is 144. Let's learn.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which option follows the same operation pattern as the given sets?\n6\u221211\u221222\u221232; 9\u221214\u221228\u221238\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 8 - 13 - 26 - 36, check out why 8 - 13 - 26 - 36 here.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If a : b = 3 : 4 and b : c = 6 : 5, then the ratio a : c is _______.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 9:10. Let's learn the simple trick behind it.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Where is the Integral Coach Factory (ICF) located?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Perambur, Chennai\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language, the code of a word is the sum of the alphabetical positions of its letters. What is the code for FARM?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Simple trick to solve, just you need to know steps of it. The correct answer is 38. Check out how to do it in time.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following letter-clusters does not belong to the group?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is FI-JM, but how, you should check this out from here.\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Five numbers are given below:\n135, 794, 342, 909, 567\nIf arranged in ascending order, how many numbers remain in the same position?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 1, but how, you should check this out from here. 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(13, 16, 45)<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>The pattern is:<br>Third Value = First Value + (Second Value x 2)<br>26 = 8 + (9 x 2)<br>19 = 5 + (7 x 2)<br>So it matches. Option A:<br>27 = 11 + (8 x 2)<br>27 = 11 + 16<br>27 = 27<br>\u2705 Answer: <strong>A. (11, 8, 27)<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 27<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In cyclic quadrilateral ABCD, <\/strong><math data-latex=\"\u2220A = 4x + 12^\u2218\"><semantics><mrow><mi>\u2220<\/mi><mi>A<\/mi><mo>=<\/mo><mn>4<\/mn><mi>x<\/mi><mo>+<\/mo><msup><mn>12<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\u2220A = 4x + 12^\u2218<\/annotation><\/semantics><\/math><strong> and <\/strong><math data-latex=\"\u2220C = 2x + 48^\u2218\"><semantics><mrow><mi>\u2220<\/mi><mi>C<\/mi><mo>=<\/mo><mn>2<\/mn><mi>x<\/mi><mo>+<\/mo><msup><mn>48<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\u2220C = 2x + 48^\u2218<\/annotation><\/semantics><\/math><strong>. What is the value of x?<\/strong><br><br>A. 15<br>B. 18<br>C. 20<br>D. 24<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>In a cyclic quadrilateral, opposite angles are supplementary:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi mathvariant=\"normal\">\u2220<\/mi><mi>A<\/mi><mo>+<\/mo><mi mathvariant=\"normal\">\u2220<\/mi><mi>C<\/mi><mo>=<\/mo><msup><mn>180<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\angle A + \\angle C = 180^\\circ<\/annotation><\/semantics><\/math>So,<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mn>4<\/mn><mi>x<\/mi><mo>+<\/mo><mn>12<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mi>x<\/mi><mo>+<\/mo><mn>48<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>180<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(4x+12) + (2x+48) = 180<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>6<\/mn><mi>x<\/mi><mo>+<\/mo><mn>60<\/mn><mo>=<\/mo><mn>180<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">6x + 60 = 180<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>6<\/mn><mi>x<\/mi><mo>=<\/mo><mn>120<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">6x = 120<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>20<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x = 20<\/annotation><\/semantics><\/math>\u2705 Answer: <strong>C. 20<\/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>A, B, C, D, E, F and G live on seven different floors of a building numbered 1 to 7 from bottom to top.<br>Only one person lives above C.<br>D lives immediately below C.<br>A lives above D but below G.<br>Only two people live below E.<br>F lives below B.<br>Who lives on floor number 3?<br><\/strong><br>A. E<br>B. B<br>C. D<br>D. F<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Let us place the floors.<br>Only one person lives above C, so C is on floor 6.<br>D lives immediately below C, so D is on floor 5.<br>A lives above D but below G, so A must be on floor 4 and G on floor 7.<br>Only two people live below E, so E is on floor 3.<br>That leaves B and F for floors 1 and 2. Since F lives below B, F is floor 1 and B is floor 2.<br>So floor 3 has <strong>E<\/strong>.<br>\u2705 Answer: <strong>A. E<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 29<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Where is the National Academy of Indian Railways (formerly Railway Staff College) located?<br><\/strong><br>A. Bhubaneswar<br>B. Perambur, Chennai<br>C. Vadodara (Baroda), Gujarat<br>D. Nashik<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>C. Vadodara (Baroda), Gujarat<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 30<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The LCM of two numbers is 1008 and their HCF is 24. If one of the numbers is 168, the other number is:<br><\/strong><br>A. 132<br>B. 144<br>C. 156<br>D. 168<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Use the identity:<br>LCM \u00d7 HCF = product of the two numbers<br>So product of the numbers is:<br>1008 \u00d7 24 = 24192<br>If one number is 168, the other is:<br>24192\/168 = 144<br>\u2705 Answer: <strong>B. 144<\/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>Which station is the headquarters of the East Coast Railway?<\/strong><br><br>A. Bhubaneswar<br>B. Perambur, Chennai<br>C. Vadodara (Baroda), Gujarat<br>D. Nashik<\/p>\n\n\n\n<p class=\"is-style-success\">\u2705 Answer: <strong>A. Bhubaneswar<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 32<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Riya, Sia and Tara invest \u20b9900, \u20b91200 and \u20b91500 respectively in a business. If the annual profit is \u20b91800, what is Tara\u2019s share?<br><\/strong><br>A. \u20b9700<br>B. \u20b9720<br>C. \u20b9750<br>D. \u20b9800<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>The investment ratio is:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>900<\/mn><mo>:<\/mo><mn>1200<\/mn><mo>:<\/mo><mn>1500<\/mn><mo>=<\/mo><mn>3<\/mn><mo>:<\/mo><mn>4<\/mn><mo>:<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">900:1200:1500 = 3:4:5<\/annotation><\/semantics><\/math><br>Total parts:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>3<\/mn><mo>+<\/mo><mn>4<\/mn><mo>+<\/mo><mn>5<\/mn><mo>=<\/mo><mn>12<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3+4+5=12<\/annotation><\/semantics><\/math>Tara\u2019s share is:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>5<\/mn><mn>12<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>1800<\/mn><mo>=<\/mo><mn>750<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{5}{12}\\times 1800 = 750<\/annotation><\/semantics><\/math><strong>\u2705 Answer: C. \u20b9750<\/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>Which option follows the same operation pattern as the given sets?<br>6\u221211\u221222\u221232; 9\u221214\u221228\u221238<\/strong><br><br>A. 8 &#8211; 13 &#8211; 26 &#8211; 36<br>B. 8 &#8211; 14 &#8211; 28 &#8211; 38<br>C. 9 &#8211; 14 &#8211; 28 &#8211; 42<br>D. 7 &#8211; 12 &#8211; 24 &#8211; 37<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Look at the pattern in each set:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>6<\/mn><mo>\u2192<\/mo><mn>11<\/mn><mo>\u2192<\/mo><mn>22<\/mn><mo>\u2192<\/mo><mn>32<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">6 \\to 11 \\to 22 \\to 32<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>9<\/mn><mo>\u2192<\/mo><mn>14<\/mn><mo>\u2192<\/mo><mn>28<\/mn><mo>\u2192<\/mo><mn>38<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">9 \\to 14 \\to 28 \\to 38<\/annotation><\/semantics><\/math><br>The operations are:<br>+5, then \u00d72, then +10<br>Check option A:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>8<\/mn><mo>\u2192<\/mo><mn>13<\/mn><mo>\u2192<\/mo><mn>26<\/mn><mo>\u2192<\/mo><mn>36<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">8 \\to 13 \\to 26 \\to 36<\/annotation><\/semantics><\/math>That follows the same pattern exactly.<br>\u2705 Answer: <strong>A. 8 &#8211; 13 &#8211; 26 &#8211; 36<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 34<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>If a : b = 3 : 4 and b : c = 6 : 5, then the ratio a : c is <strong><em>_<\/em><\/strong>__.<\/strong><br><br>A. 930<br>B. 465<br>C. 558<br>D. 372<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Given:<br>a : b = 3 : 4 and b : c = 6 : 5<br>Make the middle term equal.<br>LCM of 4 and 6 is 12.<br>So:<br>a : b = 9 : 12<br>b : c = 12 : 10<br>Therefore:<br>a : c = 9 : 10<br><strong>\u2705 Answer: A. 9:10<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 35<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Where is the Integral Coach Factory (ICF) located?<\/strong><br><br>A. Bhubaneswar<br>B. Perambur, Chennai<br>C. Vadodara (Baroda), Gujarat<br>D. Nashik<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\u2705 Answer: B. Perambur, Chennai<\/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>In a certain code language, the code of a word is the sum of the alphabetical positions of its letters. What is the code for FARM?<\/strong><br><br>A. 36<br>B. 38<br>C. 40<br>D. 42<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>FARM:<br>F = 6<br>A = 1<br>R = 18<br>M = 13<br>Add them:<br>6 + 1 + 18 + 13 = 38<br>\u2705 Answer: <strong>B. 38<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 37<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which of the following letter-clusters does not belong to the group?<\/strong><br><br>A. QV-TX<br>B. ZE-CG<br>C. KP-NR<br>D. FI-JM<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Look at the letter shifts:<br>QV \u2192 TX is +4, +3<br>ZE \u2192 CG is +4, +3<br>KP \u2192 NR is +4, +3<br>FI \u2192 JM is +4, +4<br>So the odd one out is FI-JM.<br><strong>\u2705 Answer: D. FI-JM<\/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>Five numbers are given below:<br>135, 794, 342, 909, 567<br>If arranged in ascending order, how many numbers remain in the same position?<\/strong><br><br>A. 0<br>B. 1<br>C. 2<br>D. 3<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Arrange in ascending order:<br>135, 794, 342, 909, 567<br>Compare with the original order:<br>135, 342, 567, 794, 909<br>Only <strong>135<\/strong> remains in the same position.<br>So the number of unchanged positions is <strong>1<\/strong>.<br><strong>\u2705 Answer: B. 1<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 39<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Who was appointed as India&#8217;s High Commissioner to Bangladesh in April 2026, marking a rare political appointment to a major diplomatic post?<br><\/strong><br>A. S. Jaishankar<br>B. Dinesh Trivedi<br>C. Vikas Swarup<br>D. Ajit Agarkar<\/p>\n\n\n\n<p class=\"is-style-success\">Dinesh Trivedi: Former Union Minister Dinesh Trivedi was appointed in April 2026, signaling a shift toward direct political engagement with Bangladesh.<br>\u2705 Answer: <strong>B. Dinesh Trivedi<\/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>Which Indian state topped the overall medal tally in the Khelo India Tribal Games concluded in April 2026?<\/strong><br><br>A. Odisha<br>B. Jharkhand<br>C. Karnataka<br>D. Chhattisgarh<\/p>\n\n\n\n<p class=\"is-style-success\">Karnataka: Karnataka emerged as the champion with 23 gold medals, followed by Odisha and Jharkhand.<br>\u2705 Answer: <strong>C. Karnataka<\/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><strong>In April 2026, ISRO conducted &#8220;Mission MITRA&#8221; (a team behavioral study for the Gaganyaan programme) at which high-altitude location?<\/strong><\/strong><br><br>A. Leh<br>B. Tawang<br>C. Gulmarg<br>D. Spiti Valley<\/p>\n\n\n\n<p class=\"is-style-success\">Leh: The high-altitude environment of Leh served as a natural analog for spaceflight to study team communication and stress resilience for Gaganyaan.<br><strong>\u2705 Answer: A. Leh<\/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>If a : b :: b : c; c = 6a; and b = 8, find the positive value of c.<\/strong><br><br>A. 8<br>B. 12<br>C. 18<br>D. 20<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Ratio<\/strong><br>Given:<br>a : b = b : c<br>c = 6a, b = 8<br>\u21d2 b<sup>2<\/sup> = ac<br>64 = a(6a)<br>64 = 6a<sup>2<\/sup><br><math data-latex=\"a^2 = \\frac{64}{6} \\\\ a^2 = 9 \\\\ a = \\sqrt{9}\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><mfrac><mn>64<\/mn><mn>6<\/mn><\/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><mn>9<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>a<\/mi><mo>=<\/mo><msqrt><mn>9<\/mn><\/msqrt><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">a^2 = \\frac{64}{6} \\\\ a^2 = 9 \\\\ a = \\sqrt{9}<\/annotation><\/semantics><\/math><br>\u21d2 a = 3<br>c = 6a = 18<br><strong>\u2705 Answer: C. 18<\/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>Who became the world&#8217;s first quadruple amputee (limbless) archery champion in April 2026?<\/strong><br><br>A. Sheetal Devi<br>B. Payal Nag<br>C. Jyoti Baliyan<br>D. Harvinder Singh<\/p>\n\n\n\n<p class=\"is-style-success\">Payal Nag: 18-year-old Payal Nag from Odisha won gold at the World Para Archery Series Final in Bangkok, defeating Sheetal Devi.<br><strong>\u2705 Answer: B. Payal Nag<\/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>Two trains are moving in opposite directions at speeds of 130 km\/h and 105 km\/h. The length of one train is 390 m. If they cross each other in 9 seconds, the length of the other train is:<\/strong><br><br>A. 65.27 m<br>B. 197.43 m<br>C. 235 m<br>D. 587.43 m<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Trains<\/strong><br>Speed = 130+105 = 235 km\/h<br><strong>The simple trick to convert to m\/s is by multiplying it with 5\/18.<br><\/strong>\u2192 235 \u00d7 5\/18 = 65.27 m\/s<br>Distance = 65.27 \u00d7 9 = 587.43 m<br>Other train = 587.43 \u2212 390 = <strong>197.43 m<\/strong><br>\u2705 Answer: <strong>A. 197.43<\/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>Sohan and Rohan can complete a piece of work alone in 9 days and 18 days respectively. They work on alternate days, with Sohan starting on Day 1. In how many days will the work be completed?<\/strong><br><br>A. 12<br>B. 14<br>C. 18<br>D. 22<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Work<\/strong><br>Sohan = 1\/9<br>Rohan = 1\/18<br>2 days work: (1 cycle means 2 days)<br>1\/9 + 1\/18<br><math data-latex=\"\\frac{2 + 1}{18} \\\\ \\frac{3}{18}\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mrow><mn>2<\/mn><mo>+<\/mo><mn>1<\/mn><\/mrow><mn>18<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mn>3<\/mn><mn>18<\/mn><\/mfrac><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\frac{2 + 1}{18} \\\\ \\frac{3}{18}<\/annotation><\/semantics><\/math><br>= 1\/6<br>6 cycles \u2192 12 days = full work<br><strong>\ud83c\udfaf FINAL ANSWER: A. 12\u200b<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 46<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Count the number of digits in the following series that are immediately preceded by a symbol and immediately followed by a letter.<br>A * 7 B # $ 3 C @ 5 1 D % 2 E &amp; 9 F + G<\/strong><br><br>A. 2<br>B. 3<br>C. 4<br>D. 5<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Check the numbers that are immediately preceded by a symbol and immediately followed by a letter:<br>Series:<br>A * 7 B # $ 3 C @ 5 1 D % 2 E &amp; 9 F + G<br><br><strong>Qualifying digits are:<br><\/strong>7 \u2192 preceded by * and followed by B<br>3 \u2192 preceded by $ and followed by C<br>2 \u2192 preceded by % and followed by E<br>9 \u2192 preceded by &amp; and followed by F<br>So the count is <strong>4<\/strong>.<br><strong>\u2705 Answer: C. 4<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 47<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What will come in place of the question mark if + and \u2212 are interchanged and \u00d7 and \u00f7 are interchanged?<br>30 \u00f7 5 + 6 \u00d7 2 \u2212 4 = ?<\/strong><br><br>A. 149<br>B. 151<br>C. 153<br>D. 155<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Interchange:<br>+ and \u2212<br>\u00d7 and \u00f7<br><br>So,<br>30\u00f75+6\u00d72\u22124<br>becomes<br>30\u00d75\u22126\u00f72+4<br><br>Now evaluate:<br>30\u00d75=150, 6\u00f72=3<br>150\u22123+4=151<br><strong>\u2705 Answer: B. 151<\/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>A conical tent has a base radius of 9 metres and height of 21 metres. If cloth for the curved surface costs \u20b938 per square metre, what is the total cost? (use = <\/strong><math data-latex=\"\\pi = 3.14\"><semantics><mrow><mi>\u03c0<\/mi><mo>=<\/mo><mn>3.14<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\pi = 3.14<\/annotation><\/semantics><\/math><strong>)<br><\/strong><br>A. \u20b926,000.8<br>B. \u20b932,216.4<br>C. \u20b936,482.6<br>D. \u20b942,293.8<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Cone Surface Area<\/strong><br>l = \u221a(9\u00b2 + 21\u00b2) = 30<br>CSA = \u03c0rl = \u03c0\u00d79\u00d730 = 270\u03c0<br>\u2248 847.8 m\u00b2<br>Cost = 847.8 \u00d7 38 = \u20b932,216.4<br><strong>\u2705 Answer: B. \u20b932,216.4<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 49<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What comes next in the series?<br>3, 7, 15, 31, 63, ?<\/strong><br><br>A. 123<br>B. 125<br>C. 127<br>D. 129<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Series:<br>3, 7, 15, 31, 63, ?<br><br>Differences:<br>4,8,16,32<br>The differences are doubling each time, so the next difference is:<br>64<br>Therefore:<br>63+64=127<br><strong>\u2705 Answer: C. 127<\/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>AB is parallel to CD. A transversal intersects them. If one corresponding angle is <\/strong><math data-latex=\"4x + 8^\u2218\"><semantics><mrow><mn>4<\/mn><mi>x<\/mi><mo>+<\/mo><msup><mn>8<\/mn><mo form=\"prefix\" stretchy=\"false\">\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">4x + 8^\u2218<\/annotation><\/semantics><\/math><strong> and the equal corresponding angle is <\/strong><math data-latex=\"2x + 38^\u2218\"><semantics><mrow><mn>2<\/mn><mi>x<\/mi><mo>+<\/mo><msup><mn>38<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">2x + 38^\u2218<\/annotation><\/semantics><\/math><strong>, what is the measure of the angle?<br><\/strong><br>A. <math data-latex=\"64^\\circ\"><semantics><msup><mn>64<\/mn><mo>\u2218<\/mo><\/msup><annotation encoding=\"application\/x-tex\">64^\\circ<\/annotation><\/semantics><\/math><br>B. <math data-latex=\"66^\\circ\"><semantics><msup><mn>66<\/mn><mo>\u2218<\/mo><\/msup><annotation encoding=\"application\/x-tex\">66^\\circ<\/annotation><\/semantics><\/math><br>C. <math data-latex=\"68^\\circ\"><semantics><msup><mn>68<\/mn><mo>\u2218<\/mo><\/msup><annotation encoding=\"application\/x-tex\">68^\\circ<\/annotation><\/semantics><\/math><br>D. <math data-latex=\"70^\\circ\"><semantics><msup><mn>70<\/mn><mo>\u2218<\/mo><\/msup><annotation encoding=\"application\/x-tex\">70^\\circ<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Since AB is parallel to CD, corresponding angles are equal:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>4<\/mn><mi>x<\/mi><mo>+<\/mo><mn>8<\/mn><mo>=<\/mo><mn>2<\/mn><mi>x<\/mi><mo>+<\/mo><mn>38<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">4x+8 = 2x+38<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><mi>x<\/mi><mo>=<\/mo><mn>30<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2x = 30<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>=<\/mo><mn>15<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x = 15<\/annotation><\/semantics><\/math>Now the angle:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>4<\/mn><mi>x<\/mi><mo>+<\/mo><mn>8<\/mn><mo>=<\/mo><mn>4<\/mn><mo stretchy=\"false\">(<\/mo><mn>15<\/mn><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mn>8<\/mn><mo>=<\/mo><msup><mn>68<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">4x+8 = 4(15)+8 = 68^\\circ<\/annotation><\/semantics><\/math><strong>\u2705 Answer: C<\/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 2 (Free Practice Test 1) With Solutions And Exam Tricks (Part 3: Question 51-75)<\/h2>\n\n\n\n<p>Let&#8217;s take the mock test of RRB NTPC Exam 1 part 3 which contains questions from 51 to 75. You can prepare for any competitive exams here for free. There are no hidden charges. We even give you rewards if you perform well to motivate you in your study. Here you will try to attempt RRB NTPC Graduate CBT 2 exam practice test 1. The competitive exam is divided into 4 parts each with 25 questions. You are not just taking the exercise but also learning from the solutions, explanations, and hack tricks.<\/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 = 19;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-19\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"19\">\n            <div class=\"kq-loading\">Loading quiz...<\/div>\n        <\/div>\n        \n    <div id=\"kq-auth-modal\" class=\"kq-auth-modal\" style=\"display:none;\">\n      <div class=\"kq-auth-modal-inner\">\n        <button id=\"kq-auth-close\" class=\"kq-auth-close\" aria-label=\"Close\">\u2716<\/button>\n\n        <!-- TAB NAV -->\n        <div class=\"kq-auth-tabs\" role=\"tablist\">\n          <button class=\"kq-tab active\" data-tab=\"register\" type=\"button\" role=\"tab\" aria-selected=\"true\">Register<\/button>\n          <button class=\"kq-tab\" data-tab=\"login\" type=\"button\" role=\"tab\" aria-selected=\"false\">Login<\/button>\n          <button class=\"kq-tab\" data-tab=\"forgot\" type=\"button\" role=\"tab\" aria-selected=\"false\">Forgot<\/button>\n        <\/div>\n\n        <!-- PANELS -->\n        <div class=\"kq-auth-panel-wrap\">\n\n          <!-- REGISTER -->\n          <div class=\"kq-auth-panel\" data-panel=\"register\" style=\"display:block\">\n            <div class=\"kq-auth-card\">\n              <h3>Register<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-username\" placeholder=\"Username\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-email\" placeholder=\"Email\" type=\"email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-signup-btn\" class=\"button kq-btn-small\">Register<\/button>\n              <small style=\"display:block;margin-top:8px;\">Already registered? Use Login tab.<\/small>\n            <\/div>\n          <\/div>\n\n          <!-- LOGIN -->\n          <div class=\"kq-auth-panel\" data-panel=\"login\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Login<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-login-btn\" class=\"button kq-btn-small\">Login<\/button>\n            <\/div>\n          <\/div>\n\n          <!-- FORGOT -->\n          <div class=\"kq-auth-panel\" data-panel=\"forgot\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Forgot Password<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-newpass\" placeholder=\"New Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-forgot-btn\" class=\"button kq-btn-small\">Update Password<\/button>\n            <\/div>\n          <\/div>\n\n        <\/div>\n\n      <\/div>\n    <\/div>\n    \n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">The Solution and Explanation of The Competitive Exam<\/h2>\n\n\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"Which cell organelle contains chlorophyll and is responsible for photosynthesis?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Chloroplast.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Rohan walks 10 km east, 7 km north, 6 km west, and 4 km south. How far and in which direction is he from the starting point?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 5 km, North-East and learn the real way to solve.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The average of 13 numbers is 50. The average of the first 7 numbers is 48 and that of the last 7 numbers is 52. What is the 7th number?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 50. Let's learn the trick to solve it in no time.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"As of April 2026, which country has overtaken the United States to become India's top trading partner for the financial year 2025-26?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"China is the new country which India does most of the trade.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Find the missing term in the series:\nCEG 11, EGI 14, GIK 17, IKM 20, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is KMO 23, but how, let's learn.\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"Find the mode of the following grouped data. Give the answer correct to 2 decimal places.\n$$ \\begin{array}{|c|c|} \\hline \\textbf{Age in years} & \\textbf{No. of Students} \\\\ \\hline {20-30} & {6} \\\\ \\hline {30-40} & {11} \\\\ \\hline {40-50} & {19} \\\\ \\hline {50-60} & {15} \\\\ \\hline {60-70} & {9} \\\\ \\hline {70-80} & {5}\\\\ \\hline \\end{array} $$\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 46.67, let's learn how to solve it quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Read the statements and conclusions carefully.\nStatements:\nAll pens are tools.\nSome tools are metal.\nAll metal things are durable.\nConclusions:\n(I) Some durable things are tools.\n(II) All pens are durable.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Only conclusion (I) follows. Let's learn how to solve it in 3 seconds.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who founded the Servants of India Society?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Gopal Krishna Gokhale.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A shopkeeper buys 48 dozen pencils at \u20b9240 per dozen and sells each pencil at \u20b925. What is his profit percentage?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 25%. Let's learn the trick to solve it in 3 seconds.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Solve the system of equations:\nx + y + z = 6\n2x + y + z = 8\nx + 2y + z = 7\",\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 x=2, y=1, z=3.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The price of a product decreases by 20%, increases by 25%, decreases by 10%, and finally increases by 40%. What is the net change compared with the original price?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Increase by 26% is the right answer to choose.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What is the average of the first 50 odd natural numbers?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 50, let's learn the simple trick to solve it quickly.\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who built the Brihadishvara Temple at Thanjavur?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Raja Raja I.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Choose the correct analogy:\nJNR : LPT :: SUV : ?\",\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 UWX.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Select the set in which the numbers are related in the same way as the following sets:\n(4,16,8), (5,25,10)\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is (6,36,12). Let's learn the right trick to solve it quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Barren Island, India\u2019s only active volcano, is part of which island group?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Andaman and Nicobar Islands. We have explained it simply for you.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which ratio is the largest among the following?\",\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\": \"150 men have provisions for 24 days. If 50 men leave, for how many days will the same provisions last for the remaining men?\",\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 36.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which article of the Indian Constitution directs the State to promote cottage industries in rural areas?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Article 43\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A dealer buys two articles X and Y for \u20b91000 each. He marks both at the same price. He sells X after two successive discounts of 20% and 25%, and still earns \u20b9200 profit. If he sells Y at a single discount of 40%, what is the profit percentage on Y?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 20%. Let's learn the way to solve it in 3 second.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Three of the following four letter-cluster pairs are alike in a certain way and form a group. Which one does not belong to the group?\",\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 FH-IK.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Simplify: $\\frac{\\sqrt[3]{1728}}{\\sqrt[4]{81}} \\times \\frac{3}{18} \\times 54$\",\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 36.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What should come next in the series?\n2, 6, 12, 20, 30, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 42.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which hormone is secreted by the beta cells of the pancreas and regulates blood sugar?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Insulin\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What comes next in the series?\n1, 4, 9, 16, 25, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"36\"\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>Which cell organelle contains chlorophyll and is responsible for photosynthesis?<br><\/strong><br>A. Mitochondrion<br>B. Chloroplast<br>C. Ribosome<br>D. Lysosome<\/p>\n\n\n\n<p class=\"is-style-success\">Chloroplasts contain chlorophyll, and chlorophyll is the pigment used in photosynthesis. Britannica states that chloroplasts are green because they contain chlorophyll, which is vital for photosynthesis.<br>\u2705 Answer: <strong>B. Chloroplast<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 52<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Rohan walks 10 km east, 7 km north, 6 km west, and 4 km south. How far and in which direction is he from the starting point?<\/strong><br><br>A. 5 km, North-East<br>B. 5 km, North-West<br>C. 7 km, North-East<br>D. 3 km, North-East<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Track the movement step by step:<br>10 km east<br>7 km north<br>6 km west<br>4 km south<br><br>Net movement:<br>East: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>10<\/mn><mo>\u2212<\/mo><mn>6<\/mn><mo>=<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">10-6=4<\/annotation><\/semantics><\/math><br>North: <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>7<\/mn><mo>\u2212<\/mo><mn>4<\/mn><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">7-4=3<\/annotation><\/semantics><\/math><br>So he is 4 km east and 3 km north of the starting point.<br>Distance:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msqrt><mrow><msup><mn>4<\/mn><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><\/mrow><\/msqrt><mo>=<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{4^2+3^2}=5<\/annotation><\/semantics><\/math><br>So the answer is <strong>5 km, North-East<\/strong>.<br>\u2705 Answer: <strong>A. <strong>5 km, North-East<\/strong><\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 53<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The average of 13 numbers is 50. The average of the first 7 numbers is 48 and that of the last 7 numbers is 52. What is the 7th number?<\/strong><br><br>A. 48<br>B. 49<br>C. 50<br>D. 51<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Total of 13 numbers:<br>13 \u00d7 50 = 650<br><br>Total of first 7:<br>7 \u00d7 48 = 336<br><br>Total of last 7:<br>7 \u00d7 52 = 364<br>If we add the first 7 and last 7 totals, the 7th number is counted twice:<br>336 + 364 = 650 + x<br>700 = 650+x<br>x = 50<br>\u2705 Answer: <strong>C. 50<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 54<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>As of April 2026, which country has overtaken the United States to become India&#8217;s top trading partner for the financial year 2025-26?<br><\/strong><br>A. UAE<br>B. Russia<br>C. China<br>D. Germany<\/p>\n\n\n\n<p class=\"is-style-success\">China: Recent data for FY 2025-26 indicates China has reclaimed the spot as India&#8217;s largest trading partner.<br>\u2705 Answer: <strong>C. China<\/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>Find the missing term in the series:<br>CEG 11, EGI 14, GIK 17, IKM 20, ?<\/strong><br><br>A. KMO 23<br>B. KMP 23<br>C. KMO 24<br>D. LMO 23<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Coding Series<\/strong><br>Solution<br>The pattern is:<br>First letters: C, E, G, I, K<br>Second letters: E, G, I, K, M<br>Third letters: G, I, K, M, O<br>Numbers: 11, 14, 17, 20, 23<br>So the missing term is KMO 23.<br><strong>\u2705 Answer: A. KMO 23<\/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>Find the mode of the following grouped data. Give the answer correct to 2 decimal places.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Age in years<\/th><th>No. of Students<\/th><\/tr><\/thead><tbody><tr><td>20-30<\/td><td>6<\/td><\/tr><tr><td>30-40<\/td><td>11<\/td><\/tr><tr><td>40-50<\/td><td>19<\/td><\/tr><tr><td>50-60<\/td><td>15<\/td><\/tr><tr><td>60-70<\/td><td>9<\/td><\/tr><tr><td>70-80<\/td><td>5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"is-style-info\">A. 45.67<br>B. 46.67<br>C. 47.67<br>D. 48.67<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Mode (Grouped Data)<\/strong><br>Modal class = 40\u201350 (highest frequency = 19)<br>Formula:<br>Mode = <math data-latex=\"L + \\frac{f_1 - f_0}{2f_1 - f_0 - f_2} \\times h\"><semantics><mrow><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\">L + \\frac{f_1 &#8211; f_0}{2f_1 &#8211; f_0 &#8211; f_2} \\times h<\/annotation><\/semantics><\/math><br><br><math data-latex=\"= 40 + \\frac{19 - 11}{2\\times19 - 11 - 15} \\times 10 \\\\ = 40 + \\frac{8}{38 - 26} \\times 10 \\\\ = 40 + \\frac{80}{12} \\\\ = 40 + 6.666... \\\\ = 46.67\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mo>=<\/mo><mn>40<\/mn><mo>+<\/mo><mfrac><mrow><mn>19<\/mn><mo>\u2212<\/mo><mn>11<\/mn><\/mrow><mrow><mn>2<\/mn><mo>\u00d7<\/mo><mn>19<\/mn><mo>\u2212<\/mo><mn>11<\/mn><mo>\u2212<\/mo><mn>15<\/mn><\/mrow><\/mfrac><mo>\u00d7<\/mo><mn>10<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mo>=<\/mo><mn>40<\/mn><mo>+<\/mo><mfrac><mn>8<\/mn><mrow><mn>38<\/mn><mo>\u2212<\/mo><mn>26<\/mn><\/mrow><\/mfrac><mo>\u00d7<\/mo><mn>10<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mo>=<\/mo><mn>40<\/mn><mo>+<\/mo><mfrac><mn>80<\/mn><mn>12<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mo>=<\/mo><mn>40<\/mn><mo>+<\/mo><mn>6.666&#8230;<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mo>=<\/mo><mn>46.67<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">= 40 + \\frac{19 &#8211; 11}{2\\times19 &#8211; 11 &#8211; 15} \\times 10 \\\\ = 40 + \\frac{8}{38 &#8211; 26} \\times 10 \\\\ = 40 + \\frac{80}{12} \\\\ = 40 + 6.666&#8230; \\\\ = 46.67<\/annotation><\/semantics><\/math><br><br>\u2705 Answer: <strong>B. 46.67<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 57<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Read the statements and conclusions carefully.<br>Statements:<br>All pens are tools.<br>Some tools are metal.<br>All metal things are durable.<\/strong><br><strong>Conclusions:<br>(I) Some durable things are tools.<br>(II) All pens are durable.<\/strong><br><br>A. Only conclusion (I) follows<br>B. Only conclusion (II) follows<br>C. Both conclusions follow<br>D. Neither conclusion follows<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>From the statements:<br>All pens are tools.<br>Some tools are metal.<br>All metal things are durable.<br><br>Since some tools are metal and all metal things are durable, it follows that <strong>some durable things are tools<\/strong>.<br>But we cannot say that all pens are durable, because there is no statement linking all pens to durable things directly.<br>So only conclusion <strong>(I)<\/strong> follows.<br>\u2705 Answer: <strong>A. Only conclusion (I) follows<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 58<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Who founded the Servants of India Society?<br><\/strong><br>A. Bal Gangadhar Tilak<br>B. Gopal Krishna Gokhale<br>C. Dadabhai Naoroji<br>D. Mahadev Govind Ranade<\/p>\n\n\n\n<p class=\"is-style-success\">Britannica states that the Servants of India Society was founded by Gopal Krishna Gokhale in 1905.<br><strong>The correct answer is B: Gopal Krishna Gokhale<\/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>A shopkeeper buys 48 dozen pencils at \u20b9240 per dozen and sells each pencil at \u20b925. What is his profit percentage?<\/strong><br><br>A. 20%<br>B. 25%<br>C. 30%<br>D. 35%<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\ud83d\udd34 Given<\/strong><br>Bought <strong>48 dozens<\/strong> at \u20b9240 per dozen<br>Sold each at \u20b925<br>\ud83d\udc49 1 dozen = 12<br><br><strong>\ud83e\udde0 Core Concept<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Profit&nbsp;%<\/mtext><mo>=<\/mo><mfrac><mrow><mi>S<\/mi><mi>P<\/mi><mo>\u2212<\/mo><mi>C<\/mi><mi>P<\/mi><\/mrow><mrow><mi>C<\/mi><mi>P<\/mi><\/mrow><\/mfrac><mo>\u00d7<\/mo><mn>100<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Profit \\%} = \\frac{SP &#8211; CP}{CP} \\times 100<\/annotation><\/semantics><\/math><br><strong>\u26a1 STEP 1: Work PER DOZEN (fastest trick)<\/strong><br>\ud83d\udc49 Always convert to <strong>same unit<\/strong><br>Cost Price per dozen: CP = \u20b9240<br>Selling Price per dozen: 12 x 25 = 300<br><br><strong>\ud83e\udde0 STEP 2: Profit per dozen<\/strong><br>Profit: 300 &#8211; 240 = 60<br><br><strong>\ud83e\udde0 STEP 3: Profit %<br><\/strong><math data-latex=\"\\frac{60}{240} \\times 100 \\\\ \\frac{1}{4} \\times 100 = 25\\%\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mn>60<\/mn><mn>240<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>100<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mn>1<\/mn><mn>4<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>100<\/mn><mo>=<\/mo><mn>25<\/mn><mi>%<\/mi><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\frac{60}{240} \\times 100 \\\\ \\frac{1}{4} \\times 100 = 25\\%<\/annotation><\/semantics><\/math><br><br>\u2705 Answer: <strong>B. 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 60<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Solve the system of equations:<br>x + y + z = 6<br>2x + y + z = 8<br>x + 2y + z = 7<\/strong><br><br>A. x=2, y=1, z=3<br>B. x=3, y=1, z=2<br>C. x=1, y=2, z=3<br>D. x=2, y=3, z=1<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Subtract the first equation from the second:<br><\/strong>2x + y + z = 8  &#8230;(2)<br>x + y + z = 6  &#8230;(1)<br>Subtract (-)<br>(2x &#8211; x ) + (y &#8211; y) + (z -z ) = (8 &#8211; 6)<br>x = 2<br><br><strong>Subtract the first equation from the third:<br><\/strong>x + 2y + z = 7 &#8230;(3)<br>x + y + z = 6  &#8230;(1)<br>Subtract (-)<br>(x -x) + (2y &#8211; y) + (z &#8211; z) = (7 &#8211; 6)<br>y = 1<br><br>[By the way based on options we have already got our correct answer Option A. But in order to learn, we proceed further.]<br><br>Now substitute both x = 2 and y = 1 into the first equation x + y + z = 6 &#8230;(1)<br>2 + 1 + z = 6<br>3 + z = 6<br>z = 6 &#8211; 3<br>z = 3<br>\u2705 Answer: <strong>B. x = 4, y = \u22122, z = 3<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 61<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The price of a product decreases by 20%, increases by 25%, decreases by 10%, and finally increases by 40%. What is the net change compared with the original price?<\/strong><br><br>A. Increase by 26%<br>B. Decrease by 26%<br>C. Increase by 24%<br>D. Decrease by 24%<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Successive Change<\/strong><br>Solution<br>Apply the successive percentage changes as multipliers:<br>Assume the original: 1<br>Decrease 20% \u2192 20<br>Increase 25% \u2192 1.25<br>Decrease 10% \u2192 0.9<br>Increase 40% \u2192 1.4<br>Overall factor:<br>0.8\u00d71.25\u00d70.9\u00d71.4 = 1.26<br>So the final price is 126% of the original price, which means an <strong>increase of 26%<\/strong>.<br>\u2705 Answer: <strong>A. Increase by 26%<\/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>What is the average of the first 50 odd natural numbers?<\/strong><br><br>A. 25<br>B. 50<br>C. 75<br>D. 100<\/p>\n\n\n\n<p class=\"is-style-success\">The first 50 odd natural numbers are:<br>1,3,5,\u2026,99<br>For an arithmetic sequence, the average is the mean of the first and last terms:<br>Average = (1+99)\/2 = 50<br><br>Or directly, the average of the first n odd numbers is n.<br>So the answer is 50.<br>\u2705 Answer: <strong>B. 50<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 63<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Who built the Brihadishvara Temple at Thanjavur?<\/strong><br><br>A. Raja Raja I<br>B. Rajendra I<br>C. Kulottunga I<br>D. Parantaka I<\/p>\n\n\n\n<p class=\"is-style-success\">Britannica states that Raja Raja I built the Brihadishvara Temple at Thanjavur.<br>\u2705 Answer: <strong>A. Raja Raja I<\/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>Choose the correct analogy:<br>JNR : LPT :: SUV : ?<\/strong><br><br>A. UWX<br>B. TWX<br>C. VWX<br>D. UWY<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>In the pair JNR : LPT, each letter is shifted forward by 2:<br>J \u2192 L<br>N \u2192 P<br>R \u2192 T<br>Apply the same to SUV:<br>S \u2192 U<br>U \u2192 W<br>V \u2192 X<br>So the answer is UWX.<br>\u2705 Answer: <strong>A. UWX<\/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>Select the set in which the numbers are related in the same way as the following sets:<br>(4,16,8), (5,25,10)<\/strong><br><br>A. (6,36,12)<br>B. (6,35,12)<br>C. (7,48,14)<br>D. (8,60,16)<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pattern<\/strong><br>Solution<br>The relation in the given sets is:<br>second number = square of the first<br>third number = twice the first<br>Check option A:<br>6<sup>2<\/sup> = 36,  2 \u00d7 6 = 12<br>It matches the pattern.<br>\u2705 Answer: <strong>A. (6,36,12)<\/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 66<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Barren Island, India\u2019s only active volcano, is part of which island group?<\/strong><br><br>A. Lakshadweep Islands<br>B. Andaman and Nicobar Islands<br>C. Nicobar Islands only<br>D. Andaman Islands only<\/p>\n\n\n\n<p class=\"is-style-success\">While technically part of the larger Union Territory of Andaman and Nicobar Islands, it geographically belongs to the Andaman Island chain, not the Nicobar chain. Since a larger picture is present, it would be better to choose both.<br>\u2705 Answer: <strong>B. Andaman and Nicobar Islands<\/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>Which ratio is the largest among the following?<\/strong><br><br>A. 4:9<br>B. 7:15<br>C. 11:25<br>D. 13:30<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Largest Ratio<\/strong><br>Compare:<br>4\/9 = 0.444&#8230;<br>7\/15 = 0.466&#8230;<br>11\/25 = 0.44<br>13\/30 = 0.433&#8230;<br>The largest is 7:15.<br>\ud83d\udc49 <strong>Answer B. 7:15<\/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>150 men have provisions for 24 days. If 50 men leave, for how many days will the same provisions last for the remaining men?<\/strong><br><br>A. 30<br>B. 32<br>C. 36<br>D. 40<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pattern<\/strong><br>150 men \u2192 24 days<br>Total work (150 x 24) = 3600<br>50 leave, remaining (150 &#8211; 50 = 100)<br>\u2192 days = 3600\/100 = 36<br>\u2705 Answer: <strong>C. 36<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 69<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which article of the Indian Constitution directs the State to promote cottage industries in rural areas?<\/strong><br><br>A. Article 39<br>B. Article 41<br>C. Article 42<br>D. Article 43<\/p>\n\n\n\n<p class=\"is-style-success\">Article 43 of the Constitution states that the State shall endeavour to promote cottage industries in rural areas. The Constitution text and constitutional commentary identify this as part of the Directive Principles.<br>\u2705 Answer: <strong>D. Article 43<\/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>A dealer buys two articles X and Y for \u20b91000 each. He marks both at the same price. He sells X after two successive discounts of 20% and 25%, and still earns \u20b9200 profit. If he sells Y at a single discount of 40%, what is the profit percentage on Y?<\/strong><br><br>A. 15%<br>B. 20%<br>C. 25%<br>D. 30%<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Profit<\/strong><br>CP = 1000<br>For X, two successive discounts of 20% and 25% give:<br>Let MP = x<br>SP(X) = x \u00d7 0.8 \u00d7 0.75 = 0.6x<br>Since X gives a profit of \u20b9200 on cost price \u20b91000:<br>Total = 1200<br>SP(X): 0.6x = 1200<br>x = 1200\/0.6<br>x = 2000<br><br>For Y, a single discount of 40% gives:<br>SP(Y) = 60% of 2000 is = 1200<br>Profit: 1200 &#8211; 100 = 200<br><br>Profit percentage:<br>200\/1000 \u200b\u00d7 100 = 20%<br><strong>\ud83c\udfaf FINAL ANSWER: C. 20%\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>Three of the following four letter-cluster pairs are alike in a certain way and form a group. Which one does not belong to the group?<\/strong><br><br>A. LN-MO<br>B. PU-QV<br>C. TW-UX<br>D. FH-IK<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Check the pairwise pattern:<br>LN \u2192 MO = each letter shifts by +1<br>PU \u2192 QV = each letter shifts by +1<br>TW \u2192 UX = each letter shifts by +1<br>FH \u2192 IK = each letter shifts by +3<br>So <strong>FH-IK<\/strong> does not belong to the group<br><strong>\u2705 Answer: D. FH-IK<\/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>Simplify:<\/strong> <math data-latex=\"\\frac{\\sqrt[3]{1728}}{\\sqrt[4]{81}} \\times \\frac{3}{18} \\times 54\"><semantics><mrow><mfrac><mroot><mn>1728<\/mn><mn>3<\/mn><\/mroot><mroot><mn>81<\/mn><mn>4<\/mn><\/mroot><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>3<\/mn><mn>18<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>54<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{\\sqrt[3]{1728}}{\\sqrt[4]{81}} \\times \\frac{3}{18} \\times 54<\/annotation><\/semantics><\/math><br><br>A. 32<br>B. 34<br>C. 36<br>D. 38<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Simplify<\/strong><br>Solution<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mroot><mn>1728<\/mn><mn>3<\/mn><\/mroot><mo>=<\/mo><mn>12<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt[3]{1728}=12<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mroot><mn>81<\/mn><mn>4<\/mn><\/mroot><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt[4]{81}=3<\/annotation><\/semantics><\/math>Now evaluate:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>12<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>3<\/mn><mn>18<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>54<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{12}{3}\\times \\frac{3}{18}\\times 54<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>4<\/mn><mo>\u00d7<\/mo><mfrac><mn>1<\/mn><mn>6<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>54<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=4 \\times \\frac{1}{6}\\times 54<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo>=<\/mo><mn>4<\/mn><mo>\u00d7<\/mo><mn>9<\/mn><mo>=<\/mo><mn>36<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">=4 \\times 9 = 36<\/annotation><\/semantics><\/math><br><strong>\u2705 Answer: C. 36<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 73<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What should come next in the series?<br>2, 6, 12, 20, 30, ?<\/strong><br><br>A. 38<br>B. 40<br>C. 42<br>D. 44<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Series: 2,6,12,20,30,?<br><br>Differences: 4,6,8,10<br>The differences increase by 2 each time, so the next difference is: 12<br>Thus:<br>30 + 12 = 42<br>\u2705 Answer: <strong>B. 42<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 74<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which hormone is secreted by the beta cells of the pancreas and regulates blood sugar?<\/strong><br><br>A. Adrenaline<br>B. Thyroxine<br>C. Insulin<br>D. Glucagon<\/p>\n\n\n\n<p class=\"is-style-success\">Britannica states that insulin is a hormone produced by the beta cells of the islets of Langerhans in the pancreas and that it regulates blood sugar.<br>\u2705 Answer: <strong>C. Insulin<\/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>What comes next in the series?<br>1, 4, 9, 16, 25, ?<\/strong><br><br>A. 30<br>B. 35<br>C. 36<br>D. 40<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>The series is: 1,4,9,16,25,?<br>These are perfect squares:<br><math data-latex=\"1^2, 2^2, 3^2, 4^2, 5^2, ...\"><semantics><mrow><msup><mn>1<\/mn><mn>2<\/mn><\/msup><mo separator=\"true\">,<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo separator=\"true\">,<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><mo separator=\"true\">,<\/mo><msup><mn>4<\/mn><mn>2<\/mn><\/msup><mo separator=\"true\">,<\/mo><msup><mn>5<\/mn><mn>2<\/mn><\/msup><mo separator=\"true\">,<\/mo><mi>.<\/mi><mi>.<\/mi><mi>.<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">1^2, 2^2, 3^2, 4^2, 5^2, &#8230;<\/annotation><\/semantics><\/math><br>The next is:<br><math data-latex=\"6^2 = 36\"><semantics><mrow><msup><mn>6<\/mn><mn>2<\/mn><\/msup><mo>=<\/mo><mn>36<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">6^2 = 36<\/annotation><\/semantics><\/math><br><strong>\u2705 Answer: C. 36<\/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 2 (Free Practice Mock test 1) \u2013 <strong>Full Exercise With Smart Short Hack Solutions<\/strong> (Part 4: Question 76-100)<\/h2>\n\n\n\n<p>Try the free practice test of RRB NTPC Exam 1 part 4 of CBT Shift 2 which keeps questions from 76 to 100. All exams here are totally free. There are no hidden charges. We even give you rewards if you perform well to motivate you in your study. Here you will try to attempt RRB NTPC Graduate CBT 2 exam practice test 1. The competitive exam is divided into 4 parts each with 25 questions. You are not just taking the exercise but also learning from the solutions, explanations, and tricks.<\/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 = 20;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-20\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"20\">\n            <div class=\"kq-loading\">Loading quiz...<\/div>\n        <\/div>\n        \n    <div id=\"kq-auth-modal\" class=\"kq-auth-modal\" style=\"display:none;\">\n      <div class=\"kq-auth-modal-inner\">\n        <button id=\"kq-auth-close\" class=\"kq-auth-close\" aria-label=\"Close\">\u2716<\/button>\n\n        <!-- TAB NAV -->\n        <div class=\"kq-auth-tabs\" role=\"tablist\">\n          <button class=\"kq-tab active\" data-tab=\"register\" type=\"button\" role=\"tab\" aria-selected=\"true\">Register<\/button>\n          <button class=\"kq-tab\" data-tab=\"login\" type=\"button\" role=\"tab\" aria-selected=\"false\">Login<\/button>\n          <button class=\"kq-tab\" data-tab=\"forgot\" type=\"button\" role=\"tab\" aria-selected=\"false\">Forgot<\/button>\n        <\/div>\n\n        <!-- PANELS -->\n        <div class=\"kq-auth-panel-wrap\">\n\n          <!-- REGISTER -->\n          <div class=\"kq-auth-panel\" data-panel=\"register\" style=\"display:block\">\n            <div class=\"kq-auth-card\">\n              <h3>Register<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-username\" placeholder=\"Username\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-email\" placeholder=\"Email\" type=\"email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-signup-btn\" class=\"button kq-btn-small\">Register<\/button>\n              <small style=\"display:block;margin-top:8px;\">Already registered? Use Login tab.<\/small>\n            <\/div>\n          <\/div>\n\n          <!-- LOGIN -->\n          <div class=\"kq-auth-panel\" data-panel=\"login\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Login<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-login-btn\" class=\"button kq-btn-small\">Login<\/button>\n            <\/div>\n          <\/div>\n\n          <!-- FORGOT -->\n          <div class=\"kq-auth-panel\" data-panel=\"forgot\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Forgot Password<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-newpass\" placeholder=\"New Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-forgot-btn\" class=\"button kq-btn-small\">Update Password<\/button>\n            <\/div>\n          <\/div>\n\n        <\/div>\n\n      <\/div>\n    <\/div>\n    \n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Answer And Tricks of The RRB NTPC Competitive Exam<\/h2>\n\n\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"The following dataset represents the number of books read by 25 students in a month:\n11, 7, 2, 3, 4, 6, 4, 5, 5, 10, 6, 15, 4, 7, 2, 8, 9, 9, 6, 10, 1, 12, 13, 14, 6\nWhat is the mode of the dataset?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 6, let's learn the simple trick to solve it quickly.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Which Constitutional Amendment Act lowered the voting age in India from 21 years to 18 years?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 61st Amendment Act, 1988.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"At what rate per annum simple interest will a sum of money become 4 times itself in 15 years?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 20%. the pattern behind it simple.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"P can complete one round of a circular track in 12 minutes and Q can complete one round in 18 minutes. If they start at the same point and move in the same direction, after how many minutes will they meet for the first time?\",\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 36.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Read the statements and conclusions carefully.\nStatements:\nAll mugs are cups.\nSome cups are glassware.\nAll glassware are breakable.\nConclusions:\n(I) Some breakable things are cups.\n(II) All mugs are breakable.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Only conclusion (I) follows. let's learn how to do it within 5 second.\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"Which statement is true regarding file management in Windows?\n(i) A file moved to the Recycle Bin can be restored to its original folder.\n(ii) A file path represents the hierarchical location of the file in the folder structure.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The answer is (i) True, (ii) True, but how can you solve it quickly. Learn it.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If 3 is added to each even digit and 2 is subtracted from each odd digit in the number 3579246, how many digits will appear more than once in the new number thus formed?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is to understand the key concepts hidden behind it like two.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Rosy deposited \u20b916,000 at 15% compound interest per annum, compounded annually. The total amount received after 2 years is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is \u20b921,160. Learn how to calculate it in no time.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The \"Abhay\" AI-powered chatbot was launched by which organization to help citizens verify official notices and prevent \"digital arrest\" scams?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Central Bureau of Investigation (CBI)\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which letter-cluster should replace the question mark?\nMIM : ZTW :: UQU : ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is subtract of 6 and the addition of 3 each forward. The dame pattern is for options as well.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Three of the following four letter-cluster pairs are alike in a certain way and form a group. Which one does not belong to that group?\",\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\": \"Who took oath in April 2026 as India's first openly queer Member of Parliament (MP) in the Rajya Sabha?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Menaka Guruswamy\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"How often do non-Annex I Parties submit Biennial Update Reports (BURs) to the UNFCCC?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Every two years.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Simplify: $[6.75 + \\frac{1}{2}] \u2212 [4.2 \u2212 \\frac{3}{5}]$\",\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 3.65.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What should come next in the series?\n2, 6, 12, 20, 30, ?\",\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 42.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If a : b = 4 : 7 and b : c = 14 : 9, then what is a : c?\",\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 8:9.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Find the third proportional to 9 and 12.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is addition of ten and the addition of eight each forward. The dame pattern is for options as well.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Solve for $x$:\n$7x \u2212 5 = 44$\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is addition of ten and the addition of eight each forward. The dame pattern is for options as well.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Simplify: $\\frac{25^3 + 9^3}{25^2 - 25 \\times 9 + 9^2}$\u200b\",\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 34.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language, FIRE is coded as 7164 and RIFE is coded as 6174. What is the code for R?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is not position but the pattern value. The correct answer is 6.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"India has set a massive target to increase its nuclear power capacity to 100 Giga Watts (GW). By which year does the government plan to achieve this?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"2040\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following is an example of application software?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Word processor\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Six people A, B, C, D, E and F sit in a row facing north.\nA sits immediately left of B.\nB sits immediately left of C.\nD sits immediately right of C.\nF sits immediately right of D.\nE sits at the left end.\nWho sits between C and F?\",\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 D.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A boy flying a kite holds a string of length 26 m such that it makes an angle of 30\u00b0 with the ground. Find the height of the kite from the ground.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"We use sine here but a learning trick is when you see 30 degree and height. Consider it half. The correct answer is 13 m. Learn how to solve it in 5 seconds.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What should come in place of the question mark?\n5, 11, 19, 29, 41, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"There is a pattern here the table of 2 to increase the digits to the point of 41 + 14 = 55. Let's learn the trick behind it.\"\n    }\n  }\n  }\n}\n<\/script>\n\n\n\n<div class=\"wp-block-coblocks-accordion\">\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 76<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The following dataset represents the number of books read by 25 students in a month:<br>11, 7, 2, 3, 4, 6, 4, 5, 5, 10, 6, 15, 4, 7, 2, 8, 9, 9, 6, 10, 1, 12, 13, 14, 6<br>What is the mode of the dataset?<\/strong><br><br>A. 4<br>B. 5<br>C. 6<br>D. 7<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Mode (Ungrouped Data)<\/strong><br>Concept:<br>Mode = most frequent value<br>1, 2, 2, 3, 4, 4, 4, 5, 5, <strong>6, 6, 6, 6<\/strong>, 7, 7, 8, 9, 9, 10, 10, 11, 12, 13, 14, 15<br>Frequency check:<br>6 appears <strong>4 times<\/strong> (highest)<br>\u2705 Answer: <strong>C. 6<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 77<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which Constitutional Amendment Act lowered the voting age in India from 21 years to 18 years?<\/strong><br><br>A. 61st Amendment Act, 1988<br>B. 62nd Amendment Act, 1989<br>C. 63rd Amendment Act, 1989<br>D. 64th Amendment Act, 1990<\/p>\n\n\n\n<p class=\"is-style-success\">The <strong>61st Constitutional Amendment Act, 1988<\/strong> lowered the voting age in India from 21 years to 18 years by amending Article 326. The official legislative text identifies the act and its effect on the voting age.<br>\u2705 Answer: <strong>A. 61st Amendment Act, 1988<\/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>At what rate per annum simple interest will a sum of money become 4 times itself in 15 years?<\/strong><br><br>A. 18%<br>B. 20%<br>C. 22%<br>D. 24%<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Simple Interest<\/strong><br>4 times \u21d2 Interest = 3P<br>SI = <math data-latex=\"\\frac{P\\times R\\times T}{100}\"><semantics><mfrac><mrow><mi>P<\/mi><mo>\u00d7<\/mo><mi>R<\/mi><mo>\u00d7<\/mo><mi>T<\/mi><\/mrow><mn>100<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{P\\times R\\times T}{100}<\/annotation><\/semantics><\/math><br><br>\u200b3p = <math data-latex=\"\\frac{P\\times R\\times 15}{100}\"><semantics><mfrac><mrow><mi>P<\/mi><mo>\u00d7<\/mo><mi>R<\/mi><mo>\u00d7<\/mo><mn>15<\/mn><\/mrow><mn>100<\/mn><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{P\\times R\\times 15}{100}<\/annotation><\/semantics><\/math><br><br><math data-latex=\"3 = \\frac{P\\times R\\times 15}{100 \\times P} \\\\ \\frac{3}{R} = \\frac{15}{100} \\\\ \\frac{1}{R} = \\frac{15}{100 \\times 3} \\\\ R = \\frac{300}{15}\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mn>3<\/mn><mo>=<\/mo><mfrac><mrow><mi>P<\/mi><mo>\u00d7<\/mo><mi>R<\/mi><mo>\u00d7<\/mo><mn>15<\/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>3<\/mn><mi>R<\/mi><\/mfrac><mo>=<\/mo><mfrac><mn>15<\/mn><mn>100<\/mn><\/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>15<\/mn><mrow><mn>100<\/mn><mo>\u00d7<\/mo><mn>3<\/mn><\/mrow><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>R<\/mi><mo>=<\/mo><mfrac><mn>300<\/mn><mn>15<\/mn><\/mfrac><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">3 = \\frac{P\\times R\\times 15}{100 \\times P} \\\\ \\frac{3}{R} = \\frac{15}{100} \\\\ \\frac{1}{R} = \\frac{15}{100 \\times 3} \\\\ R = \\frac{300}{15}<\/annotation><\/semantics><\/math><br>R = 20%<br><br>There is another method: A = 4 times<br><math data-latex=\"A = P (1 + \\frac{rt}{100}) \\\\ 4P = P (1 + \\frac{15r}{100}) \\\\ \\frac{4P}{P} = 1 + \\frac{15r}{100} \\\\ 4 = 1 + \\frac{15r}{100} \\\\ 4 - 1 = \\frac{15r}{100} \\\\ \\frac{3 \\times 100}{15} = r  \\\\ r = \\frac{300}{15}\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mi>A<\/mi><mo>=<\/mo><mi>P<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mrow><mi>r<\/mi><mi>t<\/mi><\/mrow><mn>100<\/mn><\/mfrac><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>4<\/mn><mi>P<\/mi><mo>=<\/mo><mi>P<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mrow><mn>15<\/mn><mi>r<\/mi><\/mrow><mn>100<\/mn><\/mfrac><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mrow><mn>4<\/mn><mi>P<\/mi><\/mrow><mi>P<\/mi><\/mfrac><mo>=<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mrow><mn>15<\/mn><mi>r<\/mi><\/mrow><mn>100<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>4<\/mn><mo>=<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mrow><mn>15<\/mn><mi>r<\/mi><\/mrow><mn>100<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>4<\/mn><mo>\u2212<\/mo><mn>1<\/mn><mo>=<\/mo><mfrac><mrow><mn>15<\/mn><mi>r<\/mi><\/mrow><mn>100<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mrow><mn>3<\/mn><mo>\u00d7<\/mo><mn>100<\/mn><\/mrow><mn>15<\/mn><\/mfrac><mo>=<\/mo><mi>r<\/mi><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>r<\/mi><mo>=<\/mo><mfrac><mn>300<\/mn><mn>15<\/mn><\/mfrac><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">A = P (1 + \\frac{rt}{100}) \\\\ 4P = P (1 + \\frac{15r}{100}) \\\\ \\frac{4P}{P} = 1 + \\frac{15r}{100} \\\\ 4 = 1 + \\frac{15r}{100} \\\\ 4 &#8211; 1 = \\frac{15r}{100} \\\\ \\frac{3 \\times 100}{15} = r  \\\\ r = \\frac{300}{15}<\/annotation><\/semantics><\/math><br>r = 20%<br>\u2705 Answer: <strong>B. 20%<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 79<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>P can complete one round of a circular track in 12 minutes and Q can complete one round in 18 minutes. If they start at the same point and move in the same direction, after how many minutes will they meet for the first time?<br><\/strong><br>A. 24<br>B. 30<br>C. 36<br>D. 42<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Circular Track<\/strong><br>P speed:<br>1 rounds in 12 min \u2192 1\/12<br><br>Q:<br>1 rounds in 18 min = 1\/18<br><br>Relative speed:<br>P = 1\/12<br>R = 1\/18<br><br>Relative =\u200b <math data-latex=\"\\frac{1}{12} - \\frac{1}{18} = \\frac{3 - 2}{36} = \\frac{1}{36}\"><semantics><mrow><mfrac><mn>1<\/mn><mn>12<\/mn><\/mfrac><mo>\u2212<\/mo><mfrac><mn>1<\/mn><mn>18<\/mn><\/mfrac><mo>=<\/mo><mfrac><mrow><mn>3<\/mn><mo>\u2212<\/mo><mn>2<\/mn><\/mrow><mn>36<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>36<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{12} &#8211; \\frac{1}{18} = \\frac{3 &#8211; 2}{36} = \\frac{1}{36}<\/annotation><\/semantics><\/math><br><br>They meet when the faster runner gains one full round, so time is:<br>Distance = one round<br><br><strong>Time to meet<\/strong><br>They need to cover <strong>1 round gap<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Time<\/mtext><mo>=<\/mo><mfrac><mtext>Distance<\/mtext><mtext>Relative&nbsp;speed<\/mtext><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Time} = \\frac{\\text{Distance}}{\\text{Relative speed}}<\/annotation><\/semantics><\/math><br><math data-latex=\"Time\\ = \\frac{1}{\\frac{1}{36}} \\\\ Time\\ = \\frac{36}{1}\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mi>T<\/mi><mi>i<\/mi><mi>m<\/mi><mi>e<\/mi><mtext>&nbsp;<\/mtext><mo>=<\/mo><mfrac><mn>1<\/mn><mfrac><mn>1<\/mn><mn>36<\/mn><\/mfrac><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>T<\/mi><mi>i<\/mi><mi>m<\/mi><mi>e<\/mi><mtext>&nbsp;<\/mtext><mo>=<\/mo><mfrac><mn>36<\/mn><mn>1<\/mn><\/mfrac><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">Time\\ = \\frac{1}{\\frac{1}{36}} \\\\ Time\\ = \\frac{36}{1}<\/annotation><\/semantics><\/math><br>Time = 36 min<br>\u2705 Answer: <strong>C. 36<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 80<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Read the statements and conclusions carefully.<br>Statements:<br>All mugs are cups.<br>Some cups are glassware.<br>All glassware are breakable.<br>Conclusions:<br>(I) Some breakable things are cups.<br>(II) All mugs are breakable.<\/strong><br><br>A. Only conclusion (I) follows<br>B. Only conclusion (II) follows<br>C. Both conclusions follow<br>D. Neither conclusion follows<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Syllogism<\/strong><br><strong>Solution<\/strong><br>From the statements:<br>All mugs are cups.<br>Some cups are glassware.<br>All glassware are breakable.<br><br>Since some cups are glassware and all glassware are breakable, it follows that <strong>some breakable things are cups<\/strong>.<br>But we cannot say all mugs are breakable, because nothing states that mugs are glassware.<br>So only conclusion <strong>(I)<\/strong> follows.<br>\ud83d\udc49 <strong>Answer A. Only conclusion (I) follows<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 81<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which statement is true regarding file management in Windows?<br>(i) A file moved to the Recycle Bin can be restored to its original folder.<br>(ii) A file path represents the hierarchical location of the file in the folder structure.<br><\/strong><br>A. (i) True, (ii) True<br>B. (i) False, (ii) False<br>C. (i) True, (ii) False<br>D. (i) False, (ii) True<\/p>\n\n\n\n<p class=\"is-style-success\">Microsoft support states that deleted files can be restored from the Recycle Bin to their original folder. Microsoft\u2019s file-path documentation also describes a path as the hierarchical string of directories leading to a file.<br>So both statements are true.<br>\u2705 Answer: <strong>A. (i) True, (ii) True<\/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>If 3 is added to each even digit and 2 is subtracted from each odd digit in the number 3579246, how many digits will appear more than once in the new number thus formed?<\/strong><br><br>A. None<br>B. One<br>C. Two<br>D. Three<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Digit Operation<\/strong><br>Number: 3579246<br>Even +3: 2\u21925, 4\u21927, 6\u21929<br>Odd -2: 3\u21921, 5\u21923, 7\u21925, 9\u21927<br><br>New number: 13<strong>5757<\/strong>9<br>Repeated digits \u2192 5,7 \u2192 2 digits<br>\u2705 Answer: <strong>C. Two<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 83<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Rosy deposited \u20b916,000 at 15% compound interest per annum, compounded annually. The total amount received after 2 years is:<\/strong><br><br>A. \u20b920,960<br>B. \u20b921,160<br>C. \u20b921,260<br>D. \u20b921,360<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Compound Interest<\/strong><br><math data-latex=\"A = P (1 + \\frac{r}{100})^2 \\\\ A = 16000 (1 + \\frac{150}{100})^2 \\\\ A = 16000 (\\frac{100 + 15}{100})^2 \\\\ A = 16000(1.15)^2\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mi>A<\/mi><mo>=<\/mo><mi>P<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mi>r<\/mi><mn>100<\/mn><\/mfrac><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>A<\/mi><mo>=<\/mo><mn>16000<\/mn><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1<\/mn><mo>+<\/mo><mfrac><mn>150<\/mn><mn>100<\/mn><\/mfrac><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>A<\/mi><mo>=<\/mo><mn>16000<\/mn><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mfrac><mrow><mn>100<\/mn><mo>+<\/mo><mn>15<\/mn><\/mrow><mn>100<\/mn><\/mfrac><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>A<\/mi><mo>=<\/mo><mn>16000<\/mn><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>1.15<\/mn><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">A = P (1 + \\frac{r}{100})^2 \\\\ A = 16000 (1 + \\frac{150}{100})^2 \\\\ A = 16000 (\\frac{100 + 15}{100})^2 \\\\ A = 16000(1.15)^2<\/annotation><\/semantics><\/math><br>A = 21160<br><strong>\u2705 Answer: <strong>B. \u20b921,160<\/strong><\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 84<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The &#8220;Abhay&#8221; AI-powered chatbot was launched by which organization to help citizens verify official notices and prevent &#8220;digital arrest&#8221; scams?<\/strong><br><br>A. Reserve Bank of India (RBI)<br>B. Central Bureau of Investigation (CBI)<br>C. Enforcement Directorate (ED)<br>D. Delhi Police<\/p>\n\n\n\n<p class=\"is-style-success\">Central Bureau of Investigation (CBI): The &#8220;Abhay&#8221; chatbot allows users to check the authenticity of CBI notices to combat cyber fraud.<br>\u2705 Answer: <strong>B. Central Bureau of Investigation (CBI)<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 85<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which letter-cluster should replace the question mark?<br>MIM : ZTW :: UQU : ?<\/strong><br><br>A. HBE<br>B. VWY<br>C. CWZ<br>D. AMP<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pattern:<br><\/strong>M, I (-4), M (+4) : Z, T (-6), W (+3)<br>U, Q (-4), U (+4) :<strong> C, W (-6), Z (+3)<\/strong><br>Option C matches the pattern.<br>\u2705 Answer: <strong>C. CWZ<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 86<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Three of the following four letter-cluster pairs are alike in a certain way and form a group. Which one does not belong to that group?<\/strong><br><br>A. UV-VW<br>B. CD-DE<br>C. KL-LM<br>D. PQ-RT<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Check the patterns:<br>UV \u2192 VW : both letters shift by +1<br>CD \u2192 DE : both letters shift by +1<br>KL \u2192 LM : both letters shift by +1<br>PQ \u2192 RT : not a +1 shift in the same way<br>So PQ-RT is the odd one out.<br>\u2705 Answer: <strong>D. PQ-RT<\/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 took oath in April 2026 as India&#8217;s first openly queer Member of Parliament (MP) in the Rajya Sabha?<\/strong><br><br>A. Menaka Guruswamy<br>B. Arundhati Katju<br>C. Laxmi Narayan Tripathi<br>D. Saurabh Kirpal<\/p>\n\n\n\n<p class=\"is-style-success\">Menaka Guruswamy: Senior advocate Menaka Guruswamy, a key lawyer in decriminalising Section 377, was nominated to the Rajya Sabha by the TMC.<br>\u2705 Answer: <strong>A. Menaka Guruswamy<\/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>How often do non-Annex I Parties submit Biennial Update Reports (BURs) to the UNFCCC?<\/strong><br><br>A. Every year<br>B. Every two years<br>C. Every three years<br>D. Every five years<\/p>\n\n\n\n<p class=\"is-style-success\">UNFCCC states that non-Annex I Parties should submit their Biennial Update Reports every two years.<br><strong>\ud83c\udfaf FINAL ANSWER: B. Every two 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 89<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Simplify the following expression: <\/strong><math data-latex=\"[6.75 + \\frac{1}{2}] \u2212 [4.2 \u2212 \\frac{3}{5}]\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">[<\/mo><mn>6.75<\/mn><mo>+<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo form=\"postfix\" stretchy=\"false\">]<\/mo><mo>\u2212<\/mo><mo form=\"prefix\" stretchy=\"false\">[<\/mo><mn>4.2<\/mn><mo>\u2212<\/mo><mfrac><mn>3<\/mn><mn>5<\/mn><\/mfrac><mo form=\"postfix\" stretchy=\"false\">]<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">[6.75 + \\frac{1}{2}] \u2212 [4.2 \u2212 \\frac{3}{5}]<\/annotation><\/semantics><\/math><br><br>A. 3.55<br>B. 3.65<br>C. 3.75<br>D. 3.85<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Simplify<br><\/strong>(6.75 + 0.5) \u2212 (4.2 \u2212 0.6)<br>= 7.25 \u2212 3.6<br>= 3.65<br>\u2705 Answer: <strong>B. 3.65<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 90<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What should come next in the series?<br>2, 6, 12, 20, 30, ?<\/strong><br><br>A. 40<br>B. 41<br>C. 42<br>D. 44<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Series:<br>2,6,12,20,30,?<br>Differences are:<br>4,6,8,10<br>The next difference is: 12<br>So:<br>30 + 12 = 42<br>\u2705 Answer: <strong>C. 42<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 91<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>If a : b = 4 : 7 and b : c = 14 : 9, then what is a : c?<\/strong><br><br>A. 8:9<br>B. 9:8<br>C. 4:5<br>D. 7:9<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Given:<br>a : b = 4 : 7, b : c = 14 : 9<br>Make b equal in both ratios:<br>a : b = 4 : 7 = 8 : 14<br>So:<br>a : c = 8 : 9<br>\u2705 Answer: <strong>A. 8:9<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 92<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\">Find the third proportional to 9 and 12.<strong><br><\/strong><br>A. 14<br>B. 15<br>C. 16<br>D. 18<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>The Pattern Trick:<br><\/strong><math data-latex=\"\\frac{12^2}{9} = \\frac{144}{9} = 16\"><semantics><mrow><mfrac><msup><mn>12<\/mn><mn>2<\/mn><\/msup><mn>9<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>144<\/mn><mn>9<\/mn><\/mfrac><mo>=<\/mo><mn>16<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{12^2}{9} = \\frac{144}{9} = 16<\/annotation><\/semantics><\/math><br><br>\ud83d\udc49 <strong>Answer A. 16<\/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>Solve for x:<br>7x \u2212 5 = 44<br><\/strong><br>A. 5<br>B. 6<br>C. 7<br>D. 8<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>7x &#8211; 5 = 44<br><\/strong>7x = 44 + 5<br>7x = 49<br>x = 49\/7<br>x = 7<br>\u2705 Answer: <strong>C. 7<\/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>Simplify <\/strong><math data-latex=\"\\frac{25^3 + 9^3}{25^2 - 25 \\times 9 + 9^2}\"><semantics><mfrac><mrow><msup><mn>25<\/mn><mn>3<\/mn><\/msup><mo>+<\/mo><msup><mn>9<\/mn><mn>3<\/mn><\/msup><\/mrow><mrow><msup><mn>25<\/mn><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mn>25<\/mn><mo>\u00d7<\/mo><mn>9<\/mn><mo>+<\/mo><msup><mn>9<\/mn><mn>2<\/mn><\/msup><\/mrow><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{25^3 + 9^3}{25^2 &#8211; 25 \\times 9 + 9^2}<\/annotation><\/semantics><\/math><br><br>A. 32<br>B. 34<br>C. 36<br>D. 38<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Use the identity:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mi>a<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><msup><mi>b<\/mi><mn>3<\/mn><\/msup><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mi>a<\/mi><mi>b<\/mi><mo>+<\/mo><msup><mi>b<\/mi><mn>2<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">a^3+b^3=(a+b)(a^2-ab+b^2)<\/annotation><\/semantics><\/math>Here <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mn>25<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">a=25<\/annotation><\/semantics><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>b<\/mi><mo>=<\/mo><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">b=9<\/annotation><\/semantics><\/math>. So the numerator is <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>a<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><msup><mi>b<\/mi><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">a^3+b^3<\/annotation><\/semantics><\/math>, and the denominator is <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mi>a<\/mi><mi>b<\/mi><mo>+<\/mo><msup><mi>b<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">a^2-ab+b^2<\/annotation><\/semantics><\/math>. Therefore the value is:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>25<\/mn><mo>+<\/mo><mn>9<\/mn><mo>=<\/mo><mn>34<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">25+9=34<\/annotation><\/semantics><\/math>\u2705 Answer: <strong>B. 34<\/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>In a certain code language, FIRE is coded as 7164 and RIFE is coded as 6174. What is the code for R?<\/strong><br><br>A. 2<br>B. 4<br>C. 6<br>D. 8<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>From the coding:<br>FIRE = 7164 gives <strong>R = 6<\/strong><br>RIFE = 6174 confirms the same mapping<br>So the code for <strong>R<\/strong> is <strong>6<\/strong>.<br><strong>\ud83c\udfaf FINAL ANSWER: C. 6<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 96<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>India has set a massive target to increase its nuclear power capacity to 100 Giga Watts (GW). By which year does the government plan to achieve this?<\/strong><br><br>A) 2030<br>B) 2035<br>C) 2040<br>D) 2047<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>2047<\/strong>: The Chairman of the Central Electricity Authority announced this tenfold increase target to be met by India&#8217;s centenary of independence.<br><strong>\u2705 Answer: D. 2047<\/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>Which of the following is an example of application software?<\/strong><br><br>A. Operating system<br>B. Word processor<br>C. Device driver<br>D. Firmware<\/p>\n\n\n\n<p class=\"is-style-success\">A <strong>word processor<\/strong> is application software because it helps users perform a specific task. Operating systems, device drivers, and firmware are system software.<br><strong>\u2705 Answer: B. Word processor<\/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>Six people A, B, C, D, E and F sit in a row facing north.<br>A sits immediately left of B.<br>B sits immediately left of C.<br>D sits immediately right of C.<br>F sits immediately right of D.<br>E sits at the left end.<br>Who sits between C and F?<\/strong><br><br>A. A<br>B. B<br>C. D<br>D. E<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pattern:<\/strong><br>Right of = clockwise<br>Left of = anti-clockwise<br>Seven People = A,B,C,D,E,F<strong><br><\/strong>Sitting Circular:<br>1 = A<br>2 = B<br>3 = C<br>4 = D<br>5 = F<br>6 = E<br><br>The question is: who sits between C and F?<br>D<br>\u2705 Answer: <strong>C. D<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 99<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>A boy flying a kite holds a string of length 26 m such that it makes an angle of 30\u00b0 with the ground. Find the height of the kite from the ground.<\/strong><br><br>A. 11.5 m<br>B. 12.0 m<br>C. 13.0 m<br>D. 13.5 m<\/p>\n\n\n\n<p class=\"is-style-success\">This is a <strong>right triangle (height problem)<\/strong> \u2014 the kite string is the hypotenuse, and the height is the vertical side.<br><br><strong>\ud83d\udd34 Given<br><\/strong>Length of string = <strong>26 m<\/strong> (hypotenuse)<br>Angle with ground = <strong>30\u00b0<\/strong><br>Need: <strong>height (opposite side)<\/strong><br><br><strong>\ud83e\udde0 Core Concept<\/strong><br>In a right triangle:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>sin<\/mi><mo>\u2061<\/mo><mi>\u03b8<\/mi><mo>=<\/mo><mfrac><mtext>Opposite<\/mtext><mtext>Hypotenuse<\/mtext><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\sin \\theta = \\frac{\\text{Opposite}}{\\text{Hypotenuse}}<\/annotation><\/semantics><\/math><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>sin<\/mi><mo>\u2061<\/mo><mi>\u03b8<\/mi><mo>=<\/mo><mfrac><mtext>height<\/mtext><mtext>hypotenuse<\/mtext><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\sin\\theta = \\frac{\\text{height}}{\\text{hypotenuse}}<\/annotation><\/semantics><\/math><br><br><strong>\ud83e\udde0 Step (direct application)<\/strong><br><math data-latex=\"sin30^\\circ = \\frac{height}{26} \\\\ \\\\ We\\ know:\\ sin30^\\circ\\ is\\ \\ \\frac{1}{2} \\\\ \\\\ Solve: \\frac{1}{2} = \\frac{h}{26} \\\\ h = 26 \\times \\frac{1}{2} \\\\ h = 13 \"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mi>s<\/mi><mi>i<\/mi><mi>n<\/mi><msup><mn>30<\/mn><mo>\u2218<\/mo><\/msup><mo>=<\/mo><mfrac><mrow><mi>h<\/mi><mi>e<\/mi><mi>i<\/mi><mi>g<\/mi><mi>h<\/mi><mi>t<\/mi><\/mrow><mn>26<\/mn><\/mfrac><\/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>W<\/mi><mi>e<\/mi><mtext>&nbsp;<\/mtext><mi>k<\/mi><mi>n<\/mi><mi>o<\/mi><mi>w<\/mi><mo lspace=\"0.2222em\" rspace=\"0.2222em\">:<\/mo><mtext>&nbsp;<\/mtext><mi>s<\/mi><mi>i<\/mi><mi>n<\/mi><msup><mn>30<\/mn><mo>\u2218<\/mo><\/msup><mtext>&nbsp;<\/mtext><mi>i<\/mi><mi>s<\/mi><mtext>&nbsp;<\/mtext><mtext>&nbsp;<\/mtext><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><\/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>S<\/mi><mi>o<\/mi><mi>l<\/mi><mi>v<\/mi><mi>e<\/mi><mo lspace=\"0.2222em\" rspace=\"0.2222em\">:<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mfrac><mi>h<\/mi><mn>26<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>h<\/mi><mo>=<\/mo><mn>26<\/mn><mo>\u00d7<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>h<\/mi><mo>=<\/mo><mn>13<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">sin30^\\circ = \\frac{height}{26} \\\\ \\\\ We\\ know:\\ sin30^\\circ\\ is\\ \\ \\frac{1}{2} \\\\ \\\\ Solve: \\frac{1}{2} = \\frac{h}{26} \\\\ h = 26 \\times \\frac{1}{2} \\\\ h = 13 <\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>C. 13 m<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 100<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What should come in place of the question mark?<br>5, 11, 19, 29, 41, ?<\/strong><br><br>A. 51<br>B. 53<br>C. 55<br>D. 57<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Series<\/strong><br>Differences:<br>6, 8, 10, 12, &#8230;<br>Next = +14<br>41 + 14 = 55<br><strong>\u2705 Answer: D. 108<\/strong><\/p>\n<\/div><\/details><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>RRB NTPC Graduate CBT 2 (Free Practice Test 1 With Solution: Try the free practice test of RRB NTPC Graduate CBT 2 competitive exam. Take quiz and learn tricks from the solutions with a way to get rewards if score well.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"googlesitekit_rrm_CAowwfjFDA:productID":"","_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","footnotes":""},"categories":[5,6,7],"tags":[3],"class_list":["post-281","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\/281","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=281"}],"version-history":[{"count":22,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/posts\/281\/revisions"}],"predecessor-version":[{"id":310,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/posts\/281\/revisions\/310"}],"wp:attachment":[{"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/media?parent=281"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/categories?post=281"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/tags?post=281"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}