{"id":30317,"date":"2023-10-13T16:32:30","date_gmt":"2023-10-13T11:02:30","guid":{"rendered":"https:\/\/mycbseguide.com\/blog\/?p=30317"},"modified":"2025-10-09T16:55:25","modified_gmt":"2025-10-09T11:25:25","slug":"cbse-class-11-applied-maths-sample-papers","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/cbse-class-11-applied-maths-sample-papers\/","title":{"rendered":"CBSE Class 11 Applied Maths Sample Papers 2025"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/cbse-class-11-applied-maths-sample-papers\/#CBSE_Class_11_Applied_Maths_Sample_Papers_2025\" >CBSE Class 11 Applied Maths Sample Papers 2025<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/cbse-class-11-applied-maths-sample-papers\/#Class_11_Applied_Maths_Model_Papers_2024-25\" >Class 11 Applied Maths Model Papers 2024-25<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/cbse-class-11-applied-maths-sample-papers\/#Class_11_%E2%80%93_Applied_Mathematics_Sample_Paper_2024-25\" >Class 11 &#8211; Applied Mathematics Sample Paper (2024-25)<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/cbse-class-11-applied-maths-sample-papers\/#Key_Features\" >Key Features:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/cbse-class-11-applied-maths-sample-papers\/#Solutions_of_Applied_Maths_Class_11\" >Solutions of Applied Maths Class 11<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/cbse-class-11-applied-maths-sample-papers\/#CBSE_Sample_Papers_for_Class_11_2025\" >CBSE Sample Papers for Class 11 2025<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/cbse-class-11-applied-maths-sample-papers\/#Why_to_choose_myCBSEGuide\" >Why to choose myCBSEGuide?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Class_11_Applied_Maths_Sample_Papers_2025\"><\/span>CBSE Class 11 Applied Maths Sample Papers 2025<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Download <strong>free CBSE Class 11 Applied Maths sample papers<\/strong> for 2025 on the <strong>myCBSEguide app<\/strong>! These model question papers are based on the latest <strong>CBSE marking scheme<\/strong> and <strong>blueprint<\/strong> of Applied Maths for the academic session 2024-25, ensuring they follow the most up-to-date exam pattern. Download the latest <strong>CBSE Class 11 Applied Maths model question papers<\/strong> for 2025 from <strong>myCBSEguide<\/strong>. These papers follow the updated <strong>CBSE blueprint<\/strong>, making them perfect for practicing essential concepts. <strong>Model question papers<\/strong> provide insights into the expected exam format and difficulty level. Use these <strong>test papers<\/strong> to refine your exam strategy and boost confidence. The content is regularly updated to reflect any changes in the CBSE curriculum. <strong>Get started now<\/strong> and boost your preparation with <a href=\"https:\/\/mycbseguide.com\/\"><strong>myCBSEguide<\/strong><\/a> for free, reliable, and comprehensive study material! Download <strong>free practice papers<\/strong> for <strong><a href=\"https:\/\/mycbseguide.com\/cbse-sample-papers-class-11.html\">CBSE Class 11<\/a><\/strong> Applied Maths from the <strong><a href=\"https:\/\/examin8.com\/\">Examin8<\/a><\/strong> and\u00a0 <a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide\"><strong>myCBSEguide app<\/strong><\/a>.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Class_11_Applied_Maths_Model_Papers_2024-25\"><\/span>Class 11 Applied Maths Model Papers 2024-25<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Applied Mathematics<\/strong> is a newly introduced subject in senior secondary classes, specifically designed to provide a more relevant option for <strong>commerce students<\/strong>. Previously, students in the commerce stream had to study core mathematics, which was not directly applicable to their field of study. The <strong>Applied Maths<\/strong> curriculum focuses on topics that are more aligned with the practical needs of commerce students, making it a valuable addition to their academic path. These papers are designed to help you understand the exam pattern and improve problem-solving skills. With detailed solutions, these practice papers provide comprehensive coverage of key topics. Access a wide range of <strong>CBSE Class 11 Applied Maths Sample Papers 2025.<\/strong><\/p>\n<p>To help students excel in this subject, we are offering <strong>CBSE<\/strong><strong> Class 11 Applied Maths Sample Papers 2025<\/strong>. These sample papers have been carefully crafted by our team of expert teachers, in accordance with the latest <strong>CBSE blueprint<\/strong> and guidelines issued by <strong>CBSE New Delhi<\/strong>. Download these <a href=\"https:\/\/mycbseguide.com\/\"><strong>sample question papers<\/strong><\/a> today to practice and improve your understanding of key concepts in <strong>Applied Maths<\/strong>.<\/p>\n<h2 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"Class_11_%E2%80%93_Applied_Mathematics_Sample_Paper_2024-25\"><\/span><strong>Class 11 &#8211; Applied Mathematics Sample Paper (2024-25)<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<hr \/>\n<p style=\"text-align: center;\"><strong>Class 11 &#8211; Applied Maths<br \/>\nSample Paper &#8211; 01 (2024-25)<\/strong><\/p>\n<hr \/>\n<p><b>Maximum Marks: 80<br \/>\nTime Allowed: : 3 hours<\/b><\/p>\n<hr \/>\n<p><b>General Instructions:<\/b><\/p>\n<p>Read the following instructions very carefully and strictly follow them:<\/p>\n<ol start=\"1\">\n<li>This Question paper contains 38 questions. All questions are compulsory.<\/li>\n<li>This Question paper is divided into five Sections &#8211; A, B, C, D and E.<\/li>\n<li>In Section A, Questions no. 1 to 18 are multiple choice questions (MCQs) and Questions no. 19 and 20 are Assertion-Reason based questions of 1 mark each.<\/li>\n<li>In Section B, Questions no. 21 to 25 are Very Short Answer (VSA)-type questions, carrying 2 marks each.<\/li>\n<li>In Section C, Questions no. 26 to 31 are Short Answer (SA)-type questions, carrying 3 marks each.<\/li>\n<li>In Section D, Questions no. 32 to 35 are Long Answer (LA)-type questions, carrying 5 marks each.<\/li>\n<li>In Section E, Questions no. 36 to 38 are case study-based questions carrying 4 marks each.<\/li>\n<li>There is no overall choice. However, an internal choice has been provided in 2 questions in Section B, 2 questions in Section C, 2 questions in Section D and one sub-part each in 2 questions of Section E.<\/li>\n<li>Use of calculators is not allowed.<\/li>\n<\/ol>\n<hr \/>\n<ol style=\"padding-left: 20px; list-style: decimal;\">\n<li style=\"text-align: center; clear: both; display: block;\"><b>Section A<\/b><\/li>\n<li>Three persons A, B and C fire a target in turn. Their probabilities of hitting the target are 0.4, 0.3 and 0.2 respectively. The probability of two hits is:\n<div style=\"margin-left: 20px;\">\n<p>a)0.336<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)0.188<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)0.024<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)0.452<\/p>\n<\/div>\n<\/li>\n<li>If two distributions A and B have same mean and their variance are 81 and 100 respectively, then which distribution has more variability\n<div style=\"margin-left: 20px;\">\n<p>a)A<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)can\u2019t say<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)B<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)both are equal<\/p>\n<\/div>\n<\/li>\n<li>Deduction of principal of home loan is allowed under section\n<div style=\"margin-left: 20px;\">\n<p>a)80D<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)80E<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)24<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)80C<\/p>\n<\/div>\n<\/li>\n<li>The value of\u00a0<span class=\"math-tex\">{tex}\\left(5 \\frac{1}{16}\\right)^{-\\frac{3}{4}}{\/tex}<\/span> is\n<div style=\"margin-left: 20px;\">\n<p>a)<span class=\"math-tex\">{tex}\\frac{9}{4}{\/tex}<\/span><\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)<span class=\"math-tex\">{tex}\\frac{4}{9}{\/tex}<\/span><\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)<span class=\"math-tex\">{tex}\\frac{27}{8}{\/tex}<\/span><\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)<span class=\"math-tex\">{tex}\\frac{8}{27}{\/tex}<\/span><\/p>\n<\/div>\n<\/li>\n<li>If f(x) =<span class=\"math-tex\">{tex}\\sqrt { &#8211; x} {\/tex}<\/span>, then domain of fof is\n<div style=\"margin-left: 20px;\">\n<p>a)<span class=\"math-tex\">{tex}({\\rm{ }}0,\\infty ){\/tex}<\/span><\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)none of these<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)<span class=\"math-tex\">{tex}( &#8211; \\infty ,\\infty ){\/tex}<\/span><\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)<span class=\"math-tex\">{tex}( &#8211; \\infty ,{\\rm{ }}0){\/tex}<\/span><\/p>\n<\/div>\n<\/li>\n<li>If\u00a0<span class=\"math-tex\">{tex}\\frac{\\log x}{a-b}=\\frac{\\log y}{b-c}=\\frac{\\log z}{c-a}{\/tex}<\/span>, then xyz is equal to:\n<div style=\"margin-left: 20px;\">\n<p>a)2<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)0<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)1<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)-1<\/p>\n<\/div>\n<\/li>\n<li>A card is picked at random from a pack of 52 playing cards. Given that the picked card is a queen, the probability of this card to be a card of hearts is:\n<div style=\"margin-left: 20px;\">\n<p>a)<span class=\"math-tex\">{tex}\\frac 4{14}{\/tex}<\/span><\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)<span class=\"math-tex\">{tex}\\frac 14{\/tex}<\/span><\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)<span class=\"math-tex\">{tex}\\frac 13{\/tex}<\/span><\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)<span class=\"math-tex\">{tex}\\frac 12{\/tex}<\/span><\/p>\n<\/div>\n<\/li>\n<li>The equation of a circle concentric with the circle x<sup>2<\/sup> + y<sup>2<\/sup> &#8211; 6x + 12y + 15 = 0 and double its area is:\n<div style=\"margin-left: 20px;\">\n<p>a)x<sup>2\u00a0<\/sup>+ y<sup>2<\/sup> &#8211; 6x + 12y + 30 = 0<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)x<sup>2\u00a0<\/sup>+ y<sup>2<\/sup>\u00a0&#8211; 6x + 12y &#8211; 30 = 0<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)x<sup>2\u00a0<\/sup>+ y<sup>2<\/sup> &#8211; 6x + 12y + 45 = 0<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)x<sup>2\u00a0<\/sup>+ y<sup>2<\/sup> &#8211; 6x + 12y &#8211; 15 = 0<\/p>\n<\/div>\n<\/li>\n<li>If ignorance is to education, then disease is to ________\n<div style=\"margin-left: 20px;\">\n<p>a)medicine<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)nurse<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)doctor<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)hospital<\/p>\n<\/div>\n<\/li>\n<li>Which of the following is not a measure of central tendency:\n<div style=\"margin-left: 20px;\">\n<p>a)range<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)mode<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)median<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)mean<\/p>\n<\/div>\n<\/li>\n<li>Characteristic of logarithm of a number 14768 is\n<div style=\"margin-left: 20px;\">\n<p>a)3<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)2<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)4<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)5<\/p>\n<\/div>\n<\/li>\n<li>The difference between simple interest and compound interest on \u20b9\u00a015000 for one yea 8% per annum calculated half-yearly is:\n<div style=\"margin-left: 20px;\">\n<p>a)\u20b9 24<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)\u20b9 20<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)\u20b9 22<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)\u20b9 26<\/p>\n<\/div>\n<\/li>\n<li>A retailer purchases a fan for \u20b9 1500 from a wholesaler and sells it to a consumer at 10% profit. If the sales are intra-state and the rate of GST is 12%, the tax (under GST) received by the Central Government is:\n<div style=\"margin-left: 20px;\">\n<p>a)\u20b9 90<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)\u20b9 18<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)\u20b9 198<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)\u20b9 99<\/p>\n<\/div>\n<\/li>\n<li>A problem in mathematics is given to three students A, B, C and their chances of solving the problem <span class=\"math-tex\">{tex}\\frac{1}{2}, \\frac{1}{3}{\/tex}<\/span>\u00a0are\u00a0<span class=\"math-tex\">{tex}\\frac 14{\/tex}<\/span> and respectively. The probability that the problem is solved is:\n<div style=\"margin-left: 20px;\">\n<p>a)<span class=\"math-tex\">{tex}\\frac 34{\/tex}<\/span><\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)<span class=\"math-tex\">{tex}\\frac 23{\/tex}<\/span><\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)<span class=\"math-tex\">{tex}\\frac 58{\/tex}<\/span><\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)<span class=\"math-tex\">{tex}\\frac 12{\/tex}<\/span><\/p>\n<\/div>\n<\/li>\n<li>A bag A contains 3 white, 2 red balls and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red, then the probability that it was drawn from bag B is\n<div style=\"margin-left: 20px;\">\n<p>a)<span class=\"math-tex\">{tex}\\frac{20}{43}{\/tex}<\/span><\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)<span class=\"math-tex\">{tex}\\frac{25}{43}{\/tex}<\/span><\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)<span class=\"math-tex\">{tex}\\frac{27}{43}{\/tex}<\/span><\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)<span class=\"math-tex\">{tex}\\frac{21}{43}{\/tex}<\/span><\/p>\n<\/div>\n<\/li>\n<li>The compound interest on \u20b9 30,000 at 7% per annum is \u20b9 4347. This period (in years) is:\n<div style=\"margin-left: 20px;\">\n<p>a)2<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)4<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)3<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)<span class=\"math-tex\">{tex}2\\frac{1}{2}{\/tex}<\/span><\/p>\n<\/div>\n<\/li>\n<li>The number of 4 digit numbers that can be formed with the digits 2, 3, 4, 7 and using each digit only once is\n<div style=\"margin-left: 20px;\">\n<p>a)24<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)96<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)120<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)100<\/p>\n<\/div>\n<\/li>\n<li>A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by: x R y\u00a0<span class=\"math-tex\">{tex}\\Leftrightarrow{\/tex}<\/span>\u00a0x is relatively prime to y. Then domain of R is\n<div style=\"margin-left: 20px;\">\n<p>a){2, 3, 4, 5}<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b){3, 5}<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c){2, 3, 5}<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d){2, 3, 4}<\/p>\n<\/div>\n<\/li>\n<li><strong>Assertion (A):<\/strong> The difference between maximum and minimum values of variate is called Range.<br \/>\n<strong>Reason (R):<\/strong> Coeff. of Range = <span class=\"math-tex\">{tex}\\frac{L-S}{L+S}{\/tex}<\/span><br \/>\nWhere, L is the largest value<br \/>\nS is the smallest value<\/p>\n<div style=\"margin-left: 20px;\">\n<p>a)Both A and R are true and R is the correct explanation of A.<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)Both A and R are true but R is not the correct explanation of A.<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)A is true but R is false.<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)A is false but R is true.<\/p>\n<\/div>\n<\/li>\n<li><strong>Assertion (A): <\/strong>If nth term of an A.P. is a<sub>n<\/sub> = pn + q, then common difference of A.P. is 2p.<br \/>\n<strong>Reason (R):<\/strong> Common difference of an A.P. is d = a<sub>n<\/sub> &#8211; a<sub>n &#8211; 1<\/sub>.<\/p>\n<div style=\"margin-left: 20px;\">\n<p>a)Both A and R are true and R is the correct explanation of A.<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>b)Both A and R are true but R is not the correct explanation of A.<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>c)A is true but R is false.<\/p>\n<\/div>\n<div style=\"margin-left: 20px;\">\n<p>d)A is false but R is true.<\/p>\n<p><strong>Boost Your Exam Preparation with the <a href=\"https:\/\/mycbseguide.com\/cbse-sample-papers-class-11.html\">myCBSEguide App<\/a> \u2013 Download Now! For more visit our <a href=\"https:\/\/mycbseguide.com\/\">Website myCBSEGuide<\/a><\/strong><br \/>\nGet ready to ace your exams by downloading the <strong>myCBSEguide app<\/strong>! Get ready for your exams with <strong>CBSE Class 11 Applied Maths Sample Papers<\/strong>\u00a02025. It provides complete study resources for <strong>CBSE<\/strong>, <strong>NCERT<\/strong>, <strong>JEE (Main)<\/strong>, <strong>NEET-UG<\/strong>, and <strong>NDA exams<\/strong>, helping you stay ahead in your studies. With access to a wide range of practice questions, sample papers, and mock tests, the <strong>myCBSEguide app<\/strong> is your go-to tool for effective exam preparation.<\/p>\n<p><a href=\"https:\/\/examin8.com\/blog\/free-mobile-app\/\"><strong>Examin8<\/strong><\/a> is the ideal app for teachers, allowing them to create customized question papers with their own branding, logo, and name. <strong>Download the myCBSEguide<\/strong> and <strong>Examin8 apps<\/strong> today to enhance your learning experience and achieve exam success.<\/p>\n<\/div>\n<\/li>\n<li style=\"text-align: center; clear: both; display: block;\"><b>Section B<\/b><\/li>\n<li>The average of five consecutive numbers is x. If next two numbers are also included, then show that the average will increase by 1.<\/li>\n<li>In a certain code language 327 means <strong>Truth is eternal<\/strong>, 7983 means <strong>&#8216;Enmity is not eternal&#8217;<\/strong> and 9426 means <strong>Truth does not perish<\/strong>. What does <strong>Enmity<\/strong>\u00a0mean in this language?\n<p style=\"text-align: center;\"><b>OR <\/b><\/p>\n<p>In a certain language <strong>TABLE<\/strong>\u00a0is coded as <strong>NBDXJ<\/strong>, how <strong>CHAIR<\/strong>\u00a0is coded?<\/li>\n<li>A pipe can fill a tank in 12 hours. By mistake, a waste pipe at the bottom is left opened and the tank is filled in 16 hours. If the tank is full, how much time will the waste pipe take to empty it?<\/li>\n<li>Differentiate the following function w.r.t. x:\u00a0<span class=\"math-tex\">{tex}\\frac{\\sqrt{x^{2}+1}-x}{\\sqrt{x^{2}+1}+x}{\/tex}<\/span>\n<p style=\"text-align: center;\"><b>OR <\/b><\/p>\n<p>Find\u00a0<span class=\"math-tex\">{tex}\\frac {dy}{dx}{\/tex}<\/span>: (x + y)<sup>2<\/sup> = 2axy<\/li>\n<li>Represent the number (11001.0101)<sub>2<\/sub> in decimal system.<\/li>\n<li style=\"text-align: center; clear: both; display: block;\"><b>Section C<\/b><\/li>\n<li>If a, b, c are pth, qth and rth terms respectively of an A.P, prove that: a(q\u00a0&#8211; r) + b(r\u00a0&#8211; p) + c(p\u00a0&#8211; q) = 0\n<p style=\"text-align: center;\"><b>OR <\/b><\/p>\n<p>If a, b, c, d are in G.P., prove that a<sup>n<\/sup> + b<sup>n<\/sup>, b<sup>n<\/sup> + c<sup>n<\/sup>, c<sup>n<\/sup> + d<sup>n<\/sup> are in G.P.<\/li>\n<li>Rohit is the husband of Vanshika. Sumita is the sister of Rohit. Anushka is the sister of Vanshika. How Anushka is related to Rohit?<\/li>\n<li>Find the domain and the range of the given\u00a0function: f(x) =\u00a0<span class=\"math-tex\">{tex}\\frac{1}{1-x^{2}}{\/tex}<\/span><\/li>\n<li>A man deposits \u20b9 5000 in the State Bank saving account allowing simple interest at 4<span class=\"math-tex\">{tex}\\frac 12{\/tex}<\/span>\u00a0percent per year. At the end of the first year, he transfers the entire amount to a fixed deposit account for 2 years at 7% per annum compounded annually. Find the total amount of money in the name of the depositor at the end of the third year, nearest to a rupee.<\/li>\n<li>A family in Delhi consumed 48 kL of water in a month. Calculate the water bill for the month. The tariff plan for Delhi is as given below:<br \/>\n<table style=\"width: 100%;\" border=\"1\" cellspacing=\"0\" cellpadding=\"3\">\n<thead>\n<tr>\n<th scope=\"col\">Monthly Consumption (in kL)<\/th>\n<th scope=\"col\">Service Charge<\/th>\n<th scope=\"col\">Water Consumption Charge per kL<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Up to 20<\/td>\n<td>\u20b9 146.41<\/td>\n<td>\u20b95.27<\/td>\n<\/tr>\n<tr>\n<td>20 &#8211; 30<\/td>\n<td>\u20b9219.62<\/td>\n<td>\u20b926.36<\/td>\n<\/tr>\n<tr>\n<td>&gt;30<\/td>\n<td>\u20b9292.82<\/td>\n<td>\u20b943.93<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Also, sewerage charges are applicable at 60% of the water consumption charges.<\/li>\n<li>Using properties of sets and their complements prove that:\n<ol style=\"list-style-type: lower-roman;\" start=\"1\">\n<li>(A <span class=\"math-tex\">{tex}\\cup{\/tex}<\/span> B) <span class=\"math-tex\">{tex}\\cap{\/tex}<\/span> (A <span class=\"math-tex\">{tex}\\cap{\/tex}<\/span> B&#8217;) = A<\/li>\n<li>A &#8211; (A <span class=\"math-tex\">{tex}\\cap{\/tex}<\/span> B) = A &#8211; B<\/li>\n<\/ol>\n<\/li>\n<li style=\"text-align: center; clear: both; display: block;\"><b>Section D<\/b><\/li>\n<li>How many three digit odd numbers can be formed by using the digits 1, 2, 3, 4, 5, 6 when\n<ol style=\"list-style-type: lower-roman;\" start=\"1\">\n<li>the repetition of digits is not allowed?<\/li>\n<li>the repetition of digits is allowed?<\/li>\n<\/ol>\n<p style=\"text-align: center;\"><b>OR <\/b><\/p>\n<p>From 7 consonants and 4 vowels, how many different words can be formed consisting of 3 consonants and 2 vowels?<\/li>\n<li>Evaluate :\u00a0<span class=\"math-tex\">{tex}\\mathop {Lim}\\limits_{x \\to 0} \\frac{{{e^{{x^2}}} &#8211; \\cos x}}{{{x^2}}}{\/tex}<\/span><\/li>\n<li>Ten competitors in a musical test were ranked by the three judges x, y and z in the following order:<br \/>\n<table style=\"width: 100%;\" border=\"1\" cellspacing=\"0\" cellpadding=\"3\">\n<tbody>\n<tr>\n<td width=\"200\">Ranks by X:<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">6<\/td>\n<td width=\"200\">5<\/td>\n<td width=\"200\">10<\/td>\n<td width=\"200\">3<\/td>\n<td width=\"200\">2<\/td>\n<td width=\"200\">4<\/td>\n<td width=\"200\">9<\/td>\n<td width=\"200\">7<\/td>\n<td width=\"200\">8<\/td>\n<\/tr>\n<tr>\n<td width=\"200\">Ranks by Y:<\/td>\n<td width=\"200\">3<\/td>\n<td width=\"200\">5<\/td>\n<td width=\"200\">8<\/td>\n<td width=\"200\">4<\/td>\n<td width=\"200\">7<\/td>\n<td width=\"200\">10<\/td>\n<td width=\"200\">2<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">6<\/td>\n<td width=\"200\">9<\/td>\n<\/tr>\n<tr>\n<td width=\"200\">Ranks by Z:<\/td>\n<td width=\"200\">6<\/td>\n<td width=\"200\">4<\/td>\n<td width=\"200\">9<\/td>\n<td width=\"200\">8<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">2<\/td>\n<td width=\"200\">3<\/td>\n<td width=\"200\">10<\/td>\n<td width=\"200\">5<\/td>\n<td width=\"200\">7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Using rank correlation method, discuss which pair of judges has the nearest approach to common likings in music.<\/p>\n<p style=\"text-align: center;\"><b>OR <\/b><\/p>\n<p>Calculate the mean and standard deviation for the following distribution:<\/p>\n<table style=\"width: 100%;\" border=\"1\" cellspacing=\"0\" cellpadding=\"3\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Marks:<\/td>\n<td style=\"text-align: center;\">20-30<\/td>\n<td style=\"text-align: center;\">30-40<\/td>\n<td style=\"text-align: center;\">40-50<\/td>\n<td style=\"text-align: center;\">50-60<\/td>\n<td style=\"text-align: center;\">60-70<\/td>\n<td style=\"text-align: center;\">70-80<\/td>\n<td style=\"text-align: center;\">80-90<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">No. of students:<\/td>\n<td style=\"text-align: center;\">3<\/td>\n<td style=\"text-align: center;\">6<\/td>\n<td style=\"text-align: center;\">13<\/td>\n<td style=\"text-align: center;\">15<\/td>\n<td style=\"text-align: center;\">14<\/td>\n<td style=\"text-align: center;\">5<\/td>\n<td style=\"text-align: center;\">4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>A person has the following informations for his tax return for the financial year 2019-20<br \/>\nSalary &#8211; \u20b9 10 Lacs<br \/>\nIncome from other sources &#8211; \u20b9 3 Lacs<br \/>\nSavings &#8211; \u20b9 2.5 Lacs Advance tax paid &#8211; \u20b9 60,000<br \/>\nThe rates of income tax for assessment year 2020-21 are as follows:<br \/>\nStandard deduction &#8211; \u20b9 50,000<\/p>\n<table style=\"width: 100%;\" border=\"1\" cellspacing=\"0\" cellpadding=\"3\">\n<thead>\n<tr>\n<th scope=\"col\">Income (\u20b9)<\/th>\n<th scope=\"col\">Old rate<\/th>\n<th scope=\"col\">New rate<\/th>\n<th scope=\"col\">Remark<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Upto \u20b9 2.5 lakhs<\/td>\n<td>0%<\/td>\n<td>0%<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\u20b9 2.5L &#8211; \u20b9 5.0L<\/td>\n<td>0%<\/td>\n<td>0%<\/td>\n<td>If net taxable income is &lt; \u20b9 5 lakh<\/td>\n<\/tr>\n<tr>\n<td>\u20b9 2.5L &#8211; \u20b9 5.0L<\/td>\n<td>5%<\/td>\n<td>5%<\/td>\n<td>If net taxable income is &gt; \u20b9 5 lakh<\/td>\n<\/tr>\n<tr>\n<td>\u20b9 5.0L &#8211; \u20b9 7.5L<\/td>\n<td>20%<\/td>\n<td>10%<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\u20b9 7.5L &#8211; 10.0 L<\/td>\n<td>20%<\/td>\n<td>15%<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\u20b9 10.0L &#8211; 12.5L<\/td>\n<td>30%<\/td>\n<td>20%<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>\u20b9 12.5L &#8211; 15.0L<\/td>\n<td>30%<\/td>\n<td>25%<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>&gt; 15L<\/td>\n<td>30%<\/td>\n<td>30%<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Exemptions and Deductions<\/td>\n<td>Yes<\/td>\n<td>No<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Education cess &#8211; 4%<br \/>\nCalculate the income tax according to<\/p>\n<ol style=\"list-style-type: lower-roman;\" start=\"1\">\n<li>old rates<\/li>\n<li>new rates<\/li>\n<\/ol>\n<\/li>\n<li style=\"text-align: center; clear: both; display: block;\"><b>Section E<\/b><\/li>\n<li><strong>Read the following text carefully and answer the questions that follow:<\/strong><br \/>\nDuring sports day of a school different patterns are made for students to perform. One such pattern is made by putting flags at B(3, 2) and C(4, -1), other flags and lines are to be put based on some calculations. Let us try the different positions.<\/p>\n<ol style=\"list-style-type: lower-roman;\" start=\"1\">\n<li>Find the Equation of BC. (1)<\/li>\n<li>Find the Equation of AC. (1)<\/li>\n<li>Find the Equation of AB. (2)<br \/>\n<strong>OR<\/strong><br \/>\nCoordinates of a point which divides medians of a triangle ABC in the ratio 2 : 1 (2)<\/li>\n<\/ol>\n<\/li>\n<li><strong>Read the following text carefully and answer the questions that follow:<\/strong><br \/>\nAn analysis of monthly wages paid to workers in two firms A\u00a0and B, belonging to the same industry, gives the following results:<\/p>\n<table style=\"width: 100%;\" border=\"1\" cellspacing=\"0\" cellpadding=\"3\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><strong>Particulars<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Firm A<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Firm B<\/strong><\/td>\n<\/tr>\n<tr>\n<td>No. of wage earners<\/td>\n<td style=\"text-align: center;\">586<\/td>\n<td style=\"text-align: center;\">648<\/td>\n<\/tr>\n<tr>\n<td>Mean of monthly wages<\/td>\n<td style=\"text-align: center;\">\u20b9 5253<\/td>\n<td style=\"text-align: center;\">\u20b9 5253<\/td>\n<\/tr>\n<tr>\n<td>Variance of the distribution of wages<\/td>\n<td style=\"text-align: center;\">100<\/td>\n<td style=\"text-align: center;\">121<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img decoding=\"async\" style=\"height: 102px; width: 200px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/imgur\/1632316421-nkf38a.jpg\" alt=\"\" \/><\/p>\n<ol style=\"list-style-type: lower-roman;\" start=\"1\">\n<li>Which firm A or B shows greater variability in individual wages? (1)<\/li>\n<li>Find the standard deviation of the distribution of wages for frim B. (1)<\/li>\n<li>Find the coefficient of variation of the distribution of wages for firm A. (2)<br \/>\n<strong>OR<\/strong><br \/>\nFind the amount paid by firm A. (2)<\/li>\n<\/ol>\n<\/li>\n<li><strong>Read the following text carefully and answer the questions that follow:<\/strong><br \/>\nMr. Kalra manufactures ball point pens. He sells pens in packets of 100 pieces. It is known that 6% of his products are defective. A packet of pens is selected at random and checked for number of defective pens.<\/p>\n<ol style=\"list-style-type: lower-roman;\" start=\"1\">\n<li>Find the probability that packet contains no defective pen. (1)<\/li>\n<li>Find the probability that packet contains atmost 4 defective pens. (1)<\/li>\n<li>Find the probability that packet contains atleast 2 defective pens. (2)<br \/>\n<strong>OR<\/strong><br \/>\nFind the probability that the packet contains exactly 3 defective pens. (2)<br \/>\nFor effective exam preparation and extensive practice, <strong>download the <a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide\">myCBSEguide App<\/a><\/strong> today! It provides <strong>complete study material<\/strong> for <strong>CBSE<\/strong>, <strong>NCERT<\/strong>, <strong>JEE Main<\/strong>, <strong>NEET UG<\/strong>, and <strong>NDA exams<\/strong>, helping students master key concepts and improve their performance. Access <strong>practice questions<\/strong>, <strong>sample papers<\/strong>, <strong>NCERT solutions<\/strong>, and <strong>detailed chapter notes<\/strong>, all in one app.Teachers can also take advantage of the <a href=\"https:\/\/play.google.com\/store\/apps\/details?id=com.examin8.exam\"><strong>Examin8 App<\/strong><\/a> to easily create customized <strong>question papers<\/strong> and <strong>online exams<\/strong>, featuring their own branding, logo, and name.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Key_Features\"><\/span>Key Features:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>Comprehensive study resources for <strong>CBSE<\/strong>, <strong>JEE Main<\/strong>, <strong>NEET UG<\/strong>, and <strong>NDA<\/strong><\/li>\n<li>Interactive <strong>mock tests<\/strong> and <strong>practice papers<\/strong> for exam preparation<\/li>\n<li>Customizable exam creation with <strong>Examin8<\/strong> for teachers<\/li>\n<li>Affordable plans with both <strong>free and premium content<\/strong><\/li>\n<\/ul>\n<p><strong>Visit my<a href=\"https:\/\/mycbseguide.com\/\">CBSEguide<\/a> Website<\/strong> for a complete study.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p style=\"text-align: center; page-break-before: always;\"><strong>Class 11 &#8211; Applied Maths<br \/>\nSample Paper &#8211; 01 (2024-25)<\/strong><\/p>\n<hr \/>\n<h2 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"Solutions_of_Applied_Maths_Class_11\"><\/span><strong>Solutions of Applied Maths Class 11<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ol style=\"padding-left: 20px;\">\n<li style=\"text-align: center; display: block;\"><b>Section A <\/b><\/li>\n<li>(b)\n<p style=\"display: inline;\">0.188<\/p>\n<p><b>Explanation: <\/b>Here,\u00a0P(A) = 0.4,P(<span class=\"math-tex\">{tex}\\bar{A}{\/tex}<\/span>) = 0.6, P(B) = 0.3, P(<span class=\"math-tex\">{tex}\\bar{B}{\/tex}<\/span>) = 0.7,<br \/>\nP(C) = 0.2 and\u00a0P(<span class=\"math-tex\">{tex}\\bar{C}{\/tex}<\/span>) = 0.8<br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0Probability of two hits\u00a0<span class=\"math-tex\">{tex}=P_{A} \\cdot P_{B} \\cdot P_{\\bar{C}}+P_{A} \\cdot P_{\\bar{B}} \\cdot P_{C}+P_{\\bar{A}} \\cdot P_{B} \\cdot P_{C}{\/tex}<\/span><br \/>\n= 0.4 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span> 0.3 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span> 0.8 + 0.4 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span> 0.7 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span> 0.2 + 0.6 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span> 0.3 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span> 0.2<br \/>\n<span class=\"math-tex\">{tex}={\/tex}<\/span> 0.096 + 0.056 + 0.036 = 0.188<\/li>\n<li>(c)\n<p style=\"display: inline;\">B<\/p>\n<p><b>Explanation: <\/b>B has more variability, because variance is greater.<\/li>\n<li>(d)\n<p style=\"display: inline;\">80C<\/p>\n<p><b>Explanation: <\/b>80C<\/li>\n<li>(d)\n<p style=\"display: inline;\"><span class=\"math-tex\">{tex}\\frac{8}{27}{\/tex}<\/span><\/p>\n<p><b>Explanation: <\/b><span class=\"math-tex\">{tex}\\left(5 \\frac{1}{16}\\right)^{-\\frac{3}{4}} =\\left(\\frac{81}{16}\\right)^{-\\frac{3}{4}}{\/tex}<\/span><span class=\"math-tex\">{tex}=\\left(\\frac{16}{81}\\right)^{\\frac{3}{4}}=\\left(\\frac{2^4}{3^4}\\right)^{\\frac{3}{4}}{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex}=\\left(\\frac{2}{3}\\right)^3=\\frac{8}{27} {\/tex}<\/span><\/li>\n<li>(b)\n<p style=\"display: inline;\">none of these<\/p>\n<p><b>Explanation: <\/b><span class=\"math-tex\">{tex}\\sqrt {f(x)} {\/tex}<\/span>\u00a0\u00a0is defined only if<br \/>\nf(x) will be non negative.<br \/>\nHence <span class=\"math-tex\">{tex} \\sqrt { &#8211; f(x)} {\\rm{ }}{\/tex}<\/span>is defined only for 0.<\/li>\n<li>(c)\n<p style=\"display: inline;\">1<\/p>\n<p><b>Explanation: <\/b>1<\/li>\n<li>(b)\n<p style=\"display: inline;\"><span class=\"math-tex\">{tex}\\frac 14{\/tex}<\/span><\/p>\n<p><b>Explanation: <\/b>No. of spade cards =13<br \/>\nNo. of queen in spade set =1<br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0n(spade queen) = <sup>13<\/sup>C<sub>1<\/sub><br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0n (Total no. of cases) = <sup>52<\/sup>C<sub>1<\/sub><br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0P (spade queen) =\u00a0<span class=\"math-tex\">{tex}\\frac{13_{\\mathrm{c}_{1}}}{52_{\\mathrm{c}_{1}}}{\/tex}<\/span>\u00a0=\u00a0<span class=\"math-tex\">{tex}\\frac{13}{52}=\\frac{1}{4}{\/tex}<\/span><\/li>\n<li>(d)\n<p style=\"display: inline;\">x<sup>2\u00a0<\/sup>+ y<sup>2<\/sup> &#8211; 6x + 12y &#8211; 15 = 0<\/p>\n<p><b>Explanation: <\/b><\/p>\n<p>Given equation of the circle is<br \/>\nx<sup>2<\/sup> + y<sup>2<\/sup> &#8211; 6x + 12y + 15 = 0 &#8230;.. (1)<br \/>\nor (x &#8211; 3)<sup>2<\/sup> + (y + 6)<sup>2<\/sup>\u00a0<span class=\"math-tex\">{tex}=(\\sqrt{30})^{2}{\/tex}<\/span><br \/>\nHence, centre is (3, -6) and radius is\u00a0<span class=\"math-tex\">{tex}(\\sqrt{30}){\/tex}<\/span><br \/>\nSince, the required circle is concentric with above circle.<br \/>\nTherefore, the center of the required circle is (3, -6)<br \/>\nNow, it given that<br \/>\nArea of the required circle<br \/>\n= 2\u00a0<span class=\"math-tex\">{tex}\\times{\/tex}<\/span>\u00a0Area of the given circle<br \/>\n<span class=\"math-tex\">{tex}\\pi r^{2}=2 \\times \\pi(\\sqrt{30})^{2}{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow r^{2} {\/tex}<\/span>\u00a0= 60<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow r =\\sqrt {60}{\/tex}<\/span><br \/>\nSo, The required equation of the circle is (x &#8211; 3)<sup>2<\/sup> + (y + 6)<sup>2<\/sup> = 60<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span>\u00a0x<sup>2<\/sup>\u00a0+ y<sup>2<\/sup> &#8211; 6x + 12y &#8211; 15 = 0<\/li>\n<li>(a)\n<p style=\"display: inline;\">medicine<\/p>\n<p><b>Explanation: <\/b>medicine<\/li>\n<li>(a)\n<p style=\"display: inline;\">range<\/p>\n<p><b>Explanation: <\/b>Meausre of central tendencies give the middle most or average value whereas range gives the difference between highest and lowest value.<\/li>\n<li>(c)\n<p style=\"display: inline;\">4<\/p>\n<p><b>Explanation: <\/b>As 14768 = 1.4768 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span> 10<sup>4<\/sup><\/li>\n<li>(a)\n<p style=\"display: inline;\">\u20b9 24<\/p>\n<p><b>Explanation: <\/b><strong>For C.I.:<\/strong><br \/>\nC.I. = 15000\u00a0<span class=\"math-tex\">{tex}\\left(1+\\frac{4}{100}\\right)^2{\/tex}<\/span>\u00a0&#8211; 15000<br \/>\n= 15000\u00a0<span class=\"math-tex\">{tex}\\left[\\frac{26}{25} \\times \\frac{26}{25}-1\\right]=\\frac{15000 \\times 51}{25 \\times 25}{\/tex}<\/span>\u00a0=\u00a0\u20b9 1224.<br \/>\nS.I. =\u00a0<span class=\"math-tex\">{tex}\\frac{15000 \\times 51}{25 \\times 25}{\/tex}<\/span>\u00a0= \u20b9 1200<br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0Difference between C.I. and S.I. =\u00a0\u00a0\u20b9 1224 &#8211;\u00a0\u20b9 1200\u00a0=\u00a0\u20b924<\/li>\n<li>(d)\n<p style=\"display: inline;\">\u20b9 99<\/p>\n<p><b>Explanation: <\/b>\u20b9 99<\/li>\n<li>(a)\n<p style=\"display: inline;\"><span class=\"math-tex\">{tex}\\frac 34{\/tex}<\/span><\/p>\n<p><b>Explanation: <\/b>as P(problem solved)<br \/>\n= 1 &#8211; P(none solves)<br \/>\n= 1 &#8211; <span class=\"math-tex\">{tex}\\frac{1}{2} \\times \\frac{2}{3} \\times \\frac{3}{4}{\/tex}<\/span>\u00a0= 1 &#8211; <span class=\"math-tex\">{tex}\\frac{1}{4}{\/tex}<\/span>\u00a0=\u00a0<span class=\"math-tex\">{tex}\\frac{3}{4}{\/tex}<\/span><\/li>\n<li>(b)\n<p style=\"display: inline;\"><span class=\"math-tex\">{tex}\\frac{25}{43}{\/tex}<\/span><\/p>\n<p><b>Explanation: <\/b><\/p>\n<p><img decoding=\"async\" style=\"height: 109px; width: 213px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/question_images\/1713334799-u5c5g5.jpg\" \/><br \/>\nE<sub>1<\/sub> : Ball drawn from bag A.<br \/>\nE<sub>2<\/sub> : Ball drawn from bag B.<br \/>\nE : Drawn ball is Red:<br \/>\nBy Bayes&#8217;s tho.,<br \/>\n<span class=\"math-tex\">{tex}P\\left(E_2 \\mid E\\right){\/tex}<\/span>\u00a0\u00a0 =\u00a0<span class=\"math-tex\">{tex}\\frac{P\\left(E_2\\right) P\\left(E \\mid E_2\\right)}{P\\left(E_1\\right) P\\left(E \\mid E_1\\right)+P\\left(E_2\\right) P\\left(E \\mid E_2\\right)}{\/tex}<\/span><br \/>\n=\u00a0<span class=\"math-tex\">{tex}\\frac{\\frac{1}{2} \\cdot \\frac{5}{9}}{\\frac{1}{2} \\cdot \\frac{2}{5}+\\frac{1}{2} \\cdot \\frac{5}{9}}{\/tex}<\/span><br \/>\n=\u00a0<span class=\"math-tex\">{tex}\\frac{\\frac{5}{18}}{\\frac{2}{10}+\\frac{5}{18}}{\/tex}<\/span>\u00a0<span class=\"math-tex\">{tex}=\\frac{5}{18} \\times \\frac{90}{43} {\/tex}<\/span><br \/>\n=\u00a0<span class=\"math-tex\">{tex}\\frac{25}{43}{\/tex}<\/span><br \/>\nP(E<sub>2<\/sub>\u00a0| E)\u00a0= <span class=\"math-tex\">{tex}\\frac{25}{43}{\/tex}<\/span><\/li>\n<li>(a)\n<p style=\"display: inline;\">2<\/p>\n<p><b>Explanation: <\/b>Amount = \u20b9(30,000 + 4347) = \u20b9 34347<br \/>\nLet the time be n years.<br \/>\nThen, using formula of compound interest A<sub>n<\/sub> = P(1 + i)<sup>n<\/sup><br \/>\nHere, A<sub>n<\/sub> = 34347, i = <span class=\"math-tex\">{tex}\\frac{7}{100}{\/tex}<\/span> = 0.04 and P = 30,000<br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span> 34347 = 30,000 (1 + 0.07)<sup>n<\/sup><br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span> (1.07)<sup>n<\/sup> = <span class=\"math-tex\">{tex}\\frac{34347}{30,000}{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span> <span class=\"math-tex\">{tex}\\left(\\frac{107}{100}\\right)^n{\/tex}<\/span> = <span class=\"math-tex\">{tex}\\frac{11449}{10000}{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span> <span class=\"math-tex\">{tex}\\left(\\frac{107}{100}\\right)^n{\/tex}<\/span> = <span class=\"math-tex\">{tex}\\left(\\frac{107}{100}\\right)^2{\/tex}<\/span><br \/>\n= n = 2 years.<\/li>\n<li>(a)\n<p style=\"display: inline;\">24<\/p>\n<p><b>Explanation: <\/b>Given digits 2, 3, 4 and 7.<br \/>\nWe have to find\u00a04-digit numbers using these digits.<br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0Required number of ways<br \/>\n=\u00a0<sup>4<\/sup>P<sub>4<\/sub>\u00a0= 4!\u00a0= 4 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span>\u00a03 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span>\u00a02 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span>\u00a01 = 24<\/li>\n<li>(a)\n<p style=\"display: inline;\">{2, 3, 4, 5}<\/p>\n<p><b>Explanation: <\/b>Relatively prime numbers are those numbers that have only 1 as the common factor.<br \/>\nSo, according to this definition we get to know that (2, 3), (2, 7), (3, 7), (3, 10), (4, 3), (4, 7), (5, 3), (5, 6), (5, 7) are relatively prime.<br \/>\nSo, R = {(2, 3), (2, 7), (3, 7), (3, 10), (4, 3), (4, 7), (5, 3), (5, 6) ,(5, 7)}.<br \/>\nTherefore, the Domain of R is the values of x or the first element of the ordered pair.<br \/>\nSo, Domain = {2, 3, 4, 5}<\/li>\n<li>(b)\n<p style=\"display: inline;\">Both A and R are true but R is not the correct explanation of A.<\/p>\n<p><b>Explanation: <\/b>Assertion: True<br \/>\nRange = maximum value -minimum value<br \/>\nR = L &#8211; S<br \/>\nReason: True<br \/>\nBut not the correct explanation of Assertion.<\/li>\n<li>(d)\n<p style=\"display: inline;\">A is false but R is true.<\/p>\n<p><b>Explanation: <\/b>In an A.P., d = a<sub>n<\/sub> &#8211; a<sub>n-1<\/sub><br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span> Reason is true.<br \/>\nNow, given a<sub>n<\/sub> = pn + q<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span> d = a<sub>n<\/sub> &#8211; a<sub>n-1<\/sub><br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span>\u00a0d = pn + q &#8211; {p (n &#8211; 1) + q}<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span>\u00a0d = pn + q &#8211; pn + p &#8211; q<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span>\u00a0d = p<br \/>\nAssertion is false.<\/p>\n<p>Visit our website <strong><a href=\"https:\/\/mycbseguide.com\/\">myCBSEGuide<\/a><\/strong>. Boost your exam preparation by downloading the <strong>myCBSEguide App<\/strong>! It offers a complete range of study materials for <strong>CBSE<\/strong>, <strong>NCERT<\/strong>, <strong>JEE Main<\/strong>, <strong>NEET UG<\/strong>, and <strong>NDA exams<\/strong>. From <strong>practice questions<\/strong> and <strong>NCERT solutions<\/strong> to <strong>sample papers<\/strong> and <strong>detailed chapter notes<\/strong>, this app is your go-to resource for comprehensive learning.<\/p>\n<p>For educators, the <a href=\"https:\/\/examin8.com\/\"><strong>Examin8 Website<\/strong><\/a>\u00a0provides a powerful platform to craft customized <strong>online tests<\/strong> and <strong>question papers<\/strong> with personalized branding, including logos and names. Teachers can easily create tailored assessments to enhance student learning.<\/p>\n<p><strong>Key Benefits of myCBSEguide App:<\/strong><\/p>\n<ul>\n<li>Extensive resources for CBSE, JEE, NEET, and NDA preparation<\/li>\n<li>Timely practice through interactive tests and mock exams<\/li>\n<li>Convenient exam creation and customization for educators via Examin8<\/li>\n<li>Affordable plans offering both free and premium content<\/li>\n<\/ul>\n<p>Get access to <strong>question papers<\/strong> for Class 11 Applied Maths, designed to reflect the current <strong>CBSE exam pattern<\/strong>. These <strong>question papers<\/strong> are an excellent resource for practicing a variety of questions from previous years. By solving these <strong>question papers<\/strong>, you can familiarize yourself with the kind of questions asked in the exam. 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Make sure to download and solve these <strong>question papers<\/strong> to build confidence and improve your exam performance.<\/p>\n<div class=\"flex-shrink-0 flex flex-col relative items-end\">\n<div>\n<div class=\"pt-0\">\n<div class=\"gizmo-bot-avatar flex h-8 w-8 items-center justify-center overflow-hidden rounded-full\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"group\/conversation-turn relative flex w-full min-w-0 flex-col agent-turn\">\n<div class=\"flex-col gap-1 md:gap-3\">\n<div class=\"flex max-w-full flex-col flex-grow\">\n<div class=\"min-h-8 text-message flex w-full flex-col items-end gap-2 whitespace-normal break-words [.text-message+&amp;]:mt-5\" dir=\"auto\" data-message-author-role=\"assistant\" data-message-id=\"2b281cd8-339b-4da1-a4ac-4aa52f01d75a\" data-message-model-slug=\"gpt-4o-mini\">\n<div class=\"flex w-full flex-col gap-1 empty:hidden first:pt-[3px]\">\n<div class=\"markdown prose w-full break-words dark:prose-invert dark\">\n<p><strong>Maximize Your Exam Success with the myCBSEguide and Examin8 Apps \u2013 Download Now!<\/strong><\/p>\n<p><strong>Boost Your Preparation with CBSE Class 11 Applied Maths Sample Papers for 2025<\/strong><br \/>\nPrepare for your <strong>CBSE Class 11 Applied Maths<\/strong> exams with expertly designed <strong>sample papers for 2025<\/strong>.<\/p>\n<p style=\"text-align: left;\"><a href=\"https:\/\/mycbseguide.com\/cbse-sample-papers-class-11.html\"><strong>Download Class 11 Mock Paper as PDF<\/strong><\/a><br \/>\nBoost your exam preparation with the <strong>myCBSEguide<\/strong> and <strong>Examin8 apps<\/strong>! Download these powerful apps today to access a wide range of study materials, practice questions, sample papers, and more. Whether you&#8217;re preparing for <a href=\"https:\/\/mycbseguide.com\/cbse-sample-papers-class-10.html\"><strong>CBSE Class 10<\/strong><\/a>, <a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-12\/1250\/\"><strong>Class 12<\/strong><\/a>, or other exams, these apps provide the tools you need to excel. Stay ahead in your studies with expert-curated content, personalized learning paths, and comprehensive resources. <strong>Get started now<\/strong> with <strong>myCBSEguide<\/strong> and <strong>Examin8<\/strong> to elevate your exam preparation and increase your chances of success<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/li>\n<li style=\"text-align: center; display: block;\"><b>Section B <\/b><\/li>\n<li>We know that the average of 5 consecutive natural numbers beginning with y i.e. y, y + 1, y + 2, y + 3, y + 4 is y +\u00a0<span class=\"math-tex\">{tex}\\frac {5-1}2{\/tex}<\/span>\u00a0= y + 2<br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0x = y + 2 [The average of n consecutive natural numbers x, x + 1, x + 2, x + 3, &#8230;, x + (n &#8211; 1) is x +<span class=\"math-tex\">{tex}(\\frac {n-1}2){\/tex}<\/span>]\nIf next two numbers i.e. y + 5 and y + 6 are also included, then their average z is given by z = y + <span class=\"math-tex\">{tex}\\frac {7-1}2{\/tex}<\/span> = y + 3\u00a0[The average of n consecutive natural numbers x, x + 1, x + 2, x + 3, &#8230;, x + (n &#8211; 1) is x +<span class=\"math-tex\">{tex}(\\frac {n-1}2){\/tex}<\/span>] &#8230; (ii)<br \/>\nFrom (i) and (ii), we obtain z = x + 1 i.e. the mean is increased by 1.<\/li>\n<li style=\"clear: both;\">In the first and second statements, common codes are 3 and 7, and common words are &#8216;is&#8217; and &#8216;eternal&#8217;.<br \/>\nIn the first and third statements, the common code is 2 and the common word is &#8216;truth&#8217;.<br \/>\nSo code 2 means &#8216;truth&#8217;<br \/>\nIn the second and third statements, the common code is 9 and the common word is &#8216;not&#8217;.<br \/>\nSo code 8 stands for the word &#8216;Enmity&#8217;.<\/p>\n<p style=\"text-align: center;\"><b>OR <\/b><\/p>\n<p>Here, the new positions are obtained by multiplying the original position by 2.<br \/>\nSo,<br \/>\n<img decoding=\"async\" style=\"height: 182px; width: 300px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/question_images\/1707907240-mx9f7k.jpg\" \/><br \/>\nSo, &#8216;CHAIR&#8217; is coded as &#8216;FPBRJ&#8217;.<\/li>\n<li>In 1 hour pipe can fill <span class=\"math-tex\">{tex}\\frac{1}{12}{\/tex}<\/span>\u00a0 of the tank.<br \/>\nWhen both the pipes were working together it took 16 hours to fill, so, in 1 hour working together they can fill <span class=\"math-tex\">{tex}\\frac{1}{16}{\/tex}<\/span>\u00a0 of the tank.<br \/>\nWork done in 1 hour by the pipe which empties the tank = <span class=\"math-tex\">{tex}\\frac{1}{12}-\\frac{1}{16}=\\frac{1}{48}{\/tex}<\/span> of the tank.<br \/>\nHence, the waste pipe working alone can empty the tank in 48 hours.<\/li>\n<li style=\"clear: both;\">Let y =\u00a0<span class=\"math-tex\">{tex}\\frac{\\sqrt{x^{2}+1}-x}{\\sqrt{x^{2}+1}+x}=\\frac{\\sqrt{x^{2}+1}-x}{\\sqrt{x^{2}+1}+x} \\times \\frac{\\sqrt{x^{2}+1}-x}{\\sqrt{x^{2}+1}-x}{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex}=\\frac{\\left(x^{2}+1\\right)+x^{2}-2 x \\sqrt{x^{2}+1}}{\\left(x^{2}+1\\right)-x^{2}}=\\frac{2 x^{2}+1-2 x \\sqrt{x^{2}+1}}{1}{\/tex}<\/span><br \/>\n= 2x<sup>2<\/sup>\u00a0+ 1 &#8211; 2x\u00a0<span class=\"math-tex\">{tex}\\sqrt{x^{2}+1}{\/tex}<\/span>, differentiating w.r.t. x, we get<br \/>\n<span class=\"math-tex\">{tex}\\frac{d y}{d x}{\/tex}<\/span>\u00a0= 2<span class=\"math-tex\">{tex}\\cdot{\/tex}<\/span>2x + 0 &#8211; 2 [x<span class=\"math-tex\">{tex}\\cdot{\/tex}<\/span><span class=\"math-tex\">{tex}\\frac{1}{2}{\/tex}<\/span>\u00a0<span class=\"math-tex\">{tex}(x^2\u00a0+ 1)^{-1 \\over2}{\/tex}<\/span>\u00a0<span class=\"math-tex\">{tex}\\cdot{\/tex}<\/span>\u00a02x +\u00a0<span class=\"math-tex\">{tex}\\sqrt{x^{2}+1}{\/tex}<\/span>\u00a0<span class=\"math-tex\">{tex}\\cdot{\/tex}<\/span>\u00a01]\n= 4x &#8211; 2\u00a0<span class=\"math-tex\">{tex}\\left[\\frac{x^{2}}{\\sqrt{x^{2}+1}}+\\sqrt{x^{2}+1}\\right]{\/tex}<\/span>\u00a0= 4x &#8211; 2\u00a0<span class=\"math-tex\">{tex}\\cdot\\frac{x^{2}+\\left(x^{2}+1\\right)}{\\sqrt{x^{2}+1}}=2\\left[2 x-\\frac{2 x^{2}+1}{\\sqrt{x^{2}+1}}\\right]{\/tex}<\/span><\/p>\n<p style=\"text-align: center;\"><b>OR <\/b><\/p>\n<p>Given\u00a0(x + y)<sup>2<\/sup> = 2axy<br \/>\nDifferentiating the equation on both sides with respect to\u00a0x,<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow \\frac{d}{d x}{\/tex}<\/span>(x + y)<sup>2\u00a0<\/sup>= <span class=\"math-tex\">{tex}\\frac{d}{d x}{\/tex}<\/span>(2axy)<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span> 2(x + y)<span class=\"math-tex\">{tex}\\frac{d}{d x}{\/tex}<\/span>(x + y) = 2a[x <span class=\"math-tex\">{tex}\\frac{d y}{d x}{\/tex}<\/span>\u00a0+ y<span class=\"math-tex\">{tex}\\frac{d}{d x}{\/tex}<\/span>(x)]\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span> 2(x + y)[1 +\u00a0<span class=\"math-tex\">{tex}\\frac{d y}{d x}{\/tex}<\/span>] = 2a[x<span class=\"math-tex\">{tex}\\frac{d y}{d x}{\/tex}<\/span>\u00a0+ y(1)]\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span> 2(x + y)+2(x + y) <span class=\"math-tex\">{tex}\\frac{d y}{d x}{\/tex}<\/span>\u00a0= 2ax<span class=\"math-tex\">{tex}\\frac{d y}{d x}{\/tex}<\/span>\u00a0+ 2ay<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow \\frac{d y}{d x}{\/tex}<\/span>[2(x + y) &#8211; 2ax] = 2ay &#8211; 2(x + y)<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow \\frac{d y}{d x}=\\frac{2[a y-x-y]}{2[x+y-a x]}{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow \\frac{d y}{d x}=\\left(\\frac{a y-x-y}{x+y-a x}\\right){\/tex}<\/span><\/li>\n<li>(11001.0101)<sub>2<\/sub> = 1 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span> 2<sup>4<\/sup> + 1 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span> 2<sup>3<\/sup> + 0 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span> 2<sup>2<\/sup> + 0 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span> 2<sup>1<\/sup> + 1 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span> 2<sup>0<\/sup>\u00a0+ 0<br \/>\n<span class=\"math-tex\">{tex}\\times{\/tex}<\/span>\u00a0<span class=\"math-tex\">{tex}\\frac {1}{2}{\/tex}<\/span>\u00a0+ 1\u00a0<span class=\"math-tex\">{tex}\\times{\/tex}<\/span>\u00a0<span class=\"math-tex\">{tex}\\frac {1}{4}{\/tex}<\/span>\u00a0+ 0\u00a0<span class=\"math-tex\">{tex}\\times{\/tex}<\/span>\u00a0<span class=\"math-tex\">{tex}\\frac {1}{8}{\/tex}<\/span>\u00a0+ 1\u00a0<span class=\"math-tex\">{tex}\\times{\/tex}<\/span>\u00a0<span class=\"math-tex\">{tex}\\frac {1}{16}{\/tex}<\/span><br \/>\n= 16 + 8 + 0 + 0 + 1 + 0 + 0.25 + 0 + 0.0625<br \/>\n= 25.3125<\/li>\n<li style=\"text-align: center; display: block;\"><b>Section C <\/b><\/li>\n<li style=\"clear: both;\">Let A be the first erm and D be the common difference of the given A.P.<br \/>\nThen, a = pth\u00a0term<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span> a = A + (p &#8211; 1) D<br \/>\nb = qth\u00a0term<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span> b = A + (q &#8211; 1) D<br \/>\nc = rth\u00a0term<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span> c = A + (r &#8211; 1)D<br \/>\nWe have.<br \/>\na(q &#8211; r) + b(r &#8211; p) + c(p &#8211; q)<br \/>\n= [A + (p &#8211; 1) D](q &#8211; r)+[A + (q &#8211; 1) D](r &#8211; p) + [A + (r &#8211; 1) D](p &#8211; q)<br \/>\n= A[(q &#8211; r) + (r &#8211; p) + (p &#8211; q)] + D[(p &#8211; 1)(q &#8211; r)\u00a0+ (q &#8211; 1)(r &#8211; p)+(r &#8211; 1)(p &#8211; q)]\n= A <span class=\"math-tex\">{tex}\\times{\/tex}<\/span> 0 + D[p(q &#8211; r) + q(r &#8211; p) + r(p &#8211; q) &#8211; (q &#8211; r) &#8211; (r &#8211; p) -(p &#8211; q)]\n= 0 + D <span class=\"math-tex\">{tex}\\times{\/tex}<\/span> 0<br \/>\n= 0<\/p>\n<p style=\"text-align: center;\"><b>OR <\/b><\/p>\n<p>Given a, b, c, d are in G.P., let r be the common ratio.<br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0b = ar, c = ar<sup>2<\/sup> and, d\u00a0= ar<sup>3<\/sup><br \/>\n(b<sup>n<\/sup> + c<sup>n<\/sup>)<sup>2<\/sup> = ((ar)<sup>n<\/sup> + (ar<sup>2<\/sup>)<sup>n<\/sup>)<sup>2<\/sup> = (anr<sup>n<\/sup> + a<sup>n<\/sup>r<sup>2n<\/sup>)<sup>2<\/sup>+ b<sup>n<\/sup>) (c<sup>n<\/sup> + d<sup>n<\/sup>) = (a<sup>n<\/sup> + (ar)<sup>n<\/sup>) ((ar<sup>2<\/sup>)<sup>n<\/sup> + (ar<sup>3<\/sup>)<sup>n<\/sup>)<br \/>\n= (a<sup>n<\/sup> + a<sup>n<\/sup>r<sup>n<\/sup>) (a<sup>n<\/sup>r<sup>2n<\/sup> + a<sup>n<\/sup>r<sup>3n<\/sup>)<br \/>\n= a<sup>n<\/sup> (1 + r<sup>n<\/sup>) a<sup>n<\/sup>r<sup>2<\/sup>(1 + r<sup>n<\/sup>)<br \/>\n= a<sup>2n<\/sup>r<sup>2n<\/sup> (1 + r<sup>n<\/sup>)<sup>2<\/sup><br \/>\nHence, (b<sup>n<\/sup> + c<sup>n<\/sup>)2 = (a<sup>n<\/sup> + b<sup>n<\/sup>) (c<sup>n<\/sup> + d<sup>n<\/sup>)<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span>\u00a0a<sup>n<\/sup> + b<sup>n<\/sup><br \/>\n= (a<sup>n<\/sup>r<sup>n<\/sup>)<sup>2\u00a0<\/sup>(1 + r<sup>n<\/sup>)<sup>2<\/sup> = a<sup>2n<\/sup>r<sup>2n<\/sup>\u00a0(1 + r<sup>n<\/sup>)2<br \/>\nand\u00a0a<sup>n<\/sup> , b<sup>n<\/sup> + c<sup>n<\/sup>, c<sup>n<\/sup> + d<sup>n<\/sup> are in G.P.<\/li>\n<li>Rohit is the husband of Vanshika<br \/>\n<img decoding=\"async\" style=\"width: 200px; height: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/imgur\/ksueFIV.png\" alt=\"\" data-imgur-src=\"ksueFIV.png\" \/><br \/>\nSumita is the sister of Rohit<br \/>\n<img decoding=\"async\" style=\"width: 300px; height: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/imgur\/2xbBSh6.png\" alt=\"\" data-imgur-src=\"2xbBSh6.png\" \/><br \/>\nAnushka is the sister of Vanshika<br \/>\n<img decoding=\"async\" style=\"width: 300px; height: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/imgur\/zQ5JW9C.png\" alt=\"\" data-imgur-src=\"zQ5JW9C.png\" \/><br \/>\nSo Anushka is Rohit&#8217;s wife&#8217;s sister<br \/>\nAnushka is the sister-in-law of Rohit.<\/li>\n<li>Given\u00a0f(x) =\u00a0<span class=\"math-tex\">{tex}\\frac{1}{1-x^{2}}{\/tex}<\/span><br \/>\nFor D<sub>f<\/sub>, f(x) must be a real number\u00a0<span class=\"math-tex\">{tex}\\Rightarrow \\frac{1}{1-x^{2}}{\/tex}<\/span>\u00a0must be a real number<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span>\u00a01 &#8211; x<sup>2<\/sup>\u00a0<span class=\"math-tex\">{tex}\\neq{\/tex}<\/span>\u00a00\u00a0<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span>\u00a0x\u00a0<span class=\"math-tex\">{tex}\\neq{\/tex}<\/span>\u00a0-1, 1<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span>\u00a0D<sub>f<\/sub>\u00a0=\u00a0set of all real numbers except -1, i.e. D<sub>f<\/sub>\u00a0= <strong>R<\/strong>\u00a0&#8211; {-1, 1}<br \/>\nFor R<sub>f<\/sub>, let y =\u00a0<span class=\"math-tex\">{tex}\\frac{1}{1-x^{2}}{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span>\u00a01 &#8211; x<sup>2<\/sup>\u00a0=\u00a0<span class=\"math-tex\">{tex}\\frac{1}{y}{\/tex}<\/span>, y\u00a0<span class=\"math-tex\">{tex}\\neq{\/tex}<\/span>\u00a00\u00a0<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span>\u00a0x<sup>2<\/sup>\u00a0= 1 &#8211;\u00a0<span class=\"math-tex\">{tex}\\frac{1}{y}{\/tex}<\/span>, y\u00a0<span class=\"math-tex\">{tex}\\neq{\/tex}<\/span>\u00a00<br \/>\nBut x<sup>2<\/sup>\u00a0<span class=\"math-tex\">{tex}\\geq{\/tex}<\/span>\u00a00 for all x\u00a0<span class=\"math-tex\">{tex}\\in{\/tex}<\/span>\u00a0D<sub>f<\/sub>\u00a0<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span>\u00a01 &#8211;\u00a0<span class=\"math-tex\">{tex}\\frac{1}{y}{\/tex}<\/span>\u00a0<span class=\"math-tex\">{tex}\\geq{\/tex}<\/span>\u00a00 but y<sup>2<\/sup>\u00a0&gt; 0, y\u00a0<span class=\"math-tex\">{tex}\\neq{\/tex}<\/span>\u00a00\u00a0(Multiply both sides by y<sup>2<\/sup>, a positive real number)<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span>\u00a0y<sup>2<\/sup>\u00a0(1 &#8211;\u00a0<span class=\"math-tex\">{tex}\\frac{1}{y}{\/tex}<\/span>)\u00a0<span class=\"math-tex\">{tex}\\geq{\/tex}<\/span>\u00a00\u00a0<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span>\u00a0y (y &#8211; 1)\u00a0<span class=\"math-tex\">{tex}\\geq{\/tex}<\/span>\u00a00\u00a0<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span>\u00a0(y &#8211; 0) (y &#8211; 1)\u00a0<span class=\"math-tex\">{tex}\\geq{\/tex}<\/span>\u00a00<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span>\u00a0either y\u00a0<span class=\"math-tex\">{tex}\\leq{\/tex}<\/span>\u00a00 or y\u00a0<span class=\"math-tex\">{tex}\\geq{\/tex}<\/span>\u00a01 but y\u00a0<span class=\"math-tex\">{tex}\\neq{\/tex}<\/span>\u00a00<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span>\u00a0R<sub>f<\/sub>\u00a0= <span class=\"math-tex\">{tex}(-\\infty, 0) \\cup[1, \\infty){\/tex}<\/span><\/li>\n<li>Here<br \/>\nPrincipal = \u00a0\u20b95000<br \/>\nRate\u00a0<span class=\"math-tex\">{tex}=4 \\frac{1}{2}{\/tex}<\/span>% p.a.\u00a0<span class=\"math-tex\">{tex}=\\frac{9}{2}{\/tex}<\/span>% p.a.<br \/>\n<span class=\"math-tex\">{tex}I=\\frac{5000-9 \\times 1}{2 \\times 100}{\/tex}<\/span><br \/>\nI = 25 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span> 9<br \/>\n=\u00a0\u20b9 5225<br \/>\nNow he transfers the whole amount to fixed deposits<br \/>\ni.e. P =\u00a0\u20b9 5225<br \/>\nR = 7%<br \/>\nT = 7% p.a. compounded annually<br \/>\nAmount at the third year.<br \/>\n<span class=\"math-tex\">{tex}A =P\\left(1+\\frac{R}{100}\\right)^n{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex}=5225\\left(1+\\frac{7}{100}\\right)^{2}{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex}=5225\\left(\\frac{107}{100}\\right)^{2}{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex}=5225 \\times \\frac{107}{100} \\times \\frac{107}{100}{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex}=\\frac{5225 \\times 11449}{10000}{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex}=\\frac{598210{25}}{10000}{\/tex}<\/span>\u00a0= \u00a0\u20b9 5982.1025\u00a0<span class=\"math-tex\">{tex}\\approx{\/tex}<\/span> 5982<\/li>\n<li>Here, the volume of water consumed is 48 kL which is above 30 kL.<br \/>\nThus, the rate for first 20 kL will be\u00a0\u20b9 5.27\/kL, for the next 10 kilolitres thr rate will be\u00a0\u20b9 26.36\/kL and for the balance 18 kiloliters, the rate will be\u00a0\u20b9 43.93 \/ kL.<br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0Water consumption charges =\u00a0\u20b9( 5.27\u00a0<span class=\"math-tex\">{tex}\\times{\/tex}<\/span>\u00a020) +\u00a0\u20b9 ( 26.36 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span>10) +\u00a0\u20b9(18 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span>43.93)<br \/>\n=\u00a0\u20b9(105.40+263.60+790.74)<br \/>\n=\u00a0\u20b9 1159.74<br \/>\nAlso, the\u00a0Sewerage charge is 60% of consumption charges.<br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0Sewerage charge = 60% of\u00a0\u20b9 1159.74 =\u00a0\u20b9695.84<br \/>\nAccording to the given tariff plan, the service charge for the consumption above 30 kL is\u00a0\u20b9 292.82<br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0Service charge =\u00a0\u20b9 292.82<br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0Total water bill = Water consumption charge + Sewerage charge + Service charge<br \/>\n=\u00a0\u20b9 1159.74 + \u20b9695.84 + \u20b9292.82 = \u20b92148.40<\/p>\n<ol style=\"list-style-type: lower-roman;\" start=\"1\">\n<li>(A <span class=\"math-tex\">{tex}\\cup{\/tex}<\/span> B) <span class=\"math-tex\">{tex}\\cap{\/tex}<\/span> (A <span class=\"math-tex\">{tex}\\cap{\/tex}<\/span> B&#8217;) = A<br \/>\nL.H.S. = (A <span class=\"math-tex\">{tex}\\cup{\/tex}<\/span>\u00a0B)\u00a0<span class=\"math-tex\">{tex}\\cap{\/tex}<\/span>\u00a0(A <span class=\"math-tex\">{tex}\\cap{\/tex}<\/span>\u00a0B&#8217;)<br \/>\n= A\u00a0<span class=\"math-tex\">{tex}\\cup{\/tex}<\/span>\u00a0(B\u00a0<span class=\"math-tex\">{tex}\\cap{\/tex}<\/span>\u00a0B&#8217;)<br \/>\n(By distributive law)<br \/>\n= A\u00a0<span class=\"math-tex\">{tex}\\cup{\/tex}<\/span>\u00a0<span class=\"math-tex\">{tex}\\phi{\/tex}<\/span>\u00a0(B <span class=\"math-tex\">{tex}\\cap{\/tex}<\/span>\u00a0B&#8217; = <span class=\"math-tex\">{tex}\\phi{\/tex}<\/span>)<br \/>\n= A<br \/>\n= R.H.S. Hence proved.<\/li>\n<li>A &#8211; (A <span class=\"math-tex\">{tex}\\cap{\/tex}<\/span>\u00a0B) = A &#8211; B<br \/>\nL.H.S. = A &#8211; (A <span class=\"math-tex\">{tex}\\cap{\/tex}<\/span>\u00a0B)<br \/>\n= A\u00a0<span class=\"math-tex\">{tex}\\cap{\/tex}<\/span>\u00a0(A <span class=\"math-tex\">{tex}\\cap{\/tex}<\/span>\u00a0B)&#8217;<br \/>\n[<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0A &#8211; B = A <span class=\"math-tex\">{tex}\\cap{\/tex}<\/span>\u00a0B&#8217;]\n=\u00a0<span class=\"math-tex\">{tex}A \\cap\\left(A^{\\prime} \\cup B^{\\prime}\\right){\/tex}<\/span>\u00a0(By Demorgan&#8217;s law)<br \/>\n=\u00a0<span class=\"math-tex\">{tex}\\left(A \\cap A^{\\prime}\\right) \\cup\\left(A \\cap B^{\\prime}\\right){\/tex}<\/span>\u00a0(By distributive law)<br \/>\n=\u00a0<span class=\"math-tex\">{tex}\\phi \\cup A \\cap B^{\\prime}\\left(\\therefore A \\cap A^{\\prime}=\\phi\\right){\/tex}<\/span><br \/>\n= A\u00a0<span class=\"math-tex\">{tex}\\cap{\/tex}<\/span>\u00a0B&#8217;<br \/>\n= A &#8211; B<br \/>\n= R.H.S. Hence proved<\/li>\n<\/ol>\n<\/li>\n<li style=\"display: block; text-align: left;\"><b>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Section D <\/b>\n<ol style=\"list-style-type: lower-roman;\" start=\"1\">\n<li>Number of ways for units place (1, 3, 5) = 3.<br \/>\nTen\u2019s place = 5 (one is occupied in units place),<br \/>\nHundred\u2019s place = 4 ways<br \/>\nRequired number of ways = 3 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span>\u00a05 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span>\u00a04 = 60.<\/li>\n<li>Number of ways for units place = (1, 3, 5) = 3<br \/>\nTen\u2019s place = 6, Hundred\u2019s place = 6<br \/>\nRequired number of numbers = 3\u00a0<span class=\"math-tex\">{tex}\\times{\/tex}<\/span>\u00a06 <span class=\"math-tex\">{tex}\\times{\/tex}<\/span>\u00a06 = 108<\/li>\n<\/ol>\n<\/li>\n<li style=\"clear: both;\">\n<p style=\"text-align: center;\"><b>OR <\/b><\/p>\n<p>Number of ways of choosing 3 consonants and 2 vowels = <sup>7<\/sup>C<sub>3<\/sub> <span class=\"math-tex\">{tex}\\cdot{\/tex}<\/span><sup>4<\/sup>C<sub>2<\/sub><br \/>\nNumber of ways of arranging 5 letters = 5!.<br \/>\nRequired number of words = <sup>7<\/sup>C<sub>3<\/sub> . <sup>4<\/sup>C<sub>2<\/sub> . 5! = 25200<\/li>\n<li><span class=\"math-tex\">{tex}\\mathop {Lim}\\limits_{x \\to 0} \\frac{{{e^{{x^2}}} &#8211; \\cos x}}{{{x^2}}}{\/tex}<\/span> <span class=\"math-tex\">{tex}= \\mathop {Lim}\\limits_{x \\to 0} \\frac{{{e^{{x^2}}} &#8211; 1 &#8211; \\cos x + 1}}{{{x^2}}}{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex}= \\mathop {Lim}\\limits_{x \\to 0} \\frac{{{e^{{x^2}}} &#8211; 1}}{{{x^2}}} + \\frac{{1 &#8211; \\cos x}}{{{x^2}}}{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex}= \\mathop {Lim}\\limits_{{x^2} \\to 0} \\left[ {\\frac{{{e^{{x^2}}} &#8211; 1}}{{{x^2}}}} \\right] + \\mathop {Lim}\\limits_{x \\to 0} \\left[ {\\frac{{2{{\\sin }^2}x\/2}}{{\\frac{{{x^2}}}{4} \\times 4}}} \\right]{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex} = 1 + \\frac{1}{2}\\mathop {Lim}\\limits_{\\frac{x}{2} \\to 0} {\\left[ {\\frac{{\\sin \\frac{x}{2}}}{{\\frac{x}{2}}}} \\right]^2}{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex} = 1 + \\frac{1}{2}(1) = \\frac{3}{2}{\/tex}<\/span><\/li>\n<li style=\"clear: both;\">\n<p style=\"text-align: left;\">Calculation of rank correlation<\/p>\n<table style=\"width: 100%;\" border=\"1\" cellspacing=\"0\" cellpadding=\"3\">\n<tbody>\n<tr>\n<td width=\"200\">Ranks by X x<sub>i<\/sub><\/td>\n<td width=\"200\">Ranks by Y y<sub>i<\/sub><\/td>\n<td width=\"200\">Range of Z z<sub>i<\/sub><\/td>\n<td width=\"200\">d<sub>i<\/sub>\u00a0= x<sub>i<\/sub>\u00a0&#8211; y<sub>i<\/sub><\/td>\n<td width=\"200\">d<sub>i<\/sub>&#8216; = y<sub>i<\/sub>\u00a0&#8211; z<sub>i<\/sub><\/td>\n<td width=\"200\">d<sub>i<\/sub>&#8221; = x<sub>i<\/sub>\u00a0&#8211; z<sub>i<\/sub><\/td>\n<td width=\"200\"><span class=\"math-tex\">{tex}d_i^2{\/tex}<\/span><\/td>\n<td width=\"200\"><span class=\"math-tex\">{tex}d_i&#8217;^2{\/tex}<\/span><\/td>\n<td width=\"200\"><span class=\"math-tex\">{tex}d_i&#8221;^2{\/tex}<\/span><\/td>\n<\/tr>\n<tr>\n<td width=\"200\">1<\/td>\n<td width=\"200\">3<\/td>\n<td width=\"200\">6<\/td>\n<td width=\"200\">-2<\/td>\n<td width=\"200\">-3<\/td>\n<td width=\"200\">-5<\/td>\n<td width=\"200\">4<\/td>\n<td width=\"200\">9<\/td>\n<td width=\"200\">25<\/td>\n<\/tr>\n<tr>\n<td width=\"200\">6<\/td>\n<td width=\"200\">5<\/td>\n<td width=\"200\">4<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">2<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">4<\/td>\n<\/tr>\n<tr>\n<td width=\"200\">5<\/td>\n<td width=\"200\">8<\/td>\n<td width=\"200\">9<\/td>\n<td width=\"200\">-3<\/td>\n<td width=\"200\">-1<\/td>\n<td width=\"200\">-4<\/td>\n<td width=\"200\">9<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">16<\/td>\n<\/tr>\n<tr>\n<td width=\"200\">10<\/td>\n<td width=\"200\">4<\/td>\n<td width=\"200\">8<\/td>\n<td width=\"200\">6<\/td>\n<td width=\"200\">-4<\/td>\n<td width=\"200\">2<\/td>\n<td width=\"200\">36<\/td>\n<td width=\"200\">16<\/td>\n<td width=\"200\">4<\/td>\n<\/tr>\n<tr>\n<td width=\"200\">3<\/td>\n<td width=\"200\">7<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">-4<\/td>\n<td width=\"200\">6<\/td>\n<td width=\"200\">2<\/td>\n<td width=\"200\">16<\/td>\n<td width=\"200\">36<\/td>\n<td width=\"200\">4<\/td>\n<\/tr>\n<tr>\n<td width=\"200\">2<\/td>\n<td width=\"200\">10<\/td>\n<td width=\"200\">2<\/td>\n<td width=\"200\">-8<\/td>\n<td width=\"200\">8<\/td>\n<td width=\"200\">0<\/td>\n<td width=\"200\">64<\/td>\n<td width=\"200\">64<\/td>\n<td width=\"200\">0<\/td>\n<\/tr>\n<tr>\n<td width=\"200\">4<\/td>\n<td width=\"200\">2<\/td>\n<td width=\"200\">3<\/td>\n<td width=\"200\">2<\/td>\n<td width=\"200\">-1<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">4<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">1<\/td>\n<\/tr>\n<tr>\n<td width=\"200\">9<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">10<\/td>\n<td width=\"200\">8<\/td>\n<td width=\"200\">-9<\/td>\n<td width=\"200\">-1<\/td>\n<td width=\"200\">64<\/td>\n<td width=\"200\">81<\/td>\n<td width=\"200\">1<\/td>\n<\/tr>\n<tr>\n<td width=\"200\">7<\/td>\n<td width=\"200\">6<\/td>\n<td width=\"200\">5<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">2<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">4<\/td>\n<\/tr>\n<tr>\n<td width=\"200\">8<\/td>\n<td width=\"200\">9<\/td>\n<td width=\"200\">7<\/td>\n<td width=\"200\">-1<\/td>\n<td width=\"200\">2<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">1<\/td>\n<td width=\"200\">4<\/td>\n<td width=\"200\">1<\/td>\n<\/tr>\n<tr>\n<td width=\"200\">Total<\/td>\n<td width=\"200\"><\/td>\n<td width=\"200\"><\/td>\n<td width=\"200\"><\/td>\n<td width=\"200\"><\/td>\n<td width=\"200\"><\/td>\n<td width=\"200\"><span class=\"math-tex\">{tex}\\Sigma d_i^2{\/tex}<\/span>\u00a0= 200<\/td>\n<td width=\"200\"><span class=\"math-tex\">{tex}\\Sigma d_i&#8217;^2{\/tex}<\/span>\u00a0= 214<\/td>\n<td width=\"200\"><span class=\"math-tex\">{tex}\\Sigma d_i&#8221;^2{\/tex}<\/span>\u00a0= 60<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Thus, we have n = 10,\u00a0<span class=\"math-tex\">{tex}\\Sigma d_i^2{\/tex}<\/span>\u00a0= 200,\u00a0<span class=\"math-tex\">{tex}\\Sigma d_i&#8217;^2{\/tex}<\/span>\u00a0= 214 and,\u00a0<span class=\"math-tex\">{tex}\\Sigma d_i&#8221;^2{\/tex}<\/span>\u00a0= 60<br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0r(X, Y) = 1 &#8211;\u00a0<span class=\"math-tex\">{tex}\\frac{6 \\Sigma d_{i}^{2}}{n\\left(n^{2}-1\\right)}{\/tex}<\/span>\u00a0= 1 &#8211;\u00a0<span class=\"math-tex\">{tex}\\frac{6 \\times 200}{10(100-1)}{\/tex}<\/span>\u00a0= 1 &#8211;\u00a0<span class=\"math-tex\">{tex}\\frac{40}{33}=\\frac{-7}{33}=\\frac{-35}{165}{\/tex}<\/span><br \/>\nr(Y, Z) = 1 &#8211;\u00a0<span class=\"math-tex\">{tex}\\frac{6 \\Sigma d_{i}&#8217;^{2}}{n\\left(n^{2}-1\\right)}{\/tex}<\/span>\u00a0= 1 &#8211;\u00a0<span class=\"math-tex\">{tex}\\frac{6 \\times 214}{10(100-1)} = \\frac {-49}{165}{\/tex}<\/span><br \/>\nand, r(X, Z) = 1 &#8211;\u00a0<span class=\"math-tex\">{tex}\\frac{6 \\Sigma d_{i}&#8221;^{2}}{n\\left(n^{2}-1\\right)}{\/tex}<\/span>\u00a0= 1 &#8211;\u00a0<span class=\"math-tex\">{tex}\\frac{6 \\times 60}{10(100-1)}{\/tex}<\/span>\u00a0= 1 &#8211;\u00a0<span class=\"math-tex\">{tex}\\frac{4}{11}=\\frac{7}{11}=\\frac{105}{165}{\/tex}<\/span><br \/>\nSince r (X, Z) is maximum. Therefore, the pair of judges X and Z has the nearest approach to common likings in music.<\/p>\n<p style=\"text-align: center;\"><b>OR <\/b><\/p>\n<p style=\"text-align: left;\">For the\u00a0Calculation of Standard Deviation we prepare the following table.<\/p>\n<table style=\"width: 100%;\" border=\"1\" cellspacing=\"0\" cellpadding=\"3\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Class-interval<\/td>\n<td style=\"text-align: center;\">Frequency (f<sub>i<\/sub>)<\/td>\n<td style=\"text-align: center;\">Mid-values (x<sub>i<\/sub>)<\/td>\n<td style=\"text-align: center;\">u<sub>i<\/sub>\u00a0=\u00a0<span class=\"math-tex\">{tex}\\frac{x_{i}-55}{10}{\/tex}<\/span><\/td>\n<td style=\"text-align: center;\">f<sub>i<\/sub>\u00a0u<sub>i<\/sub><\/td>\n<td style=\"text-align: center;\"><span class=\"math-tex\">{tex}u_{i}^{2}{\/tex}<\/span><\/td>\n<td style=\"text-align: center;\">f<sub>i<\/sub>\u00a0<span class=\"math-tex\">{tex}u_{i}^{2}{\/tex}<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">20-30<\/td>\n<td style=\"text-align: center;\">3<\/td>\n<td style=\"text-align: center;\">25<\/td>\n<td style=\"text-align: center;\">-3<\/td>\n<td style=\"text-align: center;\">-9<\/td>\n<td style=\"text-align: center;\">9<\/td>\n<td style=\"text-align: center;\">27<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">30-40<\/td>\n<td style=\"text-align: center;\">6<\/td>\n<td style=\"text-align: center;\">35<\/td>\n<td style=\"text-align: center;\">-2<\/td>\n<td style=\"text-align: center;\">-12<\/td>\n<td style=\"text-align: center;\">4<\/td>\n<td style=\"text-align: center;\">24<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">40-50<\/td>\n<td style=\"text-align: center;\">13<\/td>\n<td style=\"text-align: center;\">45<\/td>\n<td style=\"text-align: center;\">-1<\/td>\n<td style=\"text-align: center;\">-13<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">13<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">50-60<\/td>\n<td style=\"text-align: center;\">15<\/td>\n<td style=\"text-align: center;\">55<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<td style=\"text-align: center;\">0<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">60-70<\/td>\n<td style=\"text-align: center;\">14<\/td>\n<td style=\"text-align: center;\">65<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">14<\/td>\n<td style=\"text-align: center;\">1<\/td>\n<td style=\"text-align: center;\">14<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">70-80<\/td>\n<td style=\"text-align: center;\">5<\/td>\n<td style=\"text-align: center;\">75<\/td>\n<td style=\"text-align: center;\">2<\/td>\n<td style=\"text-align: center;\">10<\/td>\n<td style=\"text-align: center;\">4<\/td>\n<td style=\"text-align: center;\">20<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">80-90<\/td>\n<td style=\"text-align: center;\">4<\/td>\n<td style=\"text-align: center;\">85<\/td>\n<td style=\"text-align: center;\">3<\/td>\n<td style=\"text-align: center;\">12<\/td>\n<td style=\"text-align: center;\">9<\/td>\n<td style=\"text-align: center;\">36<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\">N =\u00a0<span class=\"math-tex\">{tex}\\sum{\/tex}<\/span>\u00a0f<sub>i<\/sub>\u00a0= 60<\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><span class=\"math-tex\">{tex}\\sum{\/tex}<\/span>\u00a0f<sub>i<\/sub>\u00a0u<sub>i<\/sub>\u00a0= 2<\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><span class=\"math-tex\">{tex}\\Sigma f_{i} u_{i}^{2}{\/tex}<\/span>\u00a0= 134<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Here, N = 60,\u00a0<span class=\"math-tex\">{tex}\\sum{\/tex}<\/span>\u00a0f<sub>i<\/sub>\u00a0u<sub>i<\/sub>\u00a0= 2,\u00a0<span class=\"math-tex\">{tex}\\Sigma f_{i} u_{i}^{2}{\/tex}<\/span>\u00a0= 134 and h = 10<br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0Mean =\u00a0<span class=\"math-tex\">{tex}\\bar{X}{\/tex}<\/span>\u00a0= A + h\u00a0<span class=\"math-tex\">{tex}\\left(\\frac{1}{N} \\Sigma f_{i} u_{i}\\right){\/tex}<\/span>\u00a0= 55 + 10\u00a0<span class=\"math-tex\">{tex}\\left(\\frac{2}{60}\\right){\/tex}<\/span>\u00a0= 55.333<br \/>\nand, Var(X) = h<sup>2<\/sup>\u00a0<span class=\"math-tex\">{tex}\\left\\{\\left(\\frac{1}{N} \\Sigma f_{i} u_{i}^{2}\\right)-\\left(\\frac{1}{N} \\Sigma f_{i} u_{i}\\right)^{2}\\right\\}{\/tex}<\/span>\u00a0= 100\u00a0<span class=\"math-tex\">{tex}\\left[\\frac{134}{60}-\\left(\\frac{2}{60}\\right)^{2}\\right]{\/tex}<\/span>\u00a0= 222.9<br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0S.D. =\u00a0<span class=\"math-tex\">{tex}\\sqrt{\\operatorname{Var}(X)}=\\sqrt{222.9}{\/tex}<\/span> = 14.94<\/p>\n<ol style=\"list-style-type: lower-roman;\" start=\"1\">\n<li>Income tax according to old rate:<br \/>\n<table style=\"width: 100%;\" border=\"1\" cellspacing=\"0\" cellpadding=\"3\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><strong>Income<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Amount (\u20b9)<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Income from salary<\/td>\n<td style=\"text-align: right;\">10,00,000<\/td>\n<\/tr>\n<tr>\n<td>Form other sources<\/td>\n<td style=\"text-align: right;\"><u>3,00,000<\/u><\/td>\n<\/tr>\n<tr>\n<td>Gross income<\/td>\n<td style=\"text-align: right;\">13,00,000<\/td>\n<\/tr>\n<tr>\n<td>Standard deduction<\/td>\n<td style=\"text-align: right;\"><u>50,000<\/u><\/td>\n<\/tr>\n<tr>\n<td>Taxable income<\/td>\n<td style=\"text-align: right;\">12,50,000<\/td>\n<\/tr>\n<tr>\n<td>Savings<\/td>\n<td style=\"text-align: right;\"><u>2,50,000<\/u><\/td>\n<\/tr>\n<tr>\n<td>Net taxable income<\/td>\n<td style=\"text-align: right;\"><u>10,00,000<\/u><\/td>\n<\/tr>\n<tr>\n<td><strong>Income tax:<\/strong><\/td>\n<td style=\"text-align: right;\"><\/td>\n<\/tr>\n<tr>\n<td>2.5 Lakh &#8211; 5 Lakh (5%)<\/td>\n<td style=\"text-align: right;\">12,500<\/td>\n<\/tr>\n<tr>\n<td>5.0 Lakh &#8211; 10 Lakh (20%)<\/td>\n<td style=\"text-align: right;\"><u>1,00,000<\/u><\/td>\n<\/tr>\n<tr>\n<td>Tax Payable<\/td>\n<td style=\"text-align: right;\">1,12,500<\/td>\n<\/tr>\n<tr>\n<td>Education cess: (4%)<\/td>\n<td style=\"text-align: right;\"><u>4,500<\/u><\/td>\n<\/tr>\n<tr>\n<td>Total payable tax<\/td>\n<td style=\"text-align: right;\">1,17,000<\/td>\n<\/tr>\n<tr>\n<td>Advance tax paid<\/td>\n<td style=\"text-align: right;\"><u>60,000<\/u><\/td>\n<\/tr>\n<tr>\n<td>Net tax Payable<\/td>\n<td style=\"text-align: right;\">57,000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Income tax according to new rate:<br \/>\n<table style=\"width: 100%;\" border=\"1\" cellspacing=\"0\" cellpadding=\"3\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><strong>Income<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Amount (\u20b9)<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Income from salary<\/td>\n<td style=\"text-align: right;\">10,00,000<\/td>\n<\/tr>\n<tr>\n<td>Form other sources<\/td>\n<td style=\"text-align: right;\"><u>3,00,000<\/u><\/td>\n<\/tr>\n<tr>\n<td>Gross income<\/td>\n<td style=\"text-align: right;\">13,00,000<\/td>\n<\/tr>\n<tr>\n<td>Net taxable income<\/td>\n<td style=\"text-align: right;\"><u>13,00,000<\/u><\/td>\n<\/tr>\n<tr>\n<td><strong>Income tax:<\/strong><\/td>\n<td style=\"text-align: right;\"><\/td>\n<\/tr>\n<tr>\n<td>2.5 Lakh &#8211; 5 Lakh (5%)<\/td>\n<td style=\"text-align: right;\">12,500<\/td>\n<\/tr>\n<tr>\n<td>5.0 Lakh &#8211; 7.5 Lakh (10%)<\/td>\n<td style=\"text-align: right;\">25,000<\/td>\n<\/tr>\n<tr>\n<td>7.5 Lakh &#8211; 10.0 Lakh (15%)<\/td>\n<td style=\"text-align: right;\">37,500<\/td>\n<\/tr>\n<tr>\n<td>10.0 Lakh &#8211; 12.5 Lakh (20%)<\/td>\n<td style=\"text-align: right;\">50,000<\/td>\n<\/tr>\n<tr>\n<td>12.5 Lakh &#8211; 13.0 Lakh (25%)<\/td>\n<td style=\"text-align: right;\"><u>12,500<\/u><\/td>\n<\/tr>\n<tr>\n<td>Tax Payable<\/td>\n<td style=\"text-align: right;\">1,37,500<\/td>\n<\/tr>\n<tr>\n<td>Education Cess: (4%)<\/td>\n<td style=\"text-align: right;\"><u>5,500<\/u><\/td>\n<\/tr>\n<tr>\n<td>Total tax payable<\/td>\n<td style=\"text-align: right;\">1,43,000<\/td>\n<\/tr>\n<tr>\n<td>Advance tax paid<\/td>\n<td style=\"text-align: right;\"><u>60,000<\/u><\/td>\n<\/tr>\n<tr>\n<td>Net tax payable<\/td>\n<td style=\"text-align: right;\">83,000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<\/ol>\n<\/li>\n<li style=\"display: block; text-align: left;\"><b>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Section E<\/b>\n<ol style=\"list-style-type: lower-roman;\" start=\"1\">\n<li>Slope of BC = <span class=\"math-tex\">{tex}\\frac{-1-2}{4-3}{\/tex}<\/span> = -3<br \/>\nEquation of BC is y &#8211; 2 = -3(x &#8211; 3)<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span> y &#8211; 2 = -3x + 9<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span> 3x + y &#8211; 11 = 0<\/li>\n<li>A(1, 2), C(4, -1)<br \/>\nSlope of AC = <span class=\"math-tex\">{tex}\\frac{-1-2}{4-1}{\/tex}<\/span> = -1<br \/>\nEquation of AC is y &#8211; 2 = -1(x &#8211; 1)<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span> y &#8211; 2 = -x + 1<br \/>\n<span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span> x + y -3 = 0<\/li>\n<li>A(1, 2), B(3, 2)<br \/>\nSlope of AB = <span class=\"math-tex\">{tex}\\frac{2-2}{3-1}{\/tex}<\/span> = 0<br \/>\nEquation of AB is y &#8211; 2 = 0(x &#8211; 1) <span class=\"math-tex\">{tex}\\Rightarrow{\/tex}<\/span> y = 2<br \/>\n<strong>OR<\/strong><br \/>\nCentroid of triangle = <span class=\"math-tex\">{tex}\\left(\\frac{1+3+4}{3}, \\frac{2+2-1}{3}\\right){\/tex}<\/span> = <span class=\"math-tex\">{tex}\\left(\\frac{8}{3}, 1\\right){\/tex}<\/span><\/li>\n<\/ol>\n<ol style=\"list-style-type: lower-roman;\" start=\"1\">\n<li>coefficient of variation of wages, of firm A = 0.19<br \/>\ncoefficient of variation of wages, of firm B =\u00a0<span class=\"math-tex\">{tex}\\frac{121}{5253} \\times 100{\/tex}<\/span>\u00a0= 0.21<br \/>\n<span class=\"math-tex\">{tex}\\therefore{\/tex}<\/span>\u00a0Firm B shows greater variability in individual wages.<\/li>\n<li>Standard deviation,\u00a0<span class=\"math-tex\">{tex}\\sigma=\\sqrt{\\sigma^{2}}=\\sqrt{121}{\/tex}<\/span> = 11<\/li>\n<li>Variance of distribution of wages,\u00a0<span class=\"math-tex\">{tex}\\sigma^2{\/tex}<\/span>\u00a0= 100<br \/>\nStandard deviation,\u00a0<span class=\"math-tex\">{tex}\\sigma=\\sqrt{\\sigma^{2}}{\/tex}<\/span>\u00a0=\u00a0<span class=\"math-tex\">{tex}\\sqrt{100}{\/tex}<\/span>\u00a0= 10<br \/>\ncoefficient of Variation =\u00a0<span class=\"math-tex\">{tex}\\frac{\\sigma}{\\bar{x}} \\times 100{\/tex}<\/span><br \/>\n=\u00a0<span class=\"math-tex\">{tex}\\frac{10}{5,253} \\times 100{\/tex}<\/span><br \/>\n= 0.19<br \/>\n<strong>OR<\/strong><br \/>\nNo. of wage earners = 586<br \/>\nMean of monthly wages,\u00a0<span class=\"math-tex\">{tex}\\bar x{\/tex}<\/span>\u00a0=\u00a0\u20b95253<br \/>\nAmount paid by firm A =\u00a0\u20b9(586\u00a0<span class=\"math-tex\">{tex}\\times{\/tex}<\/span> 5253) =\u00a0\u20b93078258<\/li>\n<li>Given n = 100, p = 6% = <span class=\"math-tex\">{tex}\\frac{6}{100} \\Rightarrow \\lambda{\/tex}<\/span> = np = 6<br \/>\nP(X = 0) <span class=\"math-tex\">{tex}=e^{-\\lambda}=e^{-6}{\/tex}<\/span><\/li>\n<li>P(X <span class=\"math-tex\">{tex}\\leq{\/tex}<\/span> 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)<br \/>\n<span class=\"math-tex\">{tex}=e^{-\\lambda}+\\frac{\\lambda e^{-\\lambda}}{1}+\\frac{\\lambda^2 e^{-\\lambda}}{2}+\\frac{\\lambda^3 e^{-\\lambda}}{6}+\\frac{\\lambda^4 e^{-\\lambda}}{24}{\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex}=e^{-\\lambda}\\left(1+\\lambda+\\frac{\\lambda^2}{2}+\\frac{\\lambda^3}{6}+\\frac{\\lambda^4}{24}\\right){\/tex}<\/span><br \/>\n<span class=\"math-tex\">{tex}=e^{-6}\\left(1+6+\\frac{36}{2}+\\frac{216}{6}+\\frac{1296}{24}\\right)=115 e^{-6}{\/tex}<\/span><\/li>\n<li>P(X <span class=\"math-tex\">{tex}\\geq{\/tex}<\/span> 2) = 1 &#8211; {P(X = 0) + P(X = 1)}<br \/>\n= 1 <span class=\"math-tex\">{tex}-\\left(e^{-\\lambda}+\\lambda e^{-\\lambda}\\right)=1-e^{-6}{\/tex}<\/span>\u00a0(1 + 6)<br \/>\n= 1 &#8211; 7e<sup>-6<\/sup><br \/>\n<strong>OR<\/strong><br \/>\n<span class=\"math-tex\">{tex}P ( X =3)=\\frac{6^3 \\cdot e^{-6}}{3!}=36 e^{-6}{\/tex}\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><br \/>\n<strong>Download the myCBSEguide App to Practice More Questions and Excel in Your Exams<\/strong><br \/>\nBoost your exam preparation by downloading the <strong>myCBSEguide app<\/strong> today! Access a wide range of practice questions, sample papers, and study resources for <a href=\"https:\/\/mycbseguide.com\/cbse-sample-papers-class-10.html\"><strong>CBSE Class 10<\/strong><\/a> and <a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-12\/1250\/#google_vignette\"><strong>Class 12<\/strong><\/a> exams. The <strong>CBSE Class 11 Applied Maths sample papers for 2025<\/strong> are created by expert educators to align with the <strong>latest CBSE syllabus<\/strong> and <strong>marking scheme<\/strong> With the <strong>myCBSEguide app<\/strong>, you can practice more questions, follow the latest <strong>CBSE syllabus<\/strong>, and get personalized study material to enhance your learning. Whether it&#8217;s solving model papers or reviewing important topics, the <strong>myCBSEguide app<\/strong> is the ultimate tool to help you prepare thoroughly and score high in your exams.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p><a href=\"https:\/\/mycbseguide.com\/\"><strong>MyCBSEguide<\/strong><\/a> offers model question papers for <strong><a href=\"https:\/\/mycbseguide.com\/cbse-sample-papers-class-11.html\">Class 11<\/a><\/strong> Applied Maths, tailored to match the CBSE syllabus for 2025. These model question papers are perfect for understanding the structure of your exams and how questions are typically framed. Download <strong>CBSE Class 11 Applied Maths sample papers for 2025<\/strong> to enhance your exam preparation. These <strong>sample papers<\/strong> are designed according to the latest <strong>CBSE syllabus<\/strong> and <strong>marking scheme<\/strong>. Practice regularly to improve problem-solving skills, boost confidence, and excel in your upcoming <strong>CBSE exams<\/strong>. Start preparing today! Start practicing with these updated model question papers on <strong><a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide\">myCBSEguide App<\/a><\/strong> today.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Sample_Papers_for_Class_11_2025\"><\/span><strong>CBSE Sample Papers for Class 11 2025<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-physics\/1340\/\"><strong>Physics<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-chemistry\/1356\/\"><strong>Chemistry<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-mathematics\/1371\/\"><strong>Mathematics<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-biology\/1388\/\"><strong>Biology<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-accountancy\/1411\/\"><strong>Accountancy<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-economics\/1423\/\"><strong>Economics<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-business-studies\/1740\/\"><strong>Business Studies<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-computer-science\/1852\/\"><strong>Computer Science<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-informatics-practices\/1874\/\"><strong>Informatics Practices<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-english-core\/1856\/\"><strong>English Core<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-%E0%A4%B9%E0%A4%BF%E0%A4%82%E0%A4%A6%E0%A5%80-%E0%A4%95%E0%A5%8B%E0%A4%B0\/1866\/\"><strong>Hindi Core<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-%E0%A4%B9%E0%A4%BF%E0%A4%82%E0%A4%A6%E0%A5%80-%E0%A4%90%E0%A4%9A%E0%A5%8D%E0%A4%9B%E0%A4%BF%E0%A4%95\/1868\/\"><strong>Hindi Elective<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-history\/1870\/\"><strong>History<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-political-science\/1880\/\"><strong>Political Science<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-geography\/1864\/\"><strong>Geography<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-sociology\/1882\/\"><strong>Sociology<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11-physical-education\/1878\/\"><strong>Physical Education<\/strong><\/a><\/li>\n<li><strong><a href=\"https:\/\/mycbseguide.com\/course\/cbse-class-11\/1339\/\">Other Subjects<\/a><\/strong><\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Why_to_choose_myCBSEGuide\"><\/span>Why to choose myCBSEGuide?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li><strong>Comprehensive Resources<\/strong>: This site offers NCERT solutions, sample papers, chapter notes, and mock tests to cover all CBSE subjects thoroughly.<\/li>\n<li><strong>Interactive &amp; Convenient Learning<\/strong>: This site features interactive quizzes, video lessons, and a mobile app for studying anytime, anywhere.<\/li>\n<li><strong>Affordable &amp; Effective<\/strong>: This provides free and premium plans with real-time updates, expert guidance, and proven success in helping students improve their exam performance.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>CBSE Class 11 Applied Maths Sample Papers 2025 Download free CBSE Class 11 Applied Maths sample papers for 2025 on the myCBSEguide app! These model question papers are based on the latest CBSE marking scheme and blueprint of Applied Maths for the academic session 2024-25, ensuring they follow the most up-to-date exam pattern. Download the &#8230; <a title=\"CBSE Class 11 Applied Maths Sample Papers 2025\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/cbse-class-11-applied-maths-sample-papers\/\" aria-label=\"More on CBSE Class 11 Applied Maths Sample Papers 2025\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1940,2045,1339,47,1999],"tags":[163,12,1959,1967],"class_list":["post-30317","post","type-post","status-publish","format-standard","hentry","category-applied-maths-cbse-class-11","category-applied-maths-sample-papers","category-cbse-sample-papers","category-cbse-class-11","category-class-11-sample-papers","tag-cbse-class-11","tag-cbse-sample-papers","tag-cbse-sample-papers-2024","tag-cbse-sample-papers-2025"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ 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