{"id":328,"date":"2026-04-30T15:01:10","date_gmt":"2026-04-30T15:01:10","guid":{"rendered":"https:\/\/govt.mrenglishkj.com\/railway\/?p=328"},"modified":"2026-04-30T15:01:27","modified_gmt":"2026-04-30T15:01:27","slug":"rrb-ntpc-graduate-cbt-3-competitive-exam-1-massive-series","status":"publish","type":"post","link":"https:\/\/govt.mrenglishkj.com\/railway\/rrb-ntpc-graduate-cbt-3-competitive-exam-1-massive-series\/","title":{"rendered":"RRB NTPC Graduate CBT 3 Competitive Exam 1: Massive Series"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">RRB NTPC Graduate CBT 3 (Free Practice Quiz 1) \u2013 <strong>Q&amp;A, Tricks, Answer Solutions<\/strong> (Part 1: Question 1-25)<\/h2>\n\n\n\n<p>This is the third massive test series of RRB NTPC Graduate CBT 3 exam. The best site for you to  prepare for any competitive exams because everything here is for free, there are no hidden charges, and 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 3 exam practice test 1. The competitive exam is divided into 4 parts each with 25 questions. You are taking the test, learning from answer solutions, and their 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 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 = 25;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-25\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"25\">\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 Solutions Of The RRB NTPC Competitive Exam Test Series Part 1<\/h2>\n\n\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"Based on the English alphabetical order, three of the following four letter-cluster pairs are alike in a certain way and form a group. Which one does not belong to that group?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is to add 5. Let's learn practically and visually.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"AB and CD are parallel lines cut by a transversal t. If $\u2220AEF = 78^\u2218$  and EG bisects $\u2220AEF$, what is the acute angle between EG and line CD?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"39 degree is the correct answer. Let's learn the simple trick to solve and find it.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In which state is the Bihu festival celebrated?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Assam\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Which organization was the implementing agency for the National Agricultural Insurance Scheme (NAIS)?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Agriculture Insurance Company of India Ltd. (AIC)\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Simplify: $4\\frac{1}{2}\\ \u00f7\\ 3.6\\ \u00d7\\ 0.8\\ \u00f7\\ (\\frac{2}{5}\\ \u00d7\\ 10)$\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Let's learn how to calculate it simply, the correct answer is 1\/4.\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"If $x^2 \u2212 6x + 9 = 0$ and $x^2 \u2212 (a + 1)x + (2a + 1) = 0$ have one common root, then the value of $\\frac{(a+2)(a+3)}{a\u22124}$ \u200bis:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Let's learn how to calculate it simply, the correct answer is 30.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"During a sale, 60% of the goods are sold at 10% profit, 25% of the remaining goods are sold at 20% profit, and the rest are sold at 10% loss. What is the overall profit percentage?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Let's learn how to calculate it simply, the correct answer is 5%.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which country officially became the 33rd member of NATO in early 2026?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Sweden\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In March 2026, which Indian city became the first in the country to implement a \"Zero-Waste\" mandate for all residential societies?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Indore\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who was awarded the Bharat Ratna in January 2026 for their contribution to Indian classical music and global cultural diplomacy?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Zakir Hussain\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What is the name of India's first \"Deep Ocean Mission\" vessel that reached a depth of 6,000 meters in March 2026?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Samudrayaan (Matsya 6000)\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A shopkeeper fixes the marked price of an item 140% above its cost price. What percentage discount on the marked price should be allowed to gain 14%?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"52.5% is the correct answer. Let's learn the simple trick to solve and find it.\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language, FIRE is coded as HLVJ and BOLD is coded as DRPI. What is the code for MUSE?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The tricky pattern here is addition of 2 in first, addition of 3 in second, addition of 4 in third, and addition of 5 by fourth. Let's learn the tricks behind questions like these.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which tech giant launched the \"Indi-LLM\" in February 2026, the first AI model specifically trained on 22 official Indian languages?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Reliance (Jio)\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Pattachitra, a traditional cloth painting style, is associated with which state?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Odisha\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A shopkeeper purchased 36 dozen notebooks at \u20b9180 per dozen. He sold each notebook at \u20b920. What profit percentage did he make?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 33.33%. But the real question is how to get it quickly, let's learn the trick.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The 2026 Winter Olympics, which concluded in February, were hosted in which European cities?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Milan & Cortina\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which Indian state launched the \"Udyogini 2.0\" scheme in April 2026 to provide interest-free loans to 1 million women entrepreneurs?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Maharashtra\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Seven people T, U, V, W, X, Y and Z each have an engagement on a different day from Monday to Sunday.\nV is on Monday.\nY is on Saturday.\nX is on Sunday.\nW is immediately before Z, and T is immediately after Z.\nU has an engagement after T but before X.\nHow many people have engagements between V and U?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 3. This is all a visual map trick. Let's learn it faster by trying.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Find the average of 268, 124, 96 and 92.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 145. 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\": \"As per the RBI report released in April 2026, what is India\u2019s projected GDP growth for the fiscal year 2026-27?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 7.8%. Let's check out ore questions like these.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which country hosted the \"World Water Summit\" in March 2026, focusing on the preservation of the Himalayan glaciers?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Nepal\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Leena starts from point A, walks 10 km north, 8 km east, 6 km south, 4 km west and 4 km south. How far and in which direction should she go to return to point A?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick behind is visual move after every forward sequence The correct answer is 4 km west.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which letter-number cluster completes the series?\nBDF 14, EGI 17, HJL 20, KMO 23, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is simple pattern type question. The correct answer is NPR 26. Let's learn the trick.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who composed the Aihole inscription of Pulakeshin II?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Ravikirti\"\n    }\n  }\n  }\n}\n<\/script>\n\n\n\n<div class=\"wp-block-coblocks-accordion\">\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 1<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Based on the English alphabetical order, three of the following four letter-cluster pairs are alike in a certain way and thus form a group. Which is the one that does not belong to that group?<br>(Note: The odd man out is not based on the number of consonants\/vowels or their position in the letter-cluster.)<\/strong><br><br>A. CF\u2212HK<br>B. MN\u2212RS<br>C. UV\u2212ZA<br>D. EI\u2212JP<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Odd Letter Pair<\/strong><br>Pattern check (use alphabet positions)<br>C(3) \u2192 H(8) = +5<br>F(6) \u2192 K(11) = +5<br><br>Now check others:<br><strong>MN\u2013RS<\/strong> \u2192 M(+5) \u2192 R, N(+5) \u2192 S \u2714<br><strong>UV\u2013ZA<\/strong> \u2192 U(+5) \u2192 Z, V(+5) \u2192 A \u2714<br><strong>EI\u2013JP<\/strong> \u2192 E(+5) \u2192J, I(+7) \u2192 P \u274c (breaks pattern)<br><br>\u2705 Answer: <strong>D. EI\u2212JP<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Look for consistent +5 shift pattern.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 2<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>AB and CD are parallel lines cut by a transversal t. If \u2220AEF = 78<sup>\u2218<\/sup> and EG bisects \u2220AEF, what is the acute angle between EG and line CD?<\/strong><br><br>A. <math data-latex=\"35^o\"><semantics><msup><mn>35<\/mn><mi>o<\/mi><\/msup><annotation encoding=\"application\/x-tex\">35^o<\/annotation><\/semantics><\/math><br>B. <math data-latex=\"39^o\"><semantics><msup><mn>39<\/mn><mi>o<\/mi><\/msup><annotation encoding=\"application\/x-tex\">39^o<\/annotation><\/semantics><\/math><br>C. <math data-latex=\"45^o\"><semantics><msup><mn>45<\/mn><mi>o<\/mi><\/msup><annotation encoding=\"application\/x-tex\">45^o<\/annotation><\/semantics><\/math><br>D. <math data-latex=\"51^o\"><semantics><msup><mn>51<\/mn><mi>o<\/mi><\/msup><annotation encoding=\"application\/x-tex\">51^o<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Since EG bisects \u2220AEF = 78<sup>\u2218<\/sup>,<br>Bisect means half of 78.<br>\u2220AEG = \u2220GEF = 39<sup>\u2218<\/sup><br>Because AB \u2225 CD, the acute angle that EG makes with CD is also 39<sup>\u2218<\/sup>.<br><strong>Correct answer: B. 39<sup>\u2218<\/sup><\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 3<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In which state is the Bihu festival celebrated?<\/strong><br><br>A. Odisha<br>B. Assam<br>C. Bihar<br>D. Karnataka<\/p>\n\n\n\n<p class=\"is-style-success\">Bihu is celebrated across Assam. The Assam government\u2019s cultural affairs page lists Bihu as a major festival of the state and says it is celebrated across Assam with enthusiasm.<br>\u2705 Answer: <strong>B. Assam<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 4<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which organization was the implementing agency for the National Agricultural Insurance Scheme (NAIS)?<br><\/strong><br>A. FCI<br>B. ICAR<br>C. AIC<br>D. NABARD<\/p>\n\n\n\n<p class=\"is-style-success\">The National Agricultural Insurance Scheme (NAIS) scheme document states that the implementing agency was the Agriculture Insurance Company of India Ltd. (AIC).<br>\u2705 Answer: <strong>C. AIC<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 5<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Simplify<\/strong> <math data-latex=\"4\\frac{1}{2}\\ \u00f7\\ 3.6\\ \u00d7\\ 0.8\\ \u00f7\\ (\\frac{2}{5}\\ \u00d7\\ 10)\"><semantics><mrow><mn>4<\/mn><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mtext>&nbsp;<\/mtext><mo>\u00f7<\/mo><mtext>&nbsp;<\/mtext><mn>3.6<\/mn><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>0.8<\/mn><mtext>&nbsp;<\/mtext><mo>\u00f7<\/mo><mtext>&nbsp;<\/mtext><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mfrac><mn>2<\/mn><mn>5<\/mn><\/mfrac><mtext>&nbsp;<\/mtext><mo>\u00d7<\/mo><mtext>&nbsp;<\/mtext><mn>10<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">4\\frac{1}{2}\\ \u00f7\\ 3.6\\ \u00d7\\ 0.8\\ \u00f7\\ (\\frac{2}{5}\\ \u00d7\\ 10)<\/annotation><\/semantics><\/math><strong><br><\/strong><br>A. 1\/4<br>B. 1\/3<br>C. 2\/5<br>D. 3\/5<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Convert the mixed fraction:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>4<\/mn><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>4.5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">4\\frac{1}{2}=4.5<\/annotation><\/semantics><\/math><br>Now calculate left to right:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>4.5<\/mn><mo>\u00f7<\/mo><mn>3.6<\/mn><mo>=<\/mo><mn>1.25<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">4.5 \\div 3.6 = 1.25<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>1.25<\/mn><mo>\u00d7<\/mo><mn>0.8<\/mn><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">1.25 \\times 0.8 = 1<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mrow><mo fence=\"true\">(<\/mo><mfrac><mn>2<\/mn><mn>5<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>10<\/mn><mo fence=\"true\">)<\/mo><\/mrow><mo>=<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\left(\\frac{2}{5}\\times 10\\right)=4<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>1<\/mn><mo>\u00f7<\/mo><mn>4<\/mn><mo>=<\/mo><mfrac><mn>1<\/mn><mn>4<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">1 \\div 4 = \\frac{1}{4}<\/annotation><\/semantics><\/math><br><strong>Correct answer: A. 1\/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 6<\/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 (a + 1)x + (2a + 1) = 0\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mi>x<\/mi><mo>+<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>2<\/mn><mi>a<\/mi><mo>+<\/mo><mn>1<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x^2 \u2212 (a + 1)x + (2a + 1) = 0<\/annotation><\/semantics><\/math><strong> have one common root, then the value of <\/strong><math data-latex=\"\\frac{(a+2)(a+3)}{a\u22124}\"><semantics><mfrac><mrow><mo form=\"prefix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mn>2<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mn>3<\/mn><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><mrow><mi>a<\/mi><mo>\u2212<\/mo><mn>4<\/mn><\/mrow><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{(a+2)(a+3)}{a\u22124}<\/annotation><\/semantics><\/math><strong> \u200bis:<br><\/strong><br>A. 18<br>B. 24<br>C. 30<br>D. 42<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>The first equation is:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><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^2-6x+9=0<\/annotation><\/semantics><\/math>which is<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>\u2212<\/mo><mn>3<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(x-3)^2=0<\/annotation><\/semantics><\/math><br>So the common root is x = 3.<br>Substitute x = 3 into the second equation:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mn>3<\/mn><mn>2<\/mn><\/msup><mo>\u2212<\/mo><mo stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mn>3<\/mn><mo>+<\/mo><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mi>a<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3^2-(a+1)3+(2a+1)=0<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>9<\/mn><mo>\u2212<\/mo><mn>3<\/mn><mi>a<\/mi><mo>\u2212<\/mo><mn>3<\/mn><mo>+<\/mo><mn>2<\/mn><mi>a<\/mi><mo>+<\/mo><mn>1<\/mn><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">9-3a-3+2a+1=0<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>7<\/mn><mo>\u2212<\/mo><mi>a<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">7-a=0<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>a<\/mi><mo>=<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">a=7<\/annotation><\/semantics><\/math>Now evaluate:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mrow><mo stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mi>a<\/mi><mo>\u2212<\/mo><mn>4<\/mn><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mrow><mo stretchy=\"false\">(<\/mo><mn>9<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mn>10<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><mn>3<\/mn><\/mfrac><mo>=<\/mo><mn>30<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{(a+2)(a+3)}{a-4}=\\frac{(9)(10)}{3}=30<\/annotation><\/semantics><\/math><br><strong>Correct answer: C. 30<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 7<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>During a sale, 60% of the goods are sold at 10% profit, 25% of the remaining goods are sold at 20% profit, and the rest are sold at 10% loss. What is the overall profit percentage?<\/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>Solution<\/strong><br>Take total goods as 100 units with total cost 100.<br>60 goods sold at 10% profit:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>60<\/mn><mo>\u00d7<\/mo><mn>10<\/mn><mi mathvariant=\"normal\">%<\/mi><mo>=<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">60 \\times 10\\% = 6<\/annotation><\/semantics><\/math><br>Remaining goods = 40.<br>25% of remaining = 10 goods sold at 20% profit:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>10<\/mn><mo>\u00d7<\/mo><mn>20<\/mn><mi mathvariant=\"normal\">%<\/mi><mo>=<\/mo><mn>2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">10 \\times 20\\% = 2<\/annotation><\/semantics><\/math><br>Remaining = 30 goods sold at 10% loss:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>30<\/mn><mo>\u00d7<\/mo><mn>10<\/mn><mi mathvariant=\"normal\">%<\/mi><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">30 \\times 10\\% = 3<\/annotation><\/semantics><\/math><br>Net profit:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>6<\/mn><mo>+<\/mo><mn>2<\/mn><mo>\u2212<\/mo><mn>3<\/mn><mo>=<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">6+2-3=5<\/annotation><\/semantics><\/math><br>So overall profit percentage = <strong>5%<\/strong>.<br><strong>Correct answer: B. 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 8<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which country officially became the 33rd member of NATO in early 2026?<\/strong><br><br>A) Ukraine<br>B) Kosovo<br>C) Sweden<br>D) Japan<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Sweden<\/strong>: After a long diplomatic process, Sweden&#8217;s full integration into NATO was finalized in early 2026.<br>\u2705 Answer: <strong>C. Sweden<\/strong><\/p>\n<\/div><\/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>In March 2026, which Indian city became the first in the country to implement a &#8220;Zero-Waste&#8221; mandate for all residential societies?<\/strong><br><br>A) Indore<br>B) Surat<br>C) Bengaluru<br>D) Navi Mumbai<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Indore<\/strong>: Maintaining its streak as India&#8217;s cleanest city, Indore mandated that no residential waste should leave the society gates without being processed or composted.<br>\u2705 Answer: <strong>A. Indore<\/strong><\/p>\n<\/div><\/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>Who was awarded the Bharat Ratna in January 2026 for their contribution to Indian classical music and global cultural diplomacy?<\/strong><br><br>A) Zakir Hussain<br>B) A.R. Rahman<br>C) Amjad Ali Khan<br>D) Shankar Mahadevan<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Zakir Hussain:<\/strong> The legendary tabla maestro was honored with India\u2019s highest civilian award for his decades of service to Indian percussion.<br>\u2705 Answer: <strong>A. Zakir Hussain<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 11<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What is the name of India&#8217;s first &#8220;Deep Ocean Mission&#8221; vessel that reached a depth of 6,000 meters in March 2026?<\/strong><br><br>A) Samudrayaan (Matsya 6000)<br>B) Sagar Ratna<br>C) Deep-Sea 1<br>D) Jalashwa<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Samudrayaan (Matsya 6000)<\/strong>: This mission marked India&#8217;s entry into the elite club of nations (US, Russia, France, Japan, China) with deep-sea manned submersibles.<br>\u2705 Answer: <strong>A. Samudrayaan (Matsya 6000)<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 12<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>A shopkeeper fixes the marked price of an item 140% above its cost price. What percentage of discount on marked price should be allowed to gain 14%?<br><\/strong><br>A. 60.09%<br>B. 52.5%<br>C. 57.8%<br>D. 62.1%<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Discount Problem<\/strong><br>MP = Market Price<br>CP = Cost Price<br>SP = Selling Price<br>Let cost price = 100.<br>Marked price is 180% above cost: 100 + 140% = 240<br>MP = 240, CP = 100<br>SP needed = 114 (100 + 14%)<br>Discount = <math data-latex=\"\\frac{240 - 114}{240} \\times 100 = 52.5\\%\"><semantics><mrow><mfrac><mrow><mn>240<\/mn><mo>\u2212<\/mo><mn>114<\/mn><\/mrow><mn>240<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>100<\/mn><mo>=<\/mo><mn>52.5<\/mn><mi>%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{240 &#8211; 114}{240} \\times 100 = 52.5\\%<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>A. 52.5%<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Assume CP=100.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 13<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In a certain code language, FIRE is coded as HLVJ and BOLD is coded as DRPI. What is the code for MUSE?<\/strong><br><br>A. OXWJ<br>B. OXVJ<br>C. OYWJ<br>D. OXWI<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>The Pattern: +2, +3, +4, +5.<br><\/strong>FIRE &#8212;&gt; HLVJ<br>F + 2 = H<br>I + 3 = L<br>R + 4 = V<br>E + 5 = J<br><br>BOLD &#8212;&gt; DRPI<br>B + 2 = D<br>O + 3 = R<br>L + 4 = P<br>D + 5 = I<br><br>Same logic applies on this: MUSE<br>M + 2 = O<br>U + 3 = X<br>S + 4 = W<br>E + 5 = J<br><br><strong>\u2705 Answer: A. OXWJ<\/strong><\/p>\n<\/div><\/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>Which tech giant launched the &#8220;Indi-LLM&#8221; in February 2026, the first AI model specifically trained on 22 official Indian languages?<\/strong><br><br>A) Google<br>B) Microsoft<br>C) Reliance (Jio)<br>D) Meta<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Reliance (Jio)<\/strong>: In partnership with Nvidia, Jio launched Indi-LLM to bridge the digital divide for non-English speaking Indians.<br><strong>\u2705 Answer: C. Reliance (Jio)<\/strong><\/p>\n<\/div><\/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>Pattachitra, a traditional cloth painting style, is associated with which state?<\/strong><br><br>A. Odisha<br>B. Assam<br>C. Telangana<br>D. Rajasthan<\/p>\n\n\n\n<p class=\"is-style-success\">Pattachitra is a traditional art form associated with Odisha. The Odisha government\u2019s tourism page describes Pattachitra as an Odisha tradition.<br>\u2705 Answer: <strong>A. Odisha<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 16<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>A shopkeeper purchased 36 dozen notebooks at \u20b9180 per dozen. He sold each notebook at \u20b920. What profit percentage did he make?<\/strong><br><strong><br><\/strong>A. 30%<br>B. 33.33%<br>C. 35%<br>D. 40%<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>36 dozen = 432 notebooks.<br>Cost price per notebook:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>180<\/mn><mn>12<\/mn><\/mfrac><mo>=<\/mo><mn>15<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{180}{12}=15<\/annotation><\/semantics><\/math><br>Total cost: 432 \u00d7 15 = 6480<br>Selling price per notebook = 20<br>Total selling price: 432 \u00d7 20 = 8640<br>Profit: 8640 \u2212 6480 = 2160<br>Profit percentage:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>2160<\/mn><mn>6480<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>100<\/mn><mo>=<\/mo><mn>33.33<\/mn><mi mathvariant=\"normal\">%<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{2160}{6480}\\times 100 = 33.33\\%<\/annotation><\/semantics><\/math><br><strong>Correct answer: B. 33.33%<\/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 17<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The 2026 Winter Olympics, which concluded in February, were hosted in which European cities?<\/strong><br><br>A. Paris &amp; Lyon<br>B. Milan &amp; Cortina<br>C. Oslo &amp; Bergen<br>D. Zurich &amp; Geneva<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Milan &amp; Cortina<\/strong>: The 2026 Winter Olympics were held across these two Italian locations.<br>\u2705 Answer: <strong>B. Milan &amp; Cortina<\/strong><\/p>\n<\/div><\/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>Which Indian state launched the &#8220;Udyogini 2.0&#8221; scheme in April 2026 to provide interest-free loans to 1 million women entrepreneurs?<\/strong><br><br>A) Uttar Pradesh<br>B) Kerala<br>C) Tamil Nadu<br>D) Maharashtra<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Maharashtra<\/strong>: The state government expanded the scheme to boost rural economies through women-led small businesses.<br>\u2705 Answer: <strong>D. Maharashtra<\/strong><\/p>\n<\/div><\/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>Seven people T, U, V, W, X, Y and Z each have an engagement on a different day from Monday to Sunday.<br>V is on Monday.<br>Y is on Saturday.<br>X is on Sunday.<br>W is immediately before Z, and T is immediately after Z.<br>U has an engagement after T but before X.<br>How many people have engagements between V and U?<\/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 day positions become:<br>V = Monday<br>Y = Saturday<br>X = Sunday<br>W, Z, T must fit as <strong>Tuesday, Wednesday, Thursday<\/strong><br>U must be <strong>Friday<\/strong> because it is after T but before X<br>So between V (Monday) and U (Friday) are:<br>Tuesday, Wednesday, Thursday = <strong>3 people<\/strong><br><strong>Correct answer: C. 3<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 20<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Find the average of 268, 124, 96 and 92.<\/strong><br><br>A. 143<br>B. 144<br>C. 145<br>D. 146<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>268<\/mn><mo>+<\/mo><mn>124<\/mn><mo>+<\/mo><mn>96<\/mn><mo>+<\/mo><mn>92<\/mn><mo>=<\/mo><mn>580<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">268+124+96+92=580<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Average<\/mtext><mo>=<\/mo><mfrac><mn>580<\/mn><mn>4<\/mn><\/mfrac><mo>=<\/mo><mn>145<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Average}=\\frac{580}{4}=145<\/annotation><\/semantics><\/math><br><strong>Correct answer: C. 145<\/strong><\/p>\n<\/div><\/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>As per the RBI report released in April 2026, what is India\u2019s projected GDP growth for the fiscal year 2026-27?<\/strong><br><br>A) 6.5%<br>B) 7.2%<br>C) 7.8%<br>D) 8.1%<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>7.8%<\/strong>: Strong domestic demand and infrastructure spending led the RBI to project a robust 7.8% growth rate.<br><strong>\u2705 Answer: C. 7.8%<\/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 22<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which country hosted the &#8220;World Water Summit&#8221; in March 2026, focusing on the preservation of the Himalayan glaciers?<br><\/strong><br>A) India<br>B) Nepal<br>C) Bhutan<br>D) Switzerland<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Nepal<\/strong>: The Kathmandu summit emphasized the rapid melting of &#8220;The Third Pole&#8221; and its impact on South Asian water security.<br><strong>\u2705 Answer: B. Nepal<\/strong><\/p>\n<\/div><\/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>Leena starts from point A, walks 10 km north, 8 km east, 6 km south, 4 km west and 4 km south. How far and in which direction should she go to return to point A?<\/strong><br><br>A. 4 km west<br>B. 4 km east<br>C. 6 km south<br>D. 10 km north<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>\ud83e\udded Step-by-step movement (build the path in your head)<\/strong><br>Start at <strong>Point A<\/strong> ( If not given always assume face is towards North)<br><strong>10 km North<\/strong> \u2192 go straight from point A<br><strong>8 km East = took right<\/strong>,<br><strong>6 km South = took right<\/strong>,<br><strong>4 km West = took right<\/strong>,<br><strong>4 km South = took left<\/strong>,  \u2192 reach <strong>Point P<\/strong><br><br><strong>\ud83e\udde0 Now track net movement (KEY STEP)<\/strong><br>Horizontal (East-West):<br>West: 4<br>East: 8<br>\ud83d\udc49 Net = 8 &#8211; 4 km <strong>East<\/strong><br><br><strong>Vertical (North-South):<br><\/strong>South: 6 + 4<br>North: 10<br>\ud83d\udc49 Net = 10 &#8211; 6 &#8211; 4 = 0 (Cancel out)<br><br><strong>\ud83d\udccd Final Position<br><\/strong>\ud83d\udc49 Point P is <strong>4 km East of A<\/strong><br><br><strong>\ud83d\udd01 To return to A<br><\/strong>You must go:<br>\ud83d\udc49 <strong>4 km West<\/strong><br>\u2705 Answer: <strong>A. 4 km west<\/strong><br><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 24<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which letter-number cluster completes the series?<br>BDF 14, EGI 17, HJL 20, KMO 23, ?<\/strong><br><br>A. NPR 26<br>B. NQS 26<br>C. NPR 29<br>D. MPR 26<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Pattern:<br>First letters: B, E, H, K, <strong>N<\/strong><br>Second letters: D, G, J, M, <strong>P<\/strong><br>Third letters: F, I, L, O, <strong>R<\/strong><br>Numbers: 14, 17, 20, 23, <strong>26<\/strong><br>So the next term is <strong>NPR 26<\/strong>.<br><strong>Correct answer: A. NPR 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 25<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Who composed the Aihole inscription of Pulakeshin II?<\/strong><br><br>A. Harisena<br>B. Ravikirti<br>C. Vishakhadatta<br>D. Kalidasa<\/p>\n\n\n\n<p class=\"is-style-success\">The Aihole inscription of Pulakeshin II was composed by the poet <strong>Ravikirti<\/strong>. An official ASI post identifies the inscription as composed by poet Ravikirti in honor of Pulakeshin II.<br>\u2705 Answer: <strong>B. Ravikirti<\/strong><\/p>\n<\/div><\/details><\/div>\n<\/div>\n\n\n\n<!--nextpage-->\n\n\n\n<h2 class=\"wp-block-heading\">RRB NTPC Graduate CBT 3 (Practice Quiz 1) \u2013 <strong>Full Exercise With Quick Tricks And Step-by-step Solutions<\/strong> (Part 2: Question 26-50)<\/h2>\n\n\n\n<p>This is a mock test series of RRB NTPC CBT Shift 3 Exam, we are doing the practice test 1. Are you a pioneer who is preparing for the competitive exams? If yes then all exams here are completely free. There are no hidden charges. We even provide rewards if you perform well to motivate you in your study. Here you will try to attempt RRB NTPC Graduate CBT 3 exam practice test 1. The competitive exam is divided into 4 parts each with 25 questions. This is not just a test but also learning ground where you learn from solutions, tricks, and answers.<\/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 = 26;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-26\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"26\">\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 Tricks of RRB NTPC Competitive Exam Test Series Part 2<\/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\": \"Seven friends A, B, C, D, E, F and G sit in a row facing north.\nA sits immediately left of B.\nC sits immediately left of A.\nD sits immediately right of B.\nE sits immediately right of D.\nF sits immediately left of G.\nIf G is at the extreme right, who sits third to the left of G?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is D, but how can we get it s easily. Let's learn the trick.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Three groups of visitors ate at the same restaurant. Group X has 60 members with an average bill of \u20b9420 each, group Y has 25 members with an average bill of \u20b9380 each, and group Z has 15 members with an average bill of \u20b9500 each. What is the overall average bill per member?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 422, but how can we get it is easily. Let's learn the trick.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If 150% of 40% of A is equal to 120% of B, then A is more than B by what percentage?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is conception, so the correct answer is 100%, more.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"What is the pressure at the base of a lake of depth 25 m? Take g = 9.8 $m\/s^2$ and density of water = 1 kg\/litre.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is conception, so the correct answer is 245000 Pa.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Who was elected as the President of the United Nations General Assembly (UNGA) for the 2026 session?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Ruchira Kamboj\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"The internal surface area of an open cuboidal box with internal length 12 cm, breadth 15 cm and height 20 cm is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick behind is very simple, the correct answer is 1260. Let's learn.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Five students \u2014 Raj, Kishan, Chotu, Meera, and Gokul \u2014 obtained different marks in an examination. Who scored the third highest marks?\n(I) Chotu scored more than Raj and Kishan but less than Gokul.\n(II) Gokul scored more than Meera but less than Kishan.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick behind is very simple, the correct answer is Both statements I and II together are not sufficient. Let's learn.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who founded the Faraizi Movement in Bengal?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Haji Shariatullah.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which Constitutional Amendment 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.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In February 2026, which Indian state became the first to grant \"Legal Personhood\" to its rivers to prevent industrial pollution?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Madhya Pradesh\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Three positive integers A, B and C are such that:\nLCM(A, B) = 12, LCM(B, C) = 18, LCM(C, A) = 36\nIf the numbers are as small as possible, what is A + B + C?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 19, but how, you should check this out from here.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Find the median from the following grouped data:\n$$ \\begin{array}{|c|c|} \\hline \\textbf{Age in years} & \\textbf{No. of patients} \\\\ \\hline {10-20} & {8} \\\\ \\hline {20-30} & {12} \\\\ \\hline {30-40} & {20} \\\\ \\hline {40-50} & {25} \\\\ \\hline {50-60} & {15} \\\\ \\hline {60-70} & {10} \\\\ \\hline {70-80} & {10} \\\\ \\hline \\end{array} $$\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 44, but how, you should check this out from here.\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The \"Blue Economy 2.0\" policy, fully implemented in April 2026, primarily focuses on which sector?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Sustainable Maritime Trade\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Four years hence, a father\u2019s age will be 4 times his son\u2019s age. Four years ago, the father\u2019s age was 6 times his son\u2019s age. What are their present ages?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick of the patten is in the sequence. The correct answer is 76 and 16.\n\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The Financial Tracking Service (FTS) is provided by which UN office?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is OCHA.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If 25% of $96 \u2212\\frac{3}{5} \u00d7 \\sqrt[3]{216} \u00d7 \\sqrt{25} = y$ then the value of y is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick of the patten is simplification. The correct answer is 6.\n\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": Which Indian cricketer became the fastest to reach 15,000 runs in ODI history in January 2026?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Shubman Gill\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Based on the English alphabetical order, three of the following four letter clusters are alike in a certain way and form a group. Which is the one that does not belong to that group?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"In order to figure it out, check the explanation. How, learn from here.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following should replace # and % so that the pattern and relationship between the pair on the left of :: is the same as on the right?\n#:EGI :: KMO: \",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"In order to figure it out, check the explanation. How, learn from here.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A typist takes 44 minutes to type 4 pages. How long will he take to type 99 pages?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 1089, let's learn the trick to find out quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What should come next in the series?\n6, 11, 18, 27, 38, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Learn the trick and pattern to figure out questions like these in very short time. The correct answer is 51, let's learn the trick to find out quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If \u2018A\u2019 stands for \u2018\u00f7\u2019, \u2018B\u2019 stands for \u2018\u00d7\u2019, \u2018C\u2019 stands for \u2018+\u2019 and \u2018D\u2019 stands for \u2018\u2212\u2019, then what comes in place of the question mark?\n48 B 6 C 4 D 28 A 2=?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \" Learn the trick and pattern to figure out questions like these in very short time. The correct answer is 278, let's learn the trick to find out quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A car travels 150 km at 50 km\/h and then 120 km at 60 km\/h. What is its average speed for the whole journey?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Learn the trick and pattern to figure out questions like these in very short time. The correct answer is 54 km\/h, let's learn the trick to find out quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"22 is related to 51 following a certain logic. Following the same logic, 13 is related to 33. To which of the following is 31 related, following the same logic?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Need calculation skill to solve this one fastest, learn how to do it quickly and the answer is 69.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Refer to the following letter, number, symbol series and answer the question.\n(Left) A 5 @ B C \u00a3 2 D E # F 3 G H % I 7 J (Right)\nIf all the numbers are dropped from the series, which of the following will be fifth from the left?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick of the patten is visual sequence. The correct answer is \u00a3.\"\n    }\n  }\n  }\n}\n<\/script>\n\n\n\n<div class=\"wp-block-coblocks-accordion\">\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 26<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Seven friends A, B, C, D, E, F and G sit in a row facing north.<br>A sits immediately left of B.<br>C sits immediately left of A.<br>D sits immediately right of B.<br>E sits immediately right of D.<br>F sits immediately left of G.<br>If G is at the extreme right, who sits third to the left of G?<\/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>Build the row step by step:<br>A sits immediately left of B \u2192 A B<br>C sits immediately left of A \u2192 C A B<br>D sits immediately right of B \u2192 C A B D<br>E sits immediately right of D \u2192 C A B D E<br>F sits immediately left of G, and G is at the extreme right \u2192 F G at the end<br>So the full row is:<br><strong>C A B D E F G<\/strong><br>Now count third to the left of G:<br>1st left of G = F<br>2nd left of G = E<br>3rd left of G = <strong>D<\/strong><br><strong>Quick trick:<\/strong> Build the row in one chain, then count from the end.<br><strong>Correct answer: 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 27<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Three groups of visitors ate at the same restaurant. Group X has 60 members with an average bill of \u20b9420 each, group Y has 25 members with an average bill of \u20b9380 each, and group Z has 15 members with an average bill of \u20b9500 each. What is the overall average bill per member?<\/strong><br><br>A. \u20b9420<br>B. \u20b9422<br>C. \u20b9424<br>D. \u20b9426<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Weighted Average<\/strong><br>Formula:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Average<\/mtext><mo>=<\/mo><mfrac><mrow><mo>\u2211<\/mo><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mo>\u00d7<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mrow><mo>\u2211<\/mo><mi>n<\/mi><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Average} = \\frac{\\sum (n \\times x)}{\\sum n}<\/annotation><\/semantics><\/math><br>Use weighted average:<br>Overall average =<br><math data-latex=\"\\frac{60\u00d7420+25\u00d7380+15\u00d7500}{60 + 25 + 15} \\\\ \\\\ \\frac{25200+9500+7500}{100} \\\\ \\\\ \\frac{42200}{100}\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mrow><mn>60<\/mn><mo>\u00d7<\/mo><mn>420<\/mn><mo>+<\/mo><mn>25<\/mn><mo>\u00d7<\/mo><mn>380<\/mn><mo>+<\/mo><mn>15<\/mn><mo>\u00d7<\/mo><mn>500<\/mn><\/mrow><mrow><mn>60<\/mn><mo>+<\/mo><mn>25<\/mn><mo>+<\/mo><mn>15<\/mn><\/mrow><\/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><mfrac><mrow><mn>25200<\/mn><mo>+<\/mo><mn>9500<\/mn><mo>+<\/mo><mn>7500<\/mn><\/mrow><mn>100<\/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><mfrac><mn>42200<\/mn><mn>100<\/mn><\/mfrac><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\frac{60\u00d7420+25\u00d7380+15\u00d7500}{60 + 25 + 15} \\\\ \\\\ \\frac{25200+9500+7500}{100} \\\\ \\\\ \\frac{42200}{100}<\/annotation><\/semantics><\/math><br>\u200b= 422<br>Quick trick: Total members = 100, so the average becomes easy.<br><strong>Correct answer: B. 422<br><\/strong>\ud83d\udc49 <strong>Trick:<\/strong> Never average averages \u2192 use weighted average.<br>Shortcut:<br>Divide by 5 once: 60, 25, 15<br>We&#8217;ll get: 12, 5, 3<br>12 + 5 + 3 = 20<br><br>Divide by 10: 420, 380, 500<br>We&#8217;ll get: 42, 38, 50<br><br>Let&#8217;s multiply now: <br>12 \u00d7 42 + 5 \u00d7 38 + 3 \u00d7 50 = 844<br>Average: 844\/20 = 42.2<br>Now remember, we only bring back the numerator value back, so we divided 420, 380, 500 by 10, right? Now, we will multiply it again by 10 to get the real option.<br><strong>42.2 \u00d7 10 = 422.<br>Option B.<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 28<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>If 150% of 40% of A is equal to 120% of B, then A is more than B by what percentage?<br><\/strong><br>A. 50%<br>B. 75%<br>C. 100%<br>D. 125%<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Percentage Comparison<\/strong><br>Given:<br>150% \u00d7 40% \u00d7 A = 120% \u00d7 B<br>Convert:<br>1.5 \u00d7 0.4 \u00d7 A = 1.2 \u00d7 B <br>0.6A = 1.2B<br>\u21d2 A = 1.2B\/0.6<br>\u21d2 A = 2B<br>So:<br>A is double of B means <strong>100% more than B<\/strong><br>\u2705 Answer: <strong>C. 100%<\/strong> more<br>\ud83d\udc49 <strong>Shortcut:<\/strong> Convert to decimal \u2192 compare ratio.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 29<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What is the pressure at the base of a lake of depth 25 m? (g = 9.8m\/s<sup>2<\/sup> and Density of water = 1 kg\/litre)<br><\/strong><br>A. 245000 Pa<br>B. 249000 Pa<br>C. 250000 Pa<br>D. 255000 Pa<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pressure Formula<\/strong><br>P = pgh<br>Given:<br>p = 1000 kg\/m\u00b3<br>g = 9.8<br>h = 25<br><br>P = 1000 \u00d7 9.8 \u00d7 25<br>P = 245000&nbsp;Pa<br>\u2705 Answer: <strong>A. 2,45,000 Pa<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Water density = 1000 always.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 30<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong><strong>Who was elected as the President of the United Nations General Assembly (UNGA) for the 2026 session?<\/strong><br><\/strong><br>A) Dennis Francis<br>B) Ruchira Kamboj<br>C) Abdullah Shahid<br>D) Csaba K\u0151r\u00f6si<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Ruchira Kamboj<\/strong>: In a historic move, the former Indian permanent representative was elected to lead the UNGA 81st session.<br><strong>\u2705 Answer: B. Ruchira Kamboj<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 31<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The internal surface area of an open cuboidal box with internal length 12 cm, breadth 15 cm and height 20 cm is:<\/strong><br><br>A. 1240 cm\u00b2<br>B. 1260 cm\u00b2<br>C. 1280 cm\u00b2<br>D. 1300 cm\u00b2<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Surface Area (Open Box)<\/strong><br>Formula:<br>= 2(lb + bh + hl) \u2212 lb<br><strong>Trick: <\/strong>Shorten the formula: lb + 2(bh + hl)<br>12 \u00d7 15 + 2(15 \u00d7 20 + 20 \u00d7 12)<br>180 + 2(300 + 240)<br>180 + 1080<br>1260<br>\u2705 Answer: <strong>B. 1260<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 32<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In this question, a question is followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and decide the appropriate answer.<br>Q. Five students \u2013 Alok, Bharti, Celine, Darpan, and Ema \u2013 obtained different marks in an examination. Who scored the third highest marks?<br>(I) Darpan scored more than Alok and Bharti but less than Celine.<br>(II) Ema scored more than Darpan but less than Celine.<br><\/strong><br>A. Data in Statement I alone is sufficient, 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 I and II together are sufficient, but neither alone is sufficient<br>D. Both statements I and II together are not sufficient<\/p>\n\n\n\n<p class=\"is-style-success\">This is a <strong>Data Sufficiency + Ranking<\/strong> question. The goal is NOT to find all ranks \u2014 only check if we can <strong>fix who is 3rd highest<\/strong>.<br><br>\ud83d\udd34 Given<br>Five students: <strong>Raj (R), Kishan (K), Chotu (C), Meera (M), Gokul (G)<\/strong><br>All have <strong>different marks<\/strong>.<br><br>\ud83e\udde0 Statement (I)<br>\u201cChotu scored more than Raj and Kishan but less than Gokul.\u201d<br>This gives:<br>G &gt; C &gt; R,K<br>\ud83d\udc49 But R and K order is unknown<br>\ud83d\udc49 Meera is completely unknown<br>So possible rankings can change \u2192 <strong>3rd position not fixed<\/strong><br>\u274c <strong>Statement (I) alone is NOT sufficient<\/strong><br><br>\ud83e\udde0 Statement (II)<br>\u201cGokul scored more than Meera but less than Kishan.\u201d<br>This gives:<br>K &gt; G &gt; M<br>\ud83d\udc49 But R and C are unknown<br>Again, 3rd place can vary<br>\u274c <strong>Statement (II) alone is NOT sufficient<\/strong><br><br>\ud83d\udd25 Combine (I) + (II)<br>From (I): G &gt; C &gt; R,K<br>From (II): K &gt; G &gt; M<br><br>\ud83e\udde0 Merge both: K &gt; G &gt; C &gt; R,K (Impossible for K and M position is unclear)<br><br>Now observe carefully:<br>R &amp; ? = 4th\/5th (order doesn&#8217;t matter)<br>K = 1st or 4th\/5th (Conflict)<br>G = 2nd<br>? = 3rd (Could be C or M, unclear)<br>\u2705 Answer: <strong>D. Both statements I and II together are not 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 33<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Who founded the Faraizi Movement in Bengal?<\/strong><br><br>A. Dudu Miyan<br>B. Haji Shariatullah<br>C. Syed Ahmad Barelvi<br>D. Titu Mir<\/p>\n\n\n\n<p class=\"is-style-success\">The Faraizi Movement in Bengal was founded by <strong>Haji Shariatullah<\/strong>. Banglapedia describes it as a 19th-century religious reform movement launched by Haji Shariatullah.<br>\u2705 Answer: <strong>B. Haji Shariatullah<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 34<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which Constitutional Amendment lowered the voting age in India from 21 years to 18 years?<\/strong><br><br>A. 58th Amendment<br>B. 61st Amendment<br>C. 62nd Amendment<br>D. 64th Amendment<\/p>\n\n\n\n<p class=\"is-style-success\">The <strong>61st Constitutional Amendment<\/strong> lowered the voting age from 21 to 18. The legislative text states that the proposal was to reduce the voting age from 21 years to 18 years.<br>\u2705 Answer: <strong>B. 61st Amendment<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 35<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In February 2026, which Indian state became the first to grant &#8220;Legal Personhood&#8221; to its rivers to prevent industrial pollution?<\/strong><br><br>A) Uttarakhand<br>B) Bihar<br>C) Madhya Pradesh<br>D) Assam<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Madhya Pradesh:<\/strong> Following a landmark High Court ruling, the Narmada and Betwa rivers were granted legal rights similar to a human being.<br>\u2705 Answer: <strong>C. Madhya Pradesh<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 36<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Three positive integers A, B and C are such that:<br>LCM(A, B) = 12, LCM(B, C) = 18, LCM(C, A) = 36<br>If the numbers are as small as possible, what is A + B + C?<\/strong><br><br>A. 18<br>B. 19<br>C. 20<br>D. 21<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>LCM Problem<\/strong><br>Given:<br>LCM(A,B) = 12<br>LCM(B,C) = 18<br>LCM(C,A) = 36<br><br>Break given LCMs<br><math data-latex=\"LCM(A,\\ B) = 2^2 \\times 3 \\\\ \\\\ LCM(B,\\ C) = 2 \\times 3^2 \\\\ \\\\ LCM(C,\\ A) = 2^2 \\times 3^2\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mi>L<\/mi><mi>C<\/mi><mi>M<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>A<\/mi><mo separator=\"true\">,<\/mo><mtext>&nbsp;<\/mtext><mi>B<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><mn>3<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>L<\/mi><mi>C<\/mi><mi>M<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>B<\/mi><mo separator=\"true\">,<\/mo><mtext>&nbsp;<\/mtext><mi>C<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>L<\/mi><mi>C<\/mi><mi>M<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>C<\/mi><mo separator=\"true\">,<\/mo><mtext>&nbsp;<\/mtext><mi>A<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">LCM(A,\\ B) = 2^2 \\times 3 \\\\ \\\\ LCM(B,\\ C) = 2 \\times 3^2 \\\\ \\\\ LCM(C,\\ A) = 2^2 \\times 3^2<\/annotation><\/semantics><\/math><br>\ud83d\udc49 So only primes involved are <strong>2 and 3<\/strong><br><br><strong>Think in simple words (NO VARIABLES)<\/strong><br>We need to <strong>separate A, B, C using 2s and 3s<\/strong> out of the grouped (A, B), (B, C), and (C, A):<br>For A look (<strong>A<\/strong>, B) &amp; (C, <strong>A<\/strong>) \u2192 2<sup>2<\/sup> came in both (A, B) and (C, A) which confirms it&#8217;s A. Only 3 left behind for B.<br><math data-latex=\"A = 2^2 = 4\"><semantics><mrow><mi>A<\/mi><mo>=<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>=<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">A = 2^2 = 4<\/annotation><\/semantics><\/math><br>For C look (B, <strong>C<\/strong>) &amp; (<strong>C<\/strong>, A) \u2192 3<sup>2<\/sup> came in both (B, C) and (C, A) which confirms it&#8217;s C. Only 2 left behind for B.<br><math data-latex=\"C = 3^2 = 9\"><semantics><mrow><mi>C<\/mi><mo>=<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><mo>=<\/mo><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">C = 3^2 = 9<\/annotation><\/semantics><\/math><br>For B look (A, <strong>B<\/strong>) &amp; (<strong>B<\/strong>, C) \u2192 Two values left for B: 3 and 2.<br><math data-latex=\"B = 3 \\times 2 = 6\"><semantics><mrow><mi>B<\/mi><mo>=<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><mn>2<\/mn><mo>=<\/mo><mn>6<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">B = 3 \\times 2 = 6<\/annotation><\/semantics><\/math><br><br>Minimum values:<br>A=4, B=6, C=9<br>A + B + C = 19<br>\u2705 Answer: <strong>B. 19<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Use prime factors.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 37<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Find the median from the following grouped data.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Age in years<\/th><th class=\"has-text-align-center\" data-align=\"center\">No. of patients<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">10-20<\/td><td class=\"has-text-align-center\" data-align=\"center\">8<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">20-30<\/td><td class=\"has-text-align-center\" data-align=\"center\">12<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">30-40<\/td><td class=\"has-text-align-center\" data-align=\"center\">20<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">40-50<\/td><td class=\"has-text-align-center\" data-align=\"center\">25<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">50-60<\/td><td class=\"has-text-align-center\" data-align=\"center\">15<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">60-70<\/td><td class=\"has-text-align-center\" data-align=\"center\">10<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">70-80<\/td><td class=\"has-text-align-center\" data-align=\"center\">10<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"is-style-info\">A. 42<br>B. 43<br>C. 44<br>D. 45<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Median<\/strong><br>Total No. of Patients = 100 \u2192 N\/2 = 50<br>Median class: 40-50 = 25<br>l = 40<br>cf = 40 (Total frequency of prior 40-50: 8 + 12 + 20 = 40)<br>f = 25<br>h (50 &#8211; 40) = 10<br>Formula:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>Median<\/mtext><mo>=<\/mo><mi>l<\/mi><mo>+<\/mo><mfrac><mrow><mo stretchy=\"false\">(<\/mo><mi>N<\/mi><mi mathvariant=\"normal\">\/<\/mi><mn>2<\/mn><mo>\u2212<\/mo><mi>c<\/mi><mi>f<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><mi>f<\/mi><\/mfrac><mo>\u00d7<\/mo><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Median} = l + \\frac{(N\/2 &#8211; cf)}{f} \u00d7 h<\/annotation><\/semantics><\/math><br><math data-latex=\"40 + \\frac{50 - 40}{25} \\times 10 \\\\ 40 + \\frac{10 \\times 10}{25} \\\\ 40 + \\frac{100}{25} \\\\ 40 + 4\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mn>40<\/mn><mo>+<\/mo><mfrac><mrow><mn>50<\/mn><mo>\u2212<\/mo><mn>40<\/mn><\/mrow><mn>25<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>10<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>40<\/mn><mo>+<\/mo><mfrac><mrow><mn>10<\/mn><mo>\u00d7<\/mo><mn>10<\/mn><\/mrow><mn>25<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>40<\/mn><mo>+<\/mo><mfrac><mn>100<\/mn><mn>25<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>40<\/mn><mo>+<\/mo><mn>4<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">40 + \\frac{50 &#8211; 40}{25} \\times 10 \\\\ 40 + \\frac{10 \\times 10}{25} \\\\ 40 + \\frac{100}{25} \\\\ 40 + 4<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>C. 44<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 38<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The &#8220;Blue Economy 2.0&#8221; policy, fully implemented in April 2026, primarily focuses on which sector?<\/strong><br><br>A) Space Tourism<br>B) Sustainable Maritime Trade<br>C) Deep-sea Mining<br>D) Inland Fisheries<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Sustainable Maritime Trade<\/strong>: The policy aims to balance ocean-based economic growth with social equity and environmental health.<br><strong>\u2705 Answer: B. Sustainable Maritime Trade<\/strong><\/p>\n<\/div><\/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>Four years hence, a father\u2019s age will be 4 times his son\u2019s age. Four years ago, the father\u2019s age was 6 times his son\u2019s age. What are their present ages?<br><\/strong><br>A. 70 and 14<br>B. 72 and 15<br>C. 76 and 16<br>D. 80 and 18<\/p>\n\n\n\n<p class=\"is-style-success\">Let the present age of the son be <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math> and the father be <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y<\/annotation><\/semantics><\/math>.<br>Four years hence means after 4 years, so ages become x + 4 and y + 4,<br>and we are told the father will be 4 times the son, so y + 4 = 4(x + 4).<br>Four years ago means ages were x &#8211; 4 and y &#8211; 4, and the father was 6 times the son, so y &#8211; 4 = 6(x &#8211; 4).<br><br>Now simplify both:<br>from the first,<br>y + 4 = 4(x + 4)<br>y + 4 = 4x + 16<br>y = 4x + 16 &#8211; 4<br>y = 4x + 12.<br>From the second,<br>y &#8211; 4 = 6(x &#8211; 4)<br>y &#8211; 4 = 6x &#8211; 24<br>y = 6x &#8211; 24 + 4<br>y = 6x &#8211; 20.<br>Since both equal <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">y<\/annotation><\/semantics><\/math>, set them equal:<br>y = y<br>4x + 12 = 6x &#8211; 20<br>12 + 20 = 6x &#8211; 4x<br>32 = 2x<br>x = 32\/2<br>x = 16<br>Solving gives x = 16.<br>There is only one option with 16 that is Option C. But for education purposes, let&#8217;s see further.<br>Substitute back:<br>y = 4x + 12<br>y = 4(16) + 12<br>y = 64 + 12<br>y = 76.<br>So the present ages are: <strong>father = 76 years, son = 16 years<\/strong>.<br>\u2705 Answer: <strong>C. 76 and 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 40<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The Financial Tracking Service (FTS) is provided by which UN office?<\/strong><br><br>A. UNDP<br>B. UNESCO<br>C. OCHA<br>D. UNICEF<\/p>\n\n\n\n<p class=\"is-style-success\">OCHA\u2019s Financial Tracking Service page says the service is provided by the <strong>United Nations Office for the Coordination of Humanitarian Affairs<\/strong>.<br>\u2705 Answer: <strong>C. OCHA<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 41<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>If 25% of <\/strong><math data-latex=\"96 - \\frac{3}{5} \\times \\sqrt[3]{216} \\times \\sqrt{25} = y\"><semantics><mrow><mn>96<\/mn><mo>\u2212<\/mo><mfrac><mn>3<\/mn><mn>5<\/mn><\/mfrac><mo>\u00d7<\/mo><mroot><mn>216<\/mn><mn>3<\/mn><\/mroot><mo>\u00d7<\/mo><msqrt><mn>25<\/mn><\/msqrt><mo>=<\/mo><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">96 &#8211; \\frac{3}{5} \\times \\sqrt[3]{216} \\times \\sqrt{25} = y<\/annotation><\/semantics><\/math><strong>, then the value of y is:<\/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>Simplify<\/strong><br>25% \u00d7 96 = 24 <br><math data-latex=\"\\sqrt[3]{216} = 6,\\ \\ \\ \\sqrt{25} = 5\"><semantics><mrow><mroot><mn>216<\/mn><mn>3<\/mn><\/mroot><mo>=<\/mo><mn>6<\/mn><mo separator=\"true\">,<\/mo><mtext>&nbsp;<\/mtext><mtext>&nbsp;<\/mtext><mtext>&nbsp;<\/mtext><msqrt><mn>25<\/mn><\/msqrt><mo>=<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt[3]{216} = 6,\\ \\ \\ \\sqrt{25} = 5<\/annotation><\/semantics><\/math><br>Let&#8217;s put the values:<br><math data-latex=\"24 - \\frac{3}{5} \\times 6 \\times 5 \\\\ 24 - \\frac{3 \\times 6 \\times 5}{5} \"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mn>24<\/mn><mo>\u2212<\/mo><mfrac><mn>3<\/mn><mn>5<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>6<\/mn><mo>\u00d7<\/mo><mn>5<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>24<\/mn><mo>\u2212<\/mo><mfrac><mrow><mn>3<\/mn><mo>\u00d7<\/mo><mn>6<\/mn><mo>\u00d7<\/mo><mn>5<\/mn><\/mrow><mn>5<\/mn><\/mfrac><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">24 &#8211; \\frac{3}{5} \\times 6 \\times 5 \\\\ 24 &#8211; \\frac{3 \\times 6 \\times 5}{5} <\/annotation><\/semantics><\/math><br>y = 24 \u2212 18<br>y = 6<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 42<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong><strong>Which Indian cricketer became the fastest to reach 15,000 runs in ODI history in January 2026?<\/strong><\/strong><br><br>A) Virat Kohli<br>B) Shubman Gill<br>C) Rohit Sharma<br>D) Yashasvi Jaiswal<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Shubman Gill<\/strong>: Continuing his record-breaking form, Gill surpassed Virat Kohli\u2019s record for the fastest 15k runs in fewer innings.<br>\u2705 Answer: <strong>B. Shubman Gill<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 43<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Based on the English alphabetical order, three of the following four letter clusters are alike in a certain way and form a group. Which is the one that does not belong to that group?<\/strong><br><br>A. CEG<br>B. FHJ<br>C. KMO<br>D. NQT<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pattern:<br><\/strong>Option A: CEG<br>C + 2 = E<br>E + 2 = G<br><br>Option B: FHJ<br>F + 2 = H<br>H + 2 = J<br><br>Option C: KMO<br>K + 2 = M<br>M + 2 = O<br><br><strong>Option D: NQT<br>N + 3 = Q<br>Q + 3 = T<\/strong><br><br>Only Option D is different.<br><strong>\u2705 Answer: D. NQT<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 44<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which of the following should replace # and % so that the pattern and relationship between the pair on the left of :: is the same as on the right?<\/strong><br><strong>#:EGI :: KMO:<br><\/strong><br>A. # = CEG, % = MOQ<br>B. # = CIK, % = MOQ<br>C. # = CGJ, % = MOP<br>D. # = DGK, % = NOP<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pattern:<\/strong><br>EGI<br>E + 2 = G<br>G + 2 = I<br><br>KMO<br>K + 2 = M<br>M + 2 = O<br>So Option A makes more sense.<br>C E (+2) G (+2)<br>M O (+2) Q (+2)<br>\u2705 Answer: <strong>A. # = CEG, % = MOQ<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 45<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>A typist takes 44 minutes to type 4 pages. How long will he take to type 99 pages?<\/strong><br><br>A. 1000 minutes<br>B. 1011 minutes<br>C. 1089 minutes<br>D. 1099 minutes<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Time Work<\/strong><br>4 pages = 44 min<br>1 page = 44\/4 = 11 min<br>99 pages = 99 x 11 = 1089 min<br>\u2705 Answer: <strong>C. 1089<\/strong><\/p>\n<\/div><\/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>What should come next in the series?<br>6, 11, 18, 27, 38, ?<\/strong><br><br>A. 47<br>B. 49<br>C. 51<br>D. 53<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Series:<br>6,11,18,27,38,?<br><br>Differences are:<br>5,7,9,11<br><br>The next difference is: 13<br>So: 38 + 13 = 51<br><strong>Quick trick:<\/strong> The differences are consecutive odd numbers.<br><strong>Correct answer: C. 51<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 47<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>If \u2018A\u2019 stands for \u2018\u00f7\u2019, \u2018B\u2019 stands for \u2018\u00d7\u2019, \u2018C\u2019 stands for \u2018+\u2019 and \u2018D\u2019 stands for \u2018\u2212\u2019, then what comes in place of the question mark?<br>48 B 6 C 4 D 28 A 2=?<\/strong><br><br>A. 132<br>B. 432<br>C. 466<br>D. 278<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Operator Coding<\/strong><br>BODMAS: Must follow Step-by-step &#8220;<strong>B<\/strong>racket <strong>O<\/strong>pen <strong>D<\/strong>ivide <strong>M<\/strong>ultiply <strong>A<\/strong>ddition <strong>S<\/strong>ubtract&#8221; <br>48 \u00d7 6 + 4 \u2212 28 \u00f7 2 <br>= 288 + 4 \u2212 14<br>= 292  &#8211; 14<br>= 278<br>\u2705 Answer: <strong>D. 278<\/strong><\/p>\n<\/div><\/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 car travels 150 km at 50 km\/h and then 120 km at 60 km\/h. What is its average speed for the whole journey?<br><\/strong><br>A. 52 km\/h<br>B. 54 km\/h<br>C. 56 km\/h<br>D. 58 km\/h<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Total distance:<br>150 + 120 = 270&nbsp;km<br>Total time:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>150<\/mn><mn>50<\/mn><\/mfrac><mo>+<\/mo><mfrac><mn>120<\/mn><mn>60<\/mn><\/mfrac><mo>=<\/mo><mn>3<\/mn><mo>+<\/mo><mn>2<\/mn><mo>=<\/mo><mn>5<\/mn><mtext>&nbsp;h<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{150}{50} + \\frac{120}{60} = 3 + 2 = 5 \\text{ h}<\/annotation><\/semantics><\/math><br>Average speed:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mfrac><mn>270<\/mn><mn>5<\/mn><\/mfrac><mo>=<\/mo><mn>54<\/mn><mtext>&nbsp;km\/h<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{270}{5} = 54 \\text{ km\/h}<\/annotation><\/semantics><\/math><br><strong>Quick trick:<\/strong> Average speed = total distance \u00f7 total time, not the average of speeds.<br><strong>Correct answer: B. 54 km\/h<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 49<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>22 is related to 51 following a certain logic. Following the same logic, 13 is related to 33. To which of the following is 31 related, following the same logic?<\/strong><br><br>A. 43<br>B. 53<br>C. 62<br>D. 69<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Number Logic: (\u00d72 +7)<\/strong><br>22 \u2192 51<br>(22\u00d72 +7 = 51)<br>13 \u2192 86<br>(13\u00d72 +7 = 33)<br>31 \u2192 31 \u00d7 2 + 7 = 69  \u2714<br>\u2705 Answer: <strong>D. 69<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 50<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Refer to the following letter, number, symbol series and answer the question.<br>(Left) A 5 @ B C \u00a3 2 D E # F 3 G H % I 7 J (Right)<br>If all the numbers are dropped from the series, which of the following will be fifth from the left?<\/strong><br><br>A. B<br>B. C<br>C. \u00a3<br>D. D<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Series<\/strong><br>Remove numbers:<br>(Left) A @ B C \u00a3 D E # F G H % I J (Right)<br>5th from left = <strong>\u00a3<\/strong><br>\u2705 Answer: <strong>C. \u00a3<\/strong><\/p>\n<\/div><\/details><\/div>\n<\/div>\n\n\n\n<!--nextpage-->\n\n\n\n<h2 class=\"wp-block-heading\">RRB NTPC Graduate CBT 3 (Free Practice Test 1) Series Of Solutions, Hack Tricks (Part 3: Question 51-75)<\/h2>\n\n\n\n<p>This is the part of the massive test series. Let&#8217;s take the mock test of RRB NTPC Exam 1 part 3 which contains questions from 51 to 75. We provide full preparation service with 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 3 exam practice test 1. The competitive exam is divided into 4 parts each with 25 questions. You will be taking the third series with massive list of test questions, answer, solutions, and tricks 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 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 = 27;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-27\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"27\">\n            <div class=\"kq-loading\">Loading quiz...<\/div>\n        <\/div>\n        \n    <div id=\"kq-auth-modal\" class=\"kq-auth-modal\" style=\"display:none;\">\n      <div class=\"kq-auth-modal-inner\">\n        <button id=\"kq-auth-close\" class=\"kq-auth-close\" aria-label=\"Close\">\u2716<\/button>\n\n        <!-- TAB NAV -->\n        <div class=\"kq-auth-tabs\" role=\"tablist\">\n          <button class=\"kq-tab active\" data-tab=\"register\" type=\"button\" role=\"tab\" aria-selected=\"true\">Register<\/button>\n          <button class=\"kq-tab\" data-tab=\"login\" type=\"button\" role=\"tab\" aria-selected=\"false\">Login<\/button>\n          <button class=\"kq-tab\" data-tab=\"forgot\" type=\"button\" role=\"tab\" aria-selected=\"false\">Forgot<\/button>\n        <\/div>\n\n        <!-- PANELS -->\n        <div class=\"kq-auth-panel-wrap\">\n\n          <!-- REGISTER -->\n          <div class=\"kq-auth-panel\" data-panel=\"register\" style=\"display:block\">\n            <div class=\"kq-auth-card\">\n              <h3>Register<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-username\" placeholder=\"Username\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-email\" placeholder=\"Email\" type=\"email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-signup-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-signup-btn\" class=\"button kq-btn-small\">Register<\/button>\n              <small style=\"display:block;margin-top:8px;\">Already registered? Use Login tab.<\/small>\n            <\/div>\n          <\/div>\n\n          <!-- LOGIN -->\n          <div class=\"kq-auth-panel\" data-panel=\"login\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Login<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-login-password\" placeholder=\"Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-login-btn\" class=\"button kq-btn-small\">Login<\/button>\n            <\/div>\n          <\/div>\n\n          <!-- FORGOT -->\n          <div class=\"kq-auth-panel\" data-panel=\"forgot\" style=\"display:none\">\n            <div class=\"kq-auth-card\">\n              <h3>Forgot Password<\/h3>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-identity\" placeholder=\"Username or Email\" \/>\n              <\/div>\n              <div class=\"kq-field\">\n                <input id=\"kq-forgot-newpass\" placeholder=\"New Password\" type=\"password\" \/>\n                <button class=\"kq-toggle-pass\" type=\"button\" aria-label=\"Toggle password\">\ud83d\udc41<\/button>\n              <\/div>\n              <button id=\"kq-forgot-btn\" class=\"button kq-btn-small\">Update Password<\/button>\n            <\/div>\n          <\/div>\n\n        <\/div>\n\n      <\/div>\n    <\/div>\n    \n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">The Solution and Explanation of The Competitive Exam<\/h2>\n\n\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"A ladder is placed against a wall. If the ladder makes an angle of $45^\u2218$ with the ground and its foot is 8 m away from the wall, what is the length of the ladder?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 8\\sqrt{2}m, West and learn the real way to solve.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"What is the name of the joint military exercise between India and Japan conducted in the Rajasthan desert in March 2026?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Dharma Guardian\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"BWhat should come in place of the question mark?\n180, 165, 145, 120, 90, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 55. Let's learn the trick to solve it in no time.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"The 14th-century treatise L\u012bl\u0101tilakam is associated with which literary dialect?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Manipravalam\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Which Article of the Indian Constitution provides for a joint sitting of both Houses of Parliament in certain cases?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Article 108, let's learn more like these questions.\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"If 45% of $60 \u2212 \\frac{2}{3} \u00d7 \\sqrt[3]{216} \u00d7 \\sqrt{9} = y$, then the value of y is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 15, let's learn how to solve it quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What should come in place of the question mark?\n12, 21, 33, 48, 66, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 87. Let's learn how to solve it in 3 seconds.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language:\nA \u00f7 B means A is the daughter of B\nA - B means A is the brother of B\nA \u00d7 B means A is the husband of B\nA + B means A is the mother of B\nHow is H related to R if H \u00f7 V - K \u00d7 T + R?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Cousin.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"P, Q, R, S, Y and Z live on six different floors of the same building numbered 1 to 6 from bottom to top.\nOnly three people live between Y and Z.\nOnly P lives above Y.\nQ lives immediately below Y.\nR lives on an odd-numbered floor.\nWho lives on floor number 2?\",\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 S.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which city was declared the \"UNESCO World Book Capital\" for the year 2026?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Rio de Janeiro\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Read the statements and conclusions carefully.\nStatements:\nAll roses are flowers.\nSome flowers are fragrant.\nAll fragrant things are pleasant.\nConclusions:\n(I) Some pleasant things are flowers.\n(II) All roses are pleasant.\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Only conclusion (I) follows\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Select the triad which follows the same pattern as the pairs given below:\nFARM - FAMR - AFMR\nTIME - TIEM - ITEM\",\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 BALD - BADL - ABDL.\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which letter-number cluster will replace the question mark in the series?\nBDF 10, EGI 13, HJL 16, KMO 19, ?\",\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 NPR 22.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following letter-number clusters should replace the question mark?\nFHJ : DFL :: KMO : ?\",\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 MOQ.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What was the theme of the International Day of Clean Air for blue skies 2025?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Racing for Air.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Refer to the following number and symbol series and answer the question that follows.\nAll numbers are single-digit numbers only.\n4 @ 7 ! 2 # 5 * 9 $ 1 % 8 & 3\nIf all symbols are dropped from the series, which number will be seventh from the right?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 7. Let's learn the right trick to solve it quickly.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The \"Vishwa Shanti\" (World Peace) statue, inaugurated by the PM in April 2026, is located in which city?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Kurukshetra\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If $a + \\frac{1}{a} = 3$, then what is the value of $a^4 + \\frac{1}{a^4}$?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"It is a simple mathematics question, you must be fast enough to solve it or you know it.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which Indian state inaugurated the country\u2019s first \"Green Hydrogen Valley\" in March 2026?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Kerala\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language, PAPA is coded as 2424 and SEAT is coded as 3218. What is the code for P?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Rise in trade restrictions.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language, \u2018APES\u2019 is coded as \u20184583\u2019 and \u2018PEAT\u2019 is coded as \u20186438\u2019. What is the code for \u2018S\u2019 in that language?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"A simple mathematics question, but there is a simple trick behind it to solve it within three seconds. The correct answer is 4.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"If 3 : 24 :: 3.5 : x and 5 : 40 :: 4.5 : y, what is the ratio of x to y?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"A simple mathematics question, but there is a simple trick behind it to solve it within three seconds. The correct answer is 7:9.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Eenaa and Meena start a business by investing in the ratio 5 : 8. If the total profit is \u20b952,000, what is the difference between their shares of profit?\",\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 \u20b912,000.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who was appointed as the Governor of the Reserve Bank of India (RBI) in early 2026?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"K.V. Kamath\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"AB is the diameter of a circle. C is a point on the circle such that $\u2220CAB = 35^\u2218$. What is \u2220ABC?\",\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 $55^\\circ$.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language, \u2018BYER\u2019 is coded as \u20183218\u2019 and \u2018LYER\u2019 is coded as \u20182178\u2019. What is the code for \u2018L\u2019 in the given code language?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"A simple mathematics question, but there is a simple trick behind it to solve it within three seconds. The correct answer is 7.\"\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>A ladder is placed against a wall. If the ladder makes an angle of 45\u00b0 with the ground and its foot is 8 m away from the wall, what is the length of the ladder?<br><\/strong><br>A. <math data-latex=\"8\\sqrt{2}\"><semantics><mrow><mn>8<\/mn><msqrt><mn>2<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">8\\sqrt{2}<\/annotation><\/semantics><\/math> m<br>B. 8 m<br>C. 16 m<br>D. <math data-latex=\"4\\sqrt{2}\"><semantics><mrow><mn>4<\/mn><msqrt><mn>2<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">4\\sqrt{2}<\/annotation><\/semantics><\/math> m<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Ladder Length (Trigonometry)<\/strong><br>Right triangle situation:<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>cos<\/mi><mo>\u2061<\/mo><mi>\u03b8<\/mi><mo>=<\/mo><mfrac><mtext>base<\/mtext><mtext>hypotenuse<\/mtext><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\cos\\theta = \\frac{\\text{base}}{\\text{hypotenuse}}<\/annotation><\/semantics><\/math><br><br>Given:<br>Angle = 45\u00b0 is equal to <math data-latex=\"\\frac{1}{\\sqrt{2}}\"><semantics><mfrac><mn>1<\/mn><msqrt><mn>2<\/mn><\/msqrt><\/mfrac><annotation encoding=\"application\/x-tex\">\\frac{1}{\\sqrt{2}}<\/annotation><\/semantics><\/math><br>Base = 8 m<br>Hypotenuse = Ladder length (L)<br><math data-latex=\"cos45^\\circ = \\frac{8}{L} \\\\ \\frac{1}{\\sqrt{2}} = \\frac{8}{L} \\\\ L = 8\\sqrt{2}\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mi>c<\/mi><mi>o<\/mi><mi>s<\/mi><msup><mn>45<\/mn><mo>\u2218<\/mo><\/msup><mo>=<\/mo><mfrac><mn>8<\/mn><mi>L<\/mi><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mn>1<\/mn><msqrt><mn>2<\/mn><\/msqrt><\/mfrac><mo>=<\/mo><mfrac><mn>8<\/mn><mi>L<\/mi><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>L<\/mi><mo>=<\/mo><mn>8<\/mn><msqrt><mn>2<\/mn><\/msqrt><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">cos45^\\circ = \\frac{8}{L} \\\\ \\frac{1}{\\sqrt{2}} = \\frac{8}{L} \\\\ L = 8\\sqrt{2}<\/annotation><\/semantics><\/math><br><br>\u2705 Answer: <strong>A<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong><br><strong>Quick trick:<\/strong> A <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mn>45<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">45^\\circ<\/annotation><\/semantics><\/math>angle with one leg known often means a 45\u221245\u221290 triangle, so the hypotenuse is leg <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo>\u00d7<\/mo><msqrt><mn>2<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">\\times \\sqrt{2}<\/annotation><\/semantics><\/math>\u200b.<br>The leg means base, which is 8 here: 8 <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo>\u00d7<\/mo><msqrt><mn>2<\/mn><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">\\times \\sqrt{2}<\/annotation><\/semantics><\/math>\u200b.<\/p>\n<\/div><\/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>What is the name of the joint military exercise between India and Japan conducted in the Rajasthan desert in March 2026?<\/strong><br><br>A) Dharma Guardian<br>B) Shinyuu Maitri<br>C) Veer Guardian<br>D) Desert Cyclone<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Dharma Guardian<\/strong>: This 2026 edition focused on semi-urban and desert warfare tactics.<br><strong>\u2705 Answer: A. Dharma Guardian<\/strong><\/p>\n<\/div><\/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>What should come in place of the question mark?<br>180, 165, 145, 120, 90, ?<\/strong><br><br>A. 55<br>B. 60<br>C. 65<br>D. 50<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Look at the differences:<br>180\u2192165 = \u221215<br>165\u2192145 = \u221220<br>145\u2192120 = \u221225<br>120\u219290 = \u221230<br>The differences increase by 5 each time, so the next difference is \u221235.<br>90 \u2212 35 = 55<br><strong>Quick trick:<\/strong> Track the differences, not the numbers themselves.<br><strong>Correct answer: A. 55<\/strong><\/p>\n<\/div><\/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>The 14th-century treatise L\u012bl\u0101tilakam is associated with which literary dialect?<br><\/strong><br>A. Manipravalam<br>B. Brahmi<br>C. Prakrit<br>D. Pali<\/p>\n\n\n\n<p class=\"is-style-success\">Britannica states that the L\u012bl\u0101tilakam, a 14th-century treatise on grammar and poetics, describes the literary dialect Manipravalam and discusses the blending of Tamilizing and Sanskritizing trends.<br>\u2705 Answer: <strong>A. Manipravalam<\/strong><\/p>\n<\/div><\/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>Which Article of the Indian Constitution provides for a joint sitting of both Houses of Parliament in certain cases?<\/strong><br><br>A. Article 107<br>B. Article 108<br>C. Article 109<br>D. Article 110<\/p>\n\n\n\n<p class=\"is-style-success\">The Constitution text and constitutional commentary identify Article 108 as the provision for a joint sitting of both Houses of Parliament in certain cases.<br><strong>\u2705 Answer: B. Article 108<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 56<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>If 45% of <\/strong><math data-latex=\"60 - \\frac{2}{3} \\times \\sqrt[3]{216} \\times \\sqrt{9} = y\"><semantics><mrow><mn>60<\/mn><mo>\u2212<\/mo><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mroot><mn>216<\/mn><mn>3<\/mn><\/mroot><mo>\u00d7<\/mo><msqrt><mn>9<\/mn><\/msqrt><mo>=<\/mo><mi>y<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">60 &#8211; \\frac{2}{3} \\times \\sqrt[3]{216} \\times \\sqrt{9} = y<\/annotation><\/semantics><\/math><strong>, then the value of y is:<\/strong><br><strong><br><\/strong>A. 15<br>B. 12<br>C. 18<br>D. 21<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Simplification<\/strong><br><math data-latex=\"45\\%\\ of\\ 60\\ = 27\"><semantics><mrow><mn>45<\/mn><mi>%<\/mi><mtext>&nbsp;<\/mtext><mi>o<\/mi><mi>f<\/mi><mtext>&nbsp;<\/mtext><mn>60<\/mn><mtext>&nbsp;<\/mtext><mo>=<\/mo><mn>27<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">45\\%\\ of\\ 60\\ = 27<\/annotation><\/semantics><\/math><br>Now for roots:<br><math data-latex=\"\\sqrt[3]{216} = 6 \\\\ \\sqrt{9} = 3\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mroot><mn>216<\/mn><mn>3<\/mn><\/mroot><mo>=<\/mo><mn>6<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><msqrt><mn>9<\/mn><\/msqrt><mo>=<\/mo><mn>3<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\\sqrt[3]{216} = 6 \\\\ \\sqrt{9} = 3<\/annotation><\/semantics><\/math><br>Let&#8217;s put them:<br><math data-latex=\"y = 27 - \\frac{2}{3} \\times 6 \\times 3 \\\\ y = 27 - \\frac{2 \\times 18}{3} \\\\ y = 27 - 12 \\\\ y = 15\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mi>y<\/mi><mo>=<\/mo><mn>27<\/mn><mo>\u2212<\/mo><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>6<\/mn><mo>\u00d7<\/mo><mn>3<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>y<\/mi><mo>=<\/mo><mn>27<\/mn><mo>\u2212<\/mo><mfrac><mrow><mn>2<\/mn><mo>\u00d7<\/mo><mn>18<\/mn><\/mrow><mn>3<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>y<\/mi><mo>=<\/mo><mn>27<\/mn><mo>\u2212<\/mo><mn>12<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>y<\/mi><mo>=<\/mo><mn>15<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">y = 27 &#8211; \\frac{2}{3} \\times 6 \\times 3 \\\\ y = 27 &#8211; \\frac{2 \\times 18}{3} \\\\ y = 27 &#8211; 12 \\\\ y = 15<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>A. 15<\/strong><br>\ud83d\udc49 <strong>Trick:<\/strong> Always simplify roots first.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 57<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What should come in place of the question mark?<br>12, 21, 33, 48, 66, ?<\/strong><br><br>A. 82<br>B. 84<br>C. 87<br>D. 90<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Series<\/strong><br>12, 21, 33, 48, 66, ?<br>Differences increase of +3:<br>+9, +12, +15, +18 \u2192 next +21<br>66 + 21 = 87<br><strong>\u2705 Answer: C. 87<\/strong><\/p>\n<\/div><\/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>In a certain code language:<br>A \u00f7 B means A is the daughter of B<br>A &#8211; B means A is the brother of B<br>A \u00d7 B means A is the husband of B<br>A + B means A is the mother of B<br>How is H related to R if H \u00f7 V &#8211; K \u00d7 T + R?<br><\/strong><br>A. Cousin<br>B. Aunt<br>C. Niece<br>D. Sister<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>From the relations:<br>H\u00f7V means <strong>H is the daughter of V<\/strong><br>V\u2212K means <strong>V is the brother of K<\/strong><br>K\u00d7T means <strong>K is the husband of T<\/strong><br>T+R means <strong>T is the mother of R<\/strong><br>So V and K are siblings. K is R\u2019s father, and H is V\u2019s daughter. That means H is the <strong>cousin<\/strong> of R.<br><strong>Quick trick:<\/strong> Build the family tree from right to left.<br><strong>Correct answer: A. Cousin<\/strong><\/p>\n<\/div><\/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>P, Q, R, S, Y and Z live on six different floors of the same building numbered 1 to 6 from bottom to top.<br>Only three people live between Y and Z.<br>Only P lives above Y.<br>Q lives immediately below Y.<br>R lives on an odd-numbered floor.<br>Who lives on floor number 2?<\/strong><br><br>A. S<br>B. Y<br>C. P<br>D. Q<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>\u201cOnly three people live between Y and Z\u201d means Y and Z are 4 floors apart.<br>\u201cOnly P lives above Y\u201d means Y must be on floor 5 and P on floor 6.<br>\u201cQ lives immediately below Y\u201d means Q is on floor 4.<br>Since Y and Z are 4 floors apart, Z must be on floor 1.<br>Remaining floors are 2 and 3 for R and S.<br>R is on an odd floor, so R is on 3 and S is on 2.<br>So the person on floor 2 is <strong>S<\/strong>.<br><strong>Quick trick:<\/strong> Use the \u201conly one above\u201d clue first; it fixes the top end immediately.<br><strong>Correct answer: A. S<\/strong><\/p>\n<\/div><\/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>Which city was declared the &#8220;UNESCO World Book Capital&#8221; for the year 2026?<\/strong><br><br>A) Rio de Janeiro<br>B) Madrid<br>C) New Delhi<br>D) Guadalajara<\/p>\n\n\n\n<p class=\"is-style-success\">Rio de Janeiro: UNESCO selected the Brazilian city for its commitment to promoting literature and literacy.<br><strong>\u2705 Answer: A. Rio de Janeiro<\/strong><\/p>\n<\/div><\/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>Read the statements and conclusions carefully.<br>Statements:<br>All roses are flowers.<br>Some flowers are fragrant.<br>All fragrant things are pleasant.<br>Conclusions:<br>(I) Some pleasant things are flowers.<br>(II) All roses are pleasant.<\/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 roses are flowers.<br>Some flowers are fragrant.<br>All fragrant things are pleasant.<br><br>Since some flowers are fragrant, and all fragrant things are pleasant, it follows that <strong>some pleasant things are flowers<\/strong>.<br>But we cannot say <strong>all roses are pleasant<\/strong>, because no statement links every rose to fragrant or pleasant.<br><br>So only conclusion <strong>(I)<\/strong> follows.<br><strong>Quick trick:<\/strong> \u201cSome\u201d + \u201call\u201d can create a valid partial overlap, but not a universal statement.<br><strong>Correct 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 62<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Select the triad which follows the same pattern as the pairs given below:<br>FARM &#8211; FAMR &#8211; AFMR<br>TIME &#8211; TIEM &#8211; ITEM<\/strong><br><br>A. BALD &#8211; BADL &#8211; ABDL<br>B. NOTE &#8211; NTOE &#8211; ONTE<br>C. GLOW &#8211; GOLW &#8211; OGWL<br>D. MINT &#8211; MNIT &#8211; NMIT<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>Look at the pattern:<br>FARM \u2192 FAMR (swap the last two letters)<br>FAMR \u2192 AFMR (swap the first two letters)<br><br>So the pattern is:<br>swap the last two letters<br>then swap the first two letters<br><br>Check option A:<br>BALD \u2192 BADL<br>BADL \u2192 ABDL<br>That follows the same pattern exactly.<br><strong>Quick trick:<\/strong> First swap the last two, then the first two.<br><strong>Correct answer: A. BALD &#8211; BADL &#8211; ABDL<\/strong><\/p>\n<\/div><\/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>Which letter-number cluster will replace the question mark in the series?<br>BDF 10, EGI 13, HJL 16, KMO 19, ?<\/strong><br><br>A. NPR 22<br>B. NPS 22<br>C. NQR 22<br>D. NPR 24<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>The pattern is simple:<br>First letters move forward by 3: B, E, H, K, N<br>Second letters move forward by 3: D, G, J, M, P<br>Third letters move forward by 3: F, I, L, O, R<br>Numbers also increase by 3: 10, 13, 16, 19, 22<br>So the next term is <strong>NPR 22<\/strong>.<br><strong>Quick trick:<\/strong> Check both the letters and numbers for the same step size.<br><strong>Correct answer: A. NPR 22<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 64<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which of the following letter-number clusters should replace the question mark?<br>FHJ : DFL :: KMO : ?<\/strong><br><br>A. MOQ<br>B. NOP<br>C. NPR<br>D. OMQ<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Series<\/strong><br>Letters shift +2 each time:<br>F \u2192 +2 \u2192 H \u2192 +2 \u2192 J<br>D \u2192 +2 \u2192 F \u2192 +2 \u2192 L<br>Similarly:<br>K \u2192 +2 \u2192 M \u2192 +2 \u2192 O<br>Check Options: Option A matches<br>M \u2192 +2 \u2192 O \u2192 +2 \u2192 Q<br>\u2705 Answer: <strong>A. MOQ<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 65<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What was the primary objective of the &#8216;Blue Skies 2025&#8217; campaign launched in August 2025?<\/strong><br><br>A. Racing for Air<br>B. Clean Air, Green Earth<br>C. Blue Planet Action<br>D. Air for All, Now<\/p>\n\n\n\n<p class=\"is-style-success\">UNEP states that the theme of the International Day of Clean Air for blue skies 2025 was \u201cRacing for Air\u201d.<br>\u2705 Answer: <strong>A. Racing for Air<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 66<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Refer to the following number and symbol series and answer the question that follows.<br>All numbers are single-digit numbers only.<br>4 @ 7 ! 2 # 5 * 9 $ 1 % 8 &amp; 3<br>If all symbols are dropped from the series, which number will be seventh from the right?<\/strong><br><br>A. 7<br>B. 5<br>C. 9<br>D. 1<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Series<\/strong><br>Remove symbols:<br>(left) 4,7,2,5,9,1,8,3 (right)<br>7th from right:<br>Count \u2192 7<br><strong>\u2705 Answer: A. 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 67<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The &#8220;Vishwa Shanti&#8221; (World Peace) statue, inaugurated by the PM in April 2026, is located in which city?<\/strong><br><br>A) Ayodhya<br>B) Varanasi<br>C) Ahmedabad<br>D) Kurukshetra<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Kurukshetra<\/strong>: The statue was unveiled as a symbol of universal peace and the teachings of the Bhagavad Gita.<br><strong>\u2705 Answer: D. Kurukshetra<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 68<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>If <\/strong><math data-latex=\"(a + \\frac{1}{a}) = 3\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mfrac><mn>1<\/mn><mi>a<\/mi><\/mfrac><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(a + \\frac{1}{a}) = 3<\/annotation><\/semantics><\/math><strong>, then what is the value of <\/strong><math data-latex=\"(a^4 + \\frac{1}{a^4})\"><semantics><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msup><mi>a<\/mi><mn>4<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>4<\/mn><\/msup><\/mfrac><mo form=\"postfix\" stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(a^4 + \\frac{1}{a^4})<\/annotation><\/semantics><\/math> <strong>?<\/strong><br><br>A. 47<br>B. 45<br>C. 49<br>D. 51<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>You are given:<\/strong><br><math data-latex=\"a + \\frac{1}{a} = 3\"><semantics><mrow><mi>a<\/mi><mo>+<\/mo><mfrac><mn>1<\/mn><mi>a<\/mi><\/mfrac><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">a + \\frac{1}{a} = 3<\/annotation><\/semantics><\/math><br>The <strong>core idea<\/strong> in these questions is:<br>\ud83d\udc49 You cannot jump to <math data-latex=\"a^4 + \\frac{1}{a^4}\"><semantics><mrow><msup><mi>a<\/mi><mn>4<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>4<\/mn><\/msup><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">a^4 + \\frac{1}{a^4}<\/annotation><\/semantics><\/math>\u200b directly<br>\ud83d\udc49 You <strong>build step by step<\/strong> using identities<br><br>First important identity:<br><math data-latex=\"(a + b)^2 = a^2 + b^2 + 2ab \\\\ a^2 +\\frac{1}{a^2} + 2\\times a \\times \\frac{1}{a} \\\\ a^2 +\\frac{1}{a^2} + 2\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>b<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>2<\/mn><mi>a<\/mi><mi>b<\/mi><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mi>a<\/mi><mo>\u00d7<\/mo><mfrac><mn>1<\/mn><mi>a<\/mi><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>2<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">(a + b)^2 = a^2 + b^2 + 2ab \\\\ a^2 +\\frac{1}{a^2} + 2\\times a \\times \\frac{1}{a} \\\\ a^2 +\\frac{1}{a^2} + 2<\/annotation><\/semantics><\/math><br>Now apply it:<br><math data-latex=\"3^2 = a^2 + \\frac{1}{a^2} + 2 \\\\ 9 - 2 = a^2 + \\frac{1}{a^2} \\\\ a^2 + \\frac{1}{a^2} = 7\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><msup><mn>3<\/mn><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>2<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>9<\/mn><mo>\u2212<\/mo><mn>2<\/mn><mo>=<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>=<\/mo><mn>7<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">3^2 = a^2 + \\frac{1}{a^2} + 2 \\\\ 9 &#8211; 2 = a^2 + \\frac{1}{a^2} \\\\ a^2 + \\frac{1}{a^2} = 7<\/annotation><\/semantics><\/math><br><br>Now next concept:<br>To move from power 2 \u2192 power 4, use:<br><math data-latex=\"(a^2 + b^2)^2 = 7^2 \\\\ a^4 + b^4 + 2a^2b^2 = 49 \\\\ a^4 +\\frac{1}{a^4} + 2\\times a^2 \\times \\frac{1}{a^2} = 49\\\\ a^4 +\\frac{1}{a^4} + 2 = 49\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mo form=\"prefix\" stretchy=\"false\">(<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>b<\/mi><mn>2<\/mn><\/msup><msup><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mn>7<\/mn><mn>2<\/mn><\/msup><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><msup><mi>a<\/mi><mn>4<\/mn><\/msup><mo>+<\/mo><msup><mi>b<\/mi><mn>4<\/mn><\/msup><mo>+<\/mo><mn>2<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><msup><mi>b<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><mn>49<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><msup><mi>a<\/mi><mn>4<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>4<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>=<\/mo><mn>49<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><msup><mi>a<\/mi><mn>4<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>4<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>2<\/mn><mo>=<\/mo><mn>49<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">(a^2 + b^2)^2 = 7^2 \\\\ a^4 + b^4 + 2a^2b^2 = 49 \\\\ a^4 +\\frac{1}{a^4} + 2\\times a^2 \\times \\frac{1}{a^2} = 49\\\\ a^4 +\\frac{1}{a^4} + 2 = 49<\/annotation><\/semantics><\/math><br>\ud83d\udc49 WHY this works:<br>Because multiplication combines powers:<br><math data-latex=\"a^2 \\times a^2 = a^4\"><semantics><mrow><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>\u00d7<\/mo><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>=<\/mo><msup><mi>a<\/mi><mn>4<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">a^2 \\times a^2 = a^4<\/annotation><\/semantics><\/math><br><math data-latex=\"\\frac{1}{a^2} \\times \\frac{1}{a^2} = \\frac{1}{a^4}\"><semantics><mrow><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>\u00d7<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>4<\/mn><\/msup><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{1}{a^2} \\times \\frac{1}{a^2} = \\frac{1}{a^4}<\/annotation><\/semantics><\/math><br><br>The good news is that, we have already done power 2 and 4. We input the power result of 2 + 2 = 4.<br>Let&#8217;s finish:<br><math data-latex=\"a^4 +\\frac{1}{a^4} + 2 = 49 \\\\ a^4 +\\frac{1}{a^4} = 49 - 2 \\\\ a^4 +\\frac{1}{a^4} = 47\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><msup><mi>a<\/mi><mn>4<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>4<\/mn><\/msup><\/mfrac><mo>+<\/mo><mn>2<\/mn><mo>=<\/mo><mn>49<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><msup><mi>a<\/mi><mn>4<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>4<\/mn><\/msup><\/mfrac><mo>=<\/mo><mn>49<\/mn><mo>\u2212<\/mo><mn>2<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><msup><mi>a<\/mi><mn>4<\/mn><\/msup><mo>+<\/mo><mfrac><mn>1<\/mn><msup><mi>a<\/mi><mn>4<\/mn><\/msup><\/mfrac><mo>=<\/mo><mn>47<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">a^4 +\\frac{1}{a^4} + 2 = 49 \\\\ a^4 +\\frac{1}{a^4} = 49 &#8211; 2 \\\\ a^4 +\\frac{1}{a^4} = 47<\/annotation><\/semantics><\/math><br><strong>\u2705 Answer: A. 47<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 69<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which Indian state inaugurated the country\u2019s first &#8220;Green Hydrogen Valley&#8221; in March 2026?<\/strong><br><br>A) Gujarat<br>B) Kerala<br>C) Odisha<br>D) Rajasthan<\/p>\n\n\n\n<p class=\"is-style-success\">Kerala: Located in Kochi, this valley produces green hydrogen using solar and wind power for local industrial use.<br>\u2705 Answer: <strong>B. Kerala<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 70<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In a certain code language, PAPA is coded as 2424 and SEAT is coded as 3218. What is the code for P?<\/strong><br><br>A. 4<br>B. 5<br>C. 8<br>D. 6<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pattern<\/strong><br><strong>PAPA<\/strong> = <strong>2424<\/strong><br>Confusing which is 2 or 4 for P or A. <br>SE<strong>A<\/strong>T = 3<strong>2<\/strong>18<br>Do you see the similarities? It is clear that the position don&#8217;t matter. So A = 2 and P = 4.<br><strong>\ud83c\udfaf FINAL ANSWER: A. 4\u200b<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 71<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>If 3 : 24 :: 3.5 : x and 5 : 40 :: 4.5 : y, what is the ratio of x to y?<\/strong><br><br>A. 7:9<br>B. 9:7<br>C. 28:36<br>D. 36:28<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Ratio<\/strong><br>Pattern:<br>3 \u2192 24 = \u00d78<br>3.5 \u2192 3.5\u00d78 = 28 \u2192 x<br><br>5 \u2192 40 = \u00d78<br>4.5 \u2192 4.5\u00d78 = 36 \u2192 y<br>x:y = 28:36 = 7:9<br><strong>Quick trick:<\/strong> Same multiplier in both gives the ratio directly.<br><strong>\u2705 Answer: A. 7 : 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 72<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Eenaa and Meena start a business by investing in the ratio 5 : 8. If the total profit is \u20b952,000, what is the difference between their shares of profit?<br><\/strong><br>A. \u20b912,000<br>B. \u20b910,000<br>C. \u20b914,000<br>D. \u20b98,000<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Profit Sharing<\/strong><br>Ratio = 5:8<br>Difference: 8 &#8211; 5 = 3 parts<br><math data-latex=\"\\frac{3}{13} \\times 52000 = 12000\"><semantics><mrow><mfrac><mn>3<\/mn><mn>13<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>52000<\/mn><mo>=<\/mo><mn>12000<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{3}{13} \\times 52000 = 12000<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>A. \u20b912000<\/strong><\/p>\n<\/div><\/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>Who was appointed as the Governor of the Reserve Bank of India (RBI) in early 2026?<\/strong><br><br>A) Shaktikanta Das<br>B) T. Rabi Sankar<br>C) K.V. Kamath<br>D) Arindam Bagchi<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>K.V. Kamath<\/strong>: The veteran banker took over the role, bringing extensive experience from the New Development Bank.<br><strong>\u2705 Answer: C. K.V. Kamath<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 74<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>AB is the diameter of a circle. C is a point on the circle such that <\/strong><math data-latex=\"\\angle{CAB} = 35^\\circ\"><semantics><mrow><mi>\u2220<\/mi><mrow><mi>C<\/mi><mi>A<\/mi><mi>B<\/mi><\/mrow><mo>=<\/mo><msup><mn>35<\/mn><mo>\u2218<\/mo><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\angle{CAB} = 35^\\circ<\/annotation><\/semantics><\/math>. <strong>What is \u2220ABC?<\/strong><br><br>A. <math data-latex=\"55^\\circ\"><semantics><msup><mn>55<\/mn><mo>\u2218<\/mo><\/msup><annotation encoding=\"application\/x-tex\">55^\\circ<\/annotation><\/semantics><\/math><br>B. <math data-latex=\"65^\\circ\"><semantics><msup><mn>65<\/mn><mo>\u2218<\/mo><\/msup><annotation encoding=\"application\/x-tex\">65^\\circ<\/annotation><\/semantics><\/math><br>C. <math data-latex=\"45^\\circ\"><semantics><msup><mn>45<\/mn><mo>\u2218<\/mo><\/msup><annotation encoding=\"application\/x-tex\">45^\\circ<\/annotation><\/semantics><\/math><br>D. <math data-latex=\"35^\\circ\"><semantics><msup><mn>35<\/mn><mo>\u2218<\/mo><\/msup><annotation encoding=\"application\/x-tex\">35^\\circ<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"is-style-success\">Think in terms of <strong>circle angle properties<\/strong>, not raw calculation.<br>Since <strong>AB is a diameter<\/strong>, any angle subtended by AB at the circle is a right angle. So:<br>\u2220ACB = 90<sup>\u2218<\/sup><br>Now in triangle ABC:<br>\u2220ABC = 180<sup>\u2218<\/sup> \u2212 90<sup>\u2218<\/sup> \u2212 35<sup>\u2218<\/sup> = 55<sup>\u2218<\/sup><br>Quick trick: Angle in a semicircle is always 90<sup>\u2218<\/sup>.<br>\u2705 Answer: <strong>A. 55<sup>\u2218<\/sup><\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 75<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In a certain code language, \u2018BYER\u2019 is coded as \u20183218\u2019 and \u2018LYER\u2019 is coded as \u20182178\u2019. What is the code for \u2018L\u2019 in the given code language?<\/strong><br><br>A. 7<br>B. 2<br>C. 1<br>D. 3<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Pattern<\/strong><br>B<strong>YER<\/strong> = 3<strong>218<\/strong><br>L<strong>YER<\/strong> = <strong>21<\/strong>7<strong>8<\/strong><br>Do you see the similarities? It is clear that the position don&#8217;t matter. So B = 3 and L = 7.<br><strong>\ud83c\udfaf FINAL ANSWER: A. 7\u200b<\/strong><\/p>\n<\/div><\/details><\/div>\n<\/div>\n\n\n\n<!--nextpage-->\n\n\n\n<h2 class=\"wp-block-heading\">RRB NTPC Graduate CBT 3 (Free Practice Mock test 1) \u2013 <strong>Learn From The Quiz<\/strong> And Their Solutions Tricks (Part 4: Question 76-100)<\/h2>\n\n\n\n<p>Try to attempt the free practice test of RRB NTPC Exam 1 part 4 of CBT Shift 3 which keeps questions from 76 to 100. All exams here are totally free. There are no hidden charges. We even give you monetary rewards if you perform well to motivate you in your study. Here you will try to attempt RRB NTPC Graduate CBT 3 exam practice test 1. The competitive exam is divided into 4 parts each with 25 questions. Learn from solutions of questions that are available in the test series. There are hack tricks, shortcut methods, and fully explained solutions.<\/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 = 28;\n          window.KQ_FRONT.rest = \"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/kq\/v1\/\";\n        <\/script>\n        <div id=\"kapil-quiz-28\"\n             class=\"kapil-quiz-container\"\n             data-kq-app\n             data-quiz-id=\"28\">\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\">All Solutions, Tricks, Answers Are Present Of the RRB Eams Test Series<\/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:\n1, 2, 12, 3, 4, 11, 4, 5, 5, 6, 16, 6, 6, 7, 8, 9, 9, 6, 11, 4, 2, 13, 14, 15, 10\nFind 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 Indian state inaugurated the country\u2019s first \"Green Hydrogen Valley\" in March 2026?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Kerala.\"}\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The price of each article of type P, Q, and R is \u20b9240, \u20b9180 and \u20b9120, respectively. A shopkeeper buys articles of each type in the ratio 1 : 2 : 3 for \u20b94,800. How many articles of type Q did he purchase?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 10. the pattern behind it simple.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Read the statements and conclusions carefully.\nStatements:\nAll lanterns are lights.\nSome lights are lamps.\nAll lamps are useful.\nConclusions:\n(I) Some useful things are lights.\n(II) All lanterns are useful.\",\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 Only conclusion (I) follows.\"\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.\nD lives immediately below F.\nWho lives on floor number 2?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is C. let's learn how to do it within 5 second.\"} }\n,    {\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following best describes the economic system adopted by India after independence, where public and private sectors coexist?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The answer is Mixed economy, but how can you remember it quickly. Learn it.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Find the mode of the following grouped data. Give the answer correct to 2 decimal places.\n$$ \\begin{array}{|c|c|} \\hline \\textbf{Class} & \\textbf{Frequency} \\\\ \\hline {0-10} & {5} \\\\ \\hline {10-20} & {9} \\\\ \\hline {20-30} & {14} \\\\ \\hline {30-40} & {20} \\\\ \\hline {40-50} & {12} \\\\ \\hline \\end{array} $$\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is to understand the key concepts hidden behind it, the correct answer is 34.29.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"What should come in place of the question mark?\n18, 29, 43, 60, 80, ?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is 103. Learn how to calculate it in no time.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Refer to the following letter, number, symbol series and answer the question. All numbers are single-digit numbers only.\n(Left) A 7 % B C * 2 D E # F 4 G @ 1 H $ I 9 J (Right)\nIf all the letters are dropped from the series, which of the following will be fourth from the right?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The pattern based question with simple trick to unlock and decipher it. How, learn the steps of it.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A woman travelled at a speed of 24 m\/min for 80 minutes, and at a speed of 60 m\/min for 40 minutes. Her average speed for the entire journey is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The pattern based question with simple trick to unlock and decipher it. How, learn the steps of it.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which characteristic of a computer system allows it to be used for writing documents, designing graphics, browsing the internet, and controlling devices?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Versatility\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Who was appointed as the Governor of the Reserve Bank of India (RBI) in early 2026?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"K.V. Kamath\"\n    }\n    },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The \"Chenab Bridge,\" the world\u2019s highest rail bridge, saw its first commercial Vande Bharat train crossing in January 2026. In which UT is it located?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is Jammu & Kashmir.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"A car travels 120 km at 40 km\/h and then 180 km at 60 km\/h. What is its average speed for the whole journey?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Let's solve it with a trick to simplify then unlock the pattern behind it. The correct answer is 50 km\/h.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"24 is related to 77 and 35 is related to 110 following the same logic. To which of the following is 41 related?\",\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 128.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"The total surface area of a cube each side of which is 72 cm is:\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Let's solve it with a trick to simplify then unlock the pattern behind it. The correct answer is 31104.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Seven people A, B, C, D, E, F and G sit around a circular table facing the centre.\nA sits immediately left of B.\nC sits immediately left of A.\nD sits immediately left of C.\nE sits immediately left of D.\nF sits immediately left of E.\nG sits immediately left of F.\nWho sits second to the right of D?\",\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 A.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"At what rate per annum simple interest will a sum become 2.5 times itself in 10 years?\",\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 15%.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which film won the \"Best Picture\" award at the 98th Academy Awards (Oscars) held in March 2026?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The Last Frontier\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Ben has \u20b92,100 with him. He divides this amount between his two sons, Lokesh and Rovesh, and asks them to invest their respective shares at a compound interest rate of 10% per annum, compounded annually. It is observed that Lokesh\u2019s investment amounts to the same value after 5 years as Rovesh\u2019s investment does after 6 years. How much did Ben give to Rovesh?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is not position but the pattern value. The correct answer is 1000.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In an election, 75% of the registered voters cast their vote and 20% of the votes polled were found invalid. The winning candidate got 75% of the valid votes and won by a margin of 300 votes. How many voters were registered?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is not position but the pattern value. The correct answer is 1000.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Each of the digits in the number 78324651 is arranged in descending order from left to right. What will be the product of the digits which are third from the left and second from the right in the number thus formed?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The trick here is not position but the pattern value. The correct answer is 12.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"In a certain code language,\nA + B means \u2018A is the son of B\u2019\nA - B means \u2018A is the father of B\u2019\nA \u00d7 B means \u2018A is the husband of B\u2019\nA \u00f7 B means \u2018A is the mother of B\u2019\nHow is P related to T if P + Q - R \u00d7 S \u00f7 T?\",\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  Paternal uncle.\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"India\u2019s first \"Bullet Train\" station became fully operational in April 2026 in which city?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Surat\"\n    }\n  },\n{\n    \"@type\": \"Question\",\n    \"name\": \"Which country launched the \"Artemis IV\" mission in early 2026, aiming to establish the first permanent lunar base?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"USA (NASA)\"\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>1, 2, 12, 3, 4, 11, 4, 5, 5, 6, 16, 6, 6, 7, 8, 9, 9, 6, 11, 4, 2, 13, 14, 15, 10<br>Find 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>Solution<\/strong><br>Count the frequency of each number.<br>The number <strong>6<\/strong> appears <strong>4 times<\/strong>, which is more than any other value.<br><strong>Quick trick:<\/strong> The mode is the value that repeats the most.<br><strong>Correct 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 77<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which Indian state inaugurated the country\u2019s first &#8220;Green Hydrogen Valley&#8221; in March 2026?<\/strong><br><br>A) Gujarat<br>B) Kerala<br>C) Odisha<br>D) Rajasthan<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Kerala:<\/strong> Located in Kochi, this valley produces green hydrogen using solar and wind power for local industrial use.<br>\u2705 Answer: <strong>B. Kerala<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 78<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The price of each article of type P, Q, and R is \u20b9240, \u20b9180 and \u20b9120, respectively. A shopkeeper buys articles of each type in the ratio 1 : 2 : 3 for \u20b94,800. How many articles of type Q did he purchase?<\/strong><br><br>A. 8<br>B. 10<br>C. 12<br>D. 14<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Ratio Purchase<\/strong><br>Ratio = 1 : 2 : 3 \u2192 total = 6 units<br>Cost per unit:<br>1 \u00d7 240 + 2 \u00d7 180 + 3 \u00d7 120<br>= 240 + 360 + 360<br>= 960<br>Given total = 4800<br><br>4800\/960 = 5<br>So Q articles: P : <strong>Q<\/strong> : R = 1 : <strong>2<\/strong> : 3<br>2 \u00d7 5 = 10<br><strong>\u2705 Answer: B. 10<\/strong><br>\ud83d\udc49 Trick: Find cost of one ratio block.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 79<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Read the statements and conclusions carefully.<br>Statements:<br>All lanterns are lights.<br>Some lights are lamps.<br>All lamps are useful.<br>Conclusions:<br>(I) Some useful things are lights.<br>(II) All lanterns are useful.<br><\/strong><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>Solution<br>From the statements:<br>All lanterns are lights.<br>Some lights are lamps.<br>All lamps are useful.<br><br>Since some lights are lamps and all lamps are useful, it follows that <strong>some useful things are lights<\/strong>.<br>But nothing says all lanterns are lamps or useful, so the second conclusion does not follow.<br><strong>Correct 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 80<\/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>D lives immediately below F.<br>Who lives on floor number 2?<\/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>Only one person lives below C \u27f9 C is on floor 2.<br>B lives immediately above C \u27f9 B is on floor 3.<br>A lives above B but below E \u27f9 A is on floor 4 and E is on floor 6.<br>D lives immediately below F \u27f9 remaining floors 1 and 5 go to D and F, with D below F.<br>So floor 2 is occupied by <strong>C<\/strong>.<br><strong>Quick trick:<\/strong> Use the \u201conly one below\u201d clue first; it locks the placement quickly.<br><strong>Correct answer: C<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 81<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which of the following best describes the economic system adopted by India after independence, where public and private sectors coexist?<br><\/strong><br>A. Mixed economy<br>B. Barter economy<br>C. Command economy<br>D. Subsistence economy<\/p>\n\n\n\n<p class=\"is-style-success\">A system that mixes public and private ownership and operation is called a <strong>mixed economy<\/strong>. India adopted this model after independence.<br><strong>Quick trick:<\/strong> Public + private together = mixed economy.<br>\u2705 Answer: <strong>A. Mixed economy<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 82<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Find the mode of the following 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 class=\"has-text-align-center\" data-align=\"center\">Class<\/th><th class=\"has-text-align-center\" data-align=\"center\">Frequency<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">0-10<\/td><td class=\"has-text-align-center\" data-align=\"center\">5<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">10-20<\/td><td class=\"has-text-align-center\" data-align=\"center\">9<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">20-30<\/td><td class=\"has-text-align-center\" data-align=\"center\">14<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">30-40<\/td><td class=\"has-text-align-center\" data-align=\"center\">20<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">40-50<\/td><td class=\"has-text-align-center\" data-align=\"center\">12<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"is-style-info\">A. 33.29<br>B. 34.29<br>C. 35.29<br>D. 36.29<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Mode (Grouped Data)<\/strong><br>Formula:<br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mtext>Mode<\/mtext><mo>=<\/mo><mi>l<\/mi><mo>+<\/mo><mfrac><mrow><msub><mi>f<\/mi><mn>1<\/mn><\/msub><mo>\u2212<\/mo><msub><mi>f<\/mi><mn>0<\/mn><\/msub><\/mrow><mrow><mn>2<\/mn><msub><mi>f<\/mi><mn>1<\/mn><\/msub><mo>\u2212<\/mo><msub><mi>f<\/mi><mn>0<\/mn><\/msub><mo>\u2212<\/mo><msub><mi>f<\/mi><mn>2<\/mn><\/msub><\/mrow><\/mfrac><mo>\u00d7<\/mo><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Mode} = l + \\frac{f_1 &#8211; f_0}{2f_1 &#8211; f_0 &#8211; f_2} \\times h<\/annotation><\/semantics><\/math><br><br>Modal class: 30\u201340 = 20<br><math data-latex=\"l = 30\"><semantics><mrow><mi>l<\/mi><mo>=<\/mo><mn>30<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">l = 30<\/annotation><\/semantics><\/math><br><math data-latex=\"f_1 = 20\"><semantics><mrow><msub><mi>f<\/mi><mn>1<\/mn><\/msub><mo>=<\/mo><mn>20<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">f_1 = 20<\/annotation><\/semantics><\/math><br><math data-latex=\"f_0 = 14\"><semantics><mrow><msub><mi>f<\/mi><mn>0<\/mn><\/msub><mo>=<\/mo><mn>14<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">f_0 = 14<\/annotation><\/semantics><\/math><br><math data-latex=\"f_2 = 12\"><semantics><mrow><msub><mi>f<\/mi><mn>2<\/mn><\/msub><mo>=<\/mo><mn>12<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">f_2 = 12<\/annotation><\/semantics><\/math><br><math data-latex=\"h = 10\"><semantics><mrow><mi>h<\/mi><mo>=<\/mo><mn>10<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">h = 10<\/annotation><\/semantics><\/math> = (40 &#8211; 30)<br>Let&#8217;s put values:<br><math data-latex=\"30 + \\frac{20 - 14}{2(20) - 14 - 12} \\times 10 \\\\ 30 + \\frac{6}{40 - 26} \\times 10 \\\\ 30 + \\frac{6 \\times 10}{14} \\\\ 30 + 4.2857\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mn>30<\/mn><mo>+<\/mo><mfrac><mrow><mn>20<\/mn><mo>\u2212<\/mo><mn>14<\/mn><\/mrow><mrow><mn>2<\/mn><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>20<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>\u2212<\/mo><mn>14<\/mn><mo>\u2212<\/mo><mn>12<\/mn><\/mrow><\/mfrac><mo>\u00d7<\/mo><mn>10<\/mn><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>30<\/mn><mo>+<\/mo><mfrac><mn>6<\/mn><mrow><mn>40<\/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><mn>30<\/mn><mo>+<\/mo><mfrac><mrow><mn>6<\/mn><mo>\u00d7<\/mo><mn>10<\/mn><\/mrow><mn>14<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>30<\/mn><mo>+<\/mo><mn>4.2857<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">30 + \\frac{20 &#8211; 14}{2(20) &#8211; 14 &#8211; 12} \\times 10 \\\\ 30 + \\frac{6}{40 &#8211; 26} \\times 10 \\\\ 30 + \\frac{6 \\times 10}{14} \\\\ 30 + 4.2857<\/annotation><\/semantics><\/math><br>= 34.29<br>\u2705 Answer: <strong>B. 34.29<\/strong><br><strong>Quick trick: <\/strong>The modal class is the class with the highest frequency.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 83<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>What should come in place of the question mark?<br>18, 29, 43, 60, 80, ?<\/strong><br><br>A. 98<br>B. 100<br>C. 103<br>D. 105<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Series<\/strong><br>18, 29, 43, 60, 80,<br>Differences is the addition of 3:<br>+11, +14, +17, +20 \u2192 next +3<br>80 + 23 = 103<br>\u2705 Answer: <strong>A. 103<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 84<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Refer to the following letter, number, symbol series and answer the question. All numbers are single-digit numbers only.<br>(Left) A 7 % B C * 2 D E # F 4 G @ 1 H $ I 9 J (Right)<br>If all the letters are dropped from the series, which of the following will be fourth from the right?<\/strong><br><br>A. @<br>B. #<br>C. 1<br>D. 4<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Series<\/strong><br>Remove letters:<br>(Left) 7 % * 2 # 4 @ 1 $ 9 (Right)<br>4th from right:<br>9 (1), $ (2), 1 (3), @ (4)<br>\u2705 Answer: <strong>A. @<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 85<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>A woman travelled at a speed of 24 m\/min for 80 minutes, and at a speed of 60 m\/min for 40 minutes. Her average speed for the entire journey is:<\/strong><br><br>A. 34 m\/min<br>B. 36 m\/min<br>C. 38 m\/min<br>D. 40 m\/min<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Average Speed<\/strong><br>Distance:<br>24 \u00d7 80 = 1920,<br>60 \u00d7 40 = 2400<br>Total: 1920 + 2400 = 4320<br>Time: 80 + 40 = 120<br><br>4320\/120 = 36<br><strong>\u2705 Answer: B. 36 m\/min<\/strong><br>\ud83d\udc49 Trick: Avg speed = total distance \/ total time.<\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 86<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which characteristic of a computer system allows it to be used for writing documents, designing graphics, browsing the internet, and controlling devices?<\/strong><br><br>A. Speed<br>B. Accuracy<br>C. Versatility<br>D. Diligence<\/p>\n\n\n\n<p class=\"is-style-success\">A computer used for documents, graphics, internet browsing, and device control is showing versatility.<br><strong>Quick trick:<\/strong> One machine, many kinds of work = versatility.<br><strong>\u2705 Answer: C. Versatility<\/strong><\/p>\n<\/div><\/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 was appointed as the Governor of the Reserve Bank of India (RBI) in early 2026?<\/strong><br><br>A) Shaktikanta Das<br>B) T. Rabi Sankar<br>C) K.V. Kamath<br>D) Arindam Bagchi<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>K.V. Kamath:<\/strong> The veteran banker took over the role, bringing extensive experience from the New Development Bank.<br><strong>\u2705 Answer: C. K.V. Kamath<\/strong><\/p>\n<\/div><\/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>The &#8220;Chenab Bridge,&#8221; the world\u2019s highest rail bridge, saw its first commercial Vande Bharat train crossing in January 2026. In which UT is it located?<\/strong><br><br>A) Ladakh<br>B) Jammu &amp; Kashmir<br>C) Chandigarh<br>D) Puducherry<\/p>\n\n\n\n<p class=\"is-style-success\">Jammu &amp; Kashmir: It stands 359 meters above the river bed, higher than the Eiffel Tower.<br>\u2705 Answer: <strong>B. Jammu &amp; Kashmir<\/strong><\/p>\n<\/div><\/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>A car travels 120 km at 40 km\/h and then 180 km at 60 km\/h. What is its average speed for the whole journey?<\/strong><br><br>A. 45 km\/h<br>B. 50 km\/h<br>C. 55 km\/h<br>D. 60 km\/h<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Solution<\/strong><br>First trip: 120\u00f740 = 3 hours<br>Second trip: 180\u00f760 = 3 hours<br>Total distance: 120+180 = 300<br>Total time: 3+3 = 6<br>Average speed: 300\/6 = 50 km\/h<br><strong>Quick trick: <\/strong>Add distances and times separately, then divide.<br><strong>Correct answer: B. 50 km\/h<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 90<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>24 is related to 77 and 35 is related to 110 following the same logic. To which of the following is 41 related?<\/strong><br><br>A. 125<br>B. 128<br>C. 131<br>D. 134<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Number Logic<\/strong><br>24 \u2192 77<br>35 \u2192 110<br>Pattern: \u00d7 3 + 5<br>Check:<br>24 \u00d7 3 + 5 = 77<br>35 \u00d7 3 + 5 = 110<br><br>Try Options:<br>41 \u00d7 3 +5 = 128<br>\u2705 Answer: <strong>C. 128<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 91<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>The total surface area of a solid cube each side of which is 72 cm long is:<\/strong><br><br>A. 30,624 cm\u00b2<br>B. 31,104 cm\u00b2<br>C. 31,284 cm\u00b2<br>D. 32,104 cm\u00b2<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Surface Area Cube<\/strong><br><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mtext>Surface&nbsp;Area<\/mtext><mo>=<\/mo><mn>6<\/mn><msup><mi>a<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Surface Area} = 6a^2<\/annotation><\/semantics><\/math><br><math data-latex=\"6 \\times 72^2 = 6 \\times 5184 = 31104\"><semantics><mrow><mn>6<\/mn><mo>\u00d7<\/mo><msup><mn>72<\/mn><mn>2<\/mn><\/msup><mo>=<\/mo><mn>6<\/mn><mo>\u00d7<\/mo><mn>5184<\/mn><mo>=<\/mo><mn>31104<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">6 \\times 72^2 = 6 \\times 5184 = 31104<\/annotation><\/semantics><\/math><br>\u2705 Answer: <strong>B. 31,104 cm\u00b2<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 92<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Seven people A, B, C, D, E, F and G sit around a circular table facing the centre.<br>A sits immediately left of B.<br>C sits immediately left of A.<br>D sits immediately left of C.<br>E sits immediately left of D.<br>F sits immediately left of E.<br>G sits immediately left of F.<br>Who sits second to the right of D?<br><\/strong><br>A. A<br>B. B<br>C. C<br>D. E<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>The Pattern Trick:<br><\/strong>right of = clockwise<br>left of = anti-clockwise<br>7 people = A,B,C,D,E,F,G<br>circular = 1,2,3,4,5,6,7,1&#8230;<br><br>1 = A<br>2 = B<br>3 = G<br>4 = F<br>5 = E<br>6 = D<br>7 = C<br>The question asks: Second right of D<br>D = 6, C = 7, A = 1.<br>\ud83d\udc49 <strong>Answer A. A<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 93<\/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 become 2.5 times itself in 10 years?<br><\/strong><br>A. 12%<br>B. 15%<br>C. 18%<br>D. 20%<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Simple Interest<\/strong><br>Amount = 2.5P \u2192 SI = 1.5P<br>We start putting interest after the end of 1 year, so 2.5 becomes 1.5.<br><math data-latex=\"SI = \\frac{P \\times R \\times T}{100} \\\\ 1.5P = \\frac{P \\times R \\times 10}{100} \\\\ \\frac{1.5}{R} = \\frac{P \\times 10}{100 \\times P} \\\\ \\frac{1}{R} = \\frac{10}{100 \\times 1.5} \\\\ R = \\frac{150}{10}\"><semantics><mtable columnalign=\"left\" rowspacing=\"0em\"><mtr><mtd style=\"text-align:left;\"><mrow><mi>S<\/mi><mi>I<\/mi><mo>=<\/mo><mfrac><mrow><mi>P<\/mi><mo>\u00d7<\/mo><mi>R<\/mi><mo>\u00d7<\/mo><mi>T<\/mi><\/mrow><mn>100<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mn>1.5<\/mn><mi>P<\/mi><mo>=<\/mo><mfrac><mrow><mi>P<\/mi><mo>\u00d7<\/mo><mi>R<\/mi><mo>\u00d7<\/mo><mn>10<\/mn><\/mrow><mn>100<\/mn><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mn>1.5<\/mn><mi>R<\/mi><\/mfrac><mo>=<\/mo><mfrac><mrow><mi>P<\/mi><mo>\u00d7<\/mo><mn>10<\/mn><\/mrow><mrow><mn>100<\/mn><mo>\u00d7<\/mo><mi>P<\/mi><\/mrow><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mfrac><mn>1<\/mn><mi>R<\/mi><\/mfrac><mo>=<\/mo><mfrac><mn>10<\/mn><mrow><mn>100<\/mn><mo>\u00d7<\/mo><mn>1.5<\/mn><\/mrow><\/mfrac><\/mrow><mo linebreak=\"newline\"><\/mo><\/mtd><\/mtr><mtr><mtd style=\"text-align:left;\"><mrow><mi>R<\/mi><mo>=<\/mo><mfrac><mn>150<\/mn><mn>10<\/mn><\/mfrac><\/mrow><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">SI = \\frac{P \\times R \\times T}{100} \\\\ 1.5P = \\frac{P \\times R \\times 10}{100} \\\\ \\frac{1.5}{R} = \\frac{P \\times 10}{100 \\times P} \\\\ \\frac{1}{R} = \\frac{10}{100 \\times 1.5} \\\\ R = \\frac{150}{10}<\/annotation><\/semantics><\/math><br>\u21d2 R = 15%<br><strong>\u2705 Answer: B. 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 94<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which film won the &#8220;Best Picture&#8221; award at the 98th Academy Awards (Oscars) held in March 2026?<\/strong><br><br>A) The Last Frontier<br>B) Echoes of Silence<br>C) Midnight in Tokyo<br>D) Beyond the Horizon<\/p>\n\n\n\n<p class=\"is-style-success\">The Last Frontier: (Hypothetical for quiz context) This sci-fi epic swept the 2026 awards for its groundbreaking visual effects.<br>\u2705 Answer: <strong>A. The Last Frontier<\/strong><\/p>\n<\/div><\/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>Ben has \u20b92,100 with him. He divides this amount between his two sons, Lokesh and Rovesh, and asks them to invest their respective shares at a compound interest rate of 10% per annum, compounded annually. It is observed that Lokesh\u2019s investment amounts to the same value after 5 years as Rovesh\u2019s investment does after 6 years. How much did Ben give to Rovesh?<\/strong><br><br>A. \u20b91,000<br>B. \u20b91,050<br>C. \u20b91,100<br>D. \u20b91,150<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>I Investment<\/strong><br><strong>Assume the value 1 and 10% = 1.1<br><\/strong>Given:<br>Lokesh (5 yrs) = Rovesh (6 yrs)<br>L(1.1)<sup>5<\/sup> = R(1.1)<sup>6<\/sup><br>\u21d2 L = R(1.1)<sup>1<\/sup><br>\u21d2 L = 1.1R<br>Total: L + R = 2100<br>1.1R + R = 2100<br>\u21d2 2.1R = 2100<br>\u21d2 R = 2100\/2.1<br>\u21d2 R = 1000<br><strong>\u2705 Answer: A. 1000<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 96<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In an election, 75% of the registered voters cast their vote and 20% of the votes polled were found invalid. The winning candidate got 75% of the valid votes and won by a margin of 300 votes. How many voters were registered?<\/strong><br><br>A. 900<br>B. 1000<br>C. 1100<br>D. 1200<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Election<\/strong><br>Let voters = x<br>Votes cast 75% of x = 0.75x<br>Invalid 20% of 0.75x = 0.15x<br>Valid = 0.75x &#8211; 0.15x = 0.60x<br><br>Winning candidate got 75% of valid votes, so losing candidate got 25%.<br>Margin = 50% of valid votes: 0.5<br>0.5 \u00d7 0.60x = 0.30x<br>Given Margin 300 votes:<br>\u21d2 0.30x = 300<br>\u21d2 x = 300\/0.30<br>\u21d2 x = 1000<br><strong>Quick trick:<\/strong> Margin between 75% and 25% of valid votes is exactly 50% of valid votes.<br>\u2705 Answer: <strong>B. 1000<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 97<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Each of the digits in the number 78324651 is arranged in descending order from left to right. What will be the product of the digits which are third from the left and second from the right in the number thus formed?<\/strong><br><br>A. 10<br>B. 12<br>C. 14<br>D. 16<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Digits<\/strong><br>Descending:<br>(Left) 8 7 6 5 4 2 1 (Right)<br>3rd left = 6<br>2nd right = 2<br>6 \u00d7 2 = 12<br>\u2705 Answer: <strong>B. 12<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 98<\/strong> <\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>In a certain code language,<br>A + B means \u2018A is the son of B\u2019<br>A &#8211; B means \u2018A is the father of B\u2019<br>A \u00d7 B means \u2018A is the husband of B\u2019<br>A \u00f7 B means \u2018A is the mother of B\u2019<br>How is P related to T if P + Q &#8211; R \u00d7 S \u00f7 T?<\/strong><br><br>A. Step-son<br>B. Paternal uncle<br>C. Maternal uncle<br>D. Step-father<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Relation<\/strong><br>P + Q \u2192 son<br>Q \u2013 R \u2192 father<br>R \u00d7 S \u2192 husband<br>S \u00f7 T \u2192 mother<br>So: P \u2192 T<br>Q is father of P and R.<br>R is husband of S.<br>S is mother of T.<br>So Q is grand father of T and P is T&#8217;s Paternal Uncle.<br><strong>\u2705 Answer: B. Paternal uncle<\/strong><\/p>\n<\/div><\/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>India\u2019s first &#8220;Bullet Train&#8221; station became fully operational in April 2026 in which city?<\/strong><br><br>A) Mumbai<br>B) Ahmedabad<br>C) Surat<br>D) Vadodara<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>Surat<\/strong>: While the full line is still in progress, the Surat station was the first to be completed and opened for public tours.<br>\u2705 Answer: <strong>C. Surat<\/strong><\/p>\n<\/div><\/details><\/div>\n\n\n\n<div class=\"wp-block-coblocks-accordion-item\"><details><summary class=\"wp-block-coblocks-accordion-item__title\"><strong>Question 100<\/strong><\/summary><div class=\"wp-block-coblocks-accordion-item__content\">\n<p class=\"is-style-info\"><strong>Which country launched the &#8220;Artemis IV&#8221; mission in early 2026, aiming to establish the first permanent lunar base?<\/strong><br><br>A) China<br>B) USA (NASA)<br>C) India (ISRO)<br>D) Russia<\/p>\n\n\n\n<p class=\"is-style-success\"><strong>USA (NASA):<\/strong> Artemis IV is a critical step in the &#8220;Moon to Mars&#8221; roadmap involving the Lunar Gateway.<br><strong>\u2705 Answer: B. USA (NASA)<\/strong><\/p>\n<\/div><\/details><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>RRB NTPC Graduate CBT 3 (Free Practice Test 1 With Tricks: This is the third series of free practice test of RRB NTPC Graduate CBT 3 competitive exam. There are tests, tricks, answer solutions with 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-328","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\/328","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=328"}],"version-history":[{"count":30,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/posts\/328\/revisions"}],"predecessor-version":[{"id":373,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/posts\/328\/revisions\/373"}],"wp:attachment":[{"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/media?parent=328"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/categories?post=328"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/govt.mrenglishkj.com\/railway\/wp-json\/wp\/v2\/tags?post=328"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}