{"id":60195,"date":"2022-01-29T17:19:58","date_gmt":"2022-01-29T11:49:58","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=60195"},"modified":"2024-02-14T12:31:58","modified_gmt":"2024-02-14T07:01:58","slug":"study-materials-ncert-exemplar-solutions-class-11-maths-chapter-4-principle-of-mathematical-induction","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-4-principle-of-mathematical-induction\/","title":{"rendered":"NCERT Exemplar Solutions for Class 11 Maths Chapter 4 &#8211; Principle of Mathematical Induction"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 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\">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\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><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><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-4-principle-of-mathematical-induction\/#Download_the_PDF_of_NCERT_Exemplar_Solutions_for_Class_11_Maths_Chapter_4_-_Principle_of_Mathematical_Induction\" title=\"Download the PDF of NCERT Exemplar Solutions for Class 11 Maths Chapter 4 \u2013 Principle of Mathematical Induction\">Download the PDF of NCERT Exemplar Solutions for Class 11 Maths Chapter 4 \u2013 Principle of Mathematical Induction<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-4-principle-of-mathematical-induction\/#41_Introduction_NCERT_Exemplar_Solutions_for_Class_11_Maths_Chapter_4\" title=\"4.1 Introduction: NCERT Exemplar Solutions for Class 11 Maths Chapter 4\">4.1 Introduction: NCERT Exemplar Solutions for Class 11 Maths Chapter 4<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-4-principle-of-mathematical-induction\/#42_Motivation\" title=\"4.2 Motivation\">4.2 Motivation<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-4-principle-of-mathematical-induction\/#43_The_Principle_of_Mathematical_Induction\" title=\"4.3 The Principle of Mathematical Induction\">4.3 The Principle of Mathematical Induction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-4-principle-of-mathematical-induction\/#Key_Features_of_NCERT_Exemplar_Solutions_for_Class_11_Maths_Chapter_4-_Principle_of_Mathematical_Induction\" title=\"Key Features of NCERT Exemplar Solutions for Class 11 Maths Chapter 4- Principle of Mathematical Induction\">Key Features of NCERT Exemplar Solutions for Class 11 Maths Chapter 4- Principle of Mathematical Induction<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-4-principle-of-mathematical-induction\/#More_Helpful_Resources_for_Class_11\" title=\"More Helpful Resources for Class 11\">More Helpful Resources for Class 11<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-4-principle-of-mathematical-induction\/#Frequently_Asked_Questions_FAQs\" title=\"Frequently Asked Questions (FAQs)\">Frequently Asked Questions (FAQs)<\/a><ul class='ez-toc-list-level-5'><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5'><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5'><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-4-principle-of-mathematical-induction\/#Explain_the_first_principle_of_Mathematical_Induction_in_Chapter_4_of_NCERT_Exemplar_Solutions_for_Class_11_Maths\" title=\"Explain the first principle of Mathematical Induction in Chapter 4 of NCERT Exemplar Solutions for Class 11 Maths.\">Explain the first principle of Mathematical Induction in Chapter 4 of NCERT Exemplar Solutions for Class 11 Maths.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-4-principle-of-mathematical-induction\/#Why_is_the_NCERT_Exemplar_Solutions_for_Class_11_Maths_Chapter_4_PDF_important_from_the_exam_point_of_view\" title=\"Why is the NCERT Exemplar Solutions for Class 11 Maths Chapter 4 PDF important from the exam point of view?\">Why is the NCERT Exemplar Solutions for Class 11 Maths Chapter 4 PDF important from the exam point of view?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-4-principle-of-mathematical-induction\/#Why_Opt_for_Infinity_Learn\" title=\"Why Opt for Infinity Learn?\">Why Opt for Infinity Learn?<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/\"><strong>NCERT Exemplar Solutions for Class 11<\/strong><\/a> Maths Chapter 4, Principle of Mathematical Induction, is covered in detail through the NCERT Exemplar Solutions offered by Infinity Learn. These solutions are crafted to assist students in excelling in their exams by providing them with a comprehensive understanding of the concepts. Each problem within Chapter 4 is broken down step-by-step in the <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/\"><strong>NCERT Exemplar Solutions<\/strong><\/a>, adhering to the latest CBSE syllabus and exam format.<\/p>\n<p>Our subject experts have meticulously prepared these solutions, incorporating a variety of questions from the textbook exercises. In addition, we provide a wealth of study materials including NCERT notes, sample papers, textbooks, past exam papers, and exemplar questions to enhance exam preparation and boost scores.<\/p>\n<p>In this particular chapter, students will explore and tackle exemplar problems revolving around the Principle of Mathematical Induction, gaining a deep understanding of its applications.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Download_the_PDF_of_NCERT_Exemplar_Solutions_for_Class_11_Maths_Chapter_4_-_Principle_of_Mathematical_Induction\"><\/span>Download the PDF of NCERT Exemplar Solutions for Class 11 Maths Chapter 4 \u2013 Principle of Mathematical Induction<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\t\t<div class=\"download-pdf-container\">\n\t\t\t<span class=\"title\">Do you need help with your Homework? 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href=\"\/surge\/?pdfemb-serveurl=https%3A%2F%2Finfinitylearn.com%2Fsurge%2Fwp-content%2Fuploads%2Fsecurepdfs%2F2022%2F01%2FClass11_Maths_Chapter4DE-4.pdf\" class=\"pdfemb-viewer\" style=\"\" data-width=\"max\" data-height=\"max\" data-mobile-width=\"0\"  data-scrollbar=\"both\" data-download=\"off\" data-tracking=\"on\" data-newwindow=\"on\" data-pagetextbox=\"off\" data-scrolltotop=\"on\" data-startzoom=\"100\" data-startfpzoom=\"100\" data-download-nonce=\"69614777cd\" data-disablerightclick=\"on\" data-toolbar=\"top\" data-toolbar-fixed=\"on\">Class11_Maths_Chapter4(DE-4)<br\/><\/a>\n<p>Now you can find answers to all your subject queries &amp; prepare for your Exams on our <a href=\"https:\/\/play.google.com\/store\/apps\/details?id=com.infinitylearn.learn&amp;referrer=utm_source%3Dsurge%26utm_medium%3Dbutton%26utm_campaign%3Dsurge\"><strong>Infinity Learn- <span style=\"color: #0000ff;\">Learning App<\/span> <\/strong><\/a><\/p>\n<p>This chapter consists of only one exercise and this will help students in learning the concepts based on the Principle of Mathematical Induction through the given solutions. The topic and subtopics that are discussed in Chapter 4 Principle of Mathematical Induction of NCERT Exemplar Solutions for Class 11 is listed below:<\/p>\n<h3><span class=\"ez-toc-section\" id=\"41_Introduction_NCERT_Exemplar_Solutions_for_Class_11_Maths_Chapter_4\"><\/span>4.1 Introduction: NCERT Exemplar Solutions for Class 11 Maths Chapter 4<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>In this section, deductive reasoning with suitable examples and also the assumptions that are based on certain universal facts are explained.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"42_Motivation\"><\/span>4.2 Motivation<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Here, the students learn about mathematical induction with the help of a real-life scenario which helps them to understand its basic working.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"43_The_Principle_of_Mathematical_Induction\"><\/span>4.3 The Principle of Mathematical Induction<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Here, the Principle of Mathematical Induction is explained by using the inductive steps and the inductive hypothesis. Let us suppose the statement is P(n), where n is a natural number.<\/p>\n<ul>\n<li>If n = 1 then the statement is true, it means P(1) is true.<\/li>\n<li>If the statement n = k (where k is some positive integer) is true, then the statement n = k + 1 is also true, which means, the truth of P(k) implies the truth of P (k + 1).<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Key_Features_of_NCERT_Exemplar_Solutions_for_Class_11_Maths_Chapter_4-_Principle_of_Mathematical_Induction\"><\/span>Key Features of NCERT Exemplar Solutions for Class 11 Maths Chapter 4- Principle of Mathematical Induction<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>After learning the Principle of Mathematical Induction of Class 11 students are able to know about the Steps involved in the proof of induction. Students also learn about the applications and principles of mathematical induction from the given solutions of NCERT questions. The concepts explained and used in the solutions of this chapter are as follows:<\/p>\n<ul>\n<li>Deductive reasoning is one of the basic keys to mathematical thinking. Until we have observed each and every case it depends on working with different cases and developing a conjecture by observing incidences. Hence, in simple words \u2018induction\u2019 is the generalization from particular cases or facts.<\/li>\n<li>The principle of mathematical induction is a tool that is used to prove a large number of mathematical statements. Let us suppose each statement is P(n), where n is a positive integer in which n=1 examines that the case is correct. Therefore, if P(k) is true for some positive integer k, then P (k+1) is also true.<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"More_Helpful_Resources_for_Class_11\"><\/span>More Helpful Resources for Class 11<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/\"><strong>NCERT Solutions for Class 11<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/maths\/\"><strong>NCERT Solutions for Class 11 Maths<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/physics\/\"><strong>NCERT Solutions for Class 11 Physics<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/chemistry\/\"><strong>NCERT Solutions for Class 11 Chemistry<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-syllabus\/class-11\/\"><strong>NCERT Syllabus for Class 11<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-books\/class-11\/\"><strong>NCERT Books for Class 11<\/strong><\/a><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Frequently_Asked_Questions_FAQs\"><\/span>Frequently Asked Questions (FAQs)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"Explain_the_first_principle_of_Mathematical_Induction_in_Chapter_4_of_NCERT_Exemplar_Solutions_for_Class_11_Maths\"><\/span>Explain the first principle of Mathematical Induction in Chapter 4 of NCERT Exemplar Solutions for Class 11 Maths.<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe first principle of Mathematical Induction states that both the base step and inductive step are true, for all natural numbers. Many kinds of problems that are based on this concept are available in the NCERT textbook of Class 11. Exercise-wise problems and their solutions are also available which helps students to score well in the annual exam.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"Why_is_the_NCERT_Exemplar_Solutions_for_Class_11_Maths_Chapter_4_PDF_important_from_the_exam_point_of_view\"><\/span>Why is the NCERT Exemplar Solutions for Class 11 Maths Chapter 4 PDF important from the exam point of view?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe NCERT Exemplar Solutions for Class 11 Maths Chapter 4 gives better concepts about the induction and deduction techniques with the help of which equations and statements are proved. With the help of solutions students get clear knowledge about the principle and applications of Mathematical Induction. These solutions will increase the confidence level among students who are preparing for the Class 11 exams.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"Why_Opt_for_Infinity_Learn\"><\/span>Why Opt for Infinity Learn?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tIn this chapter Infinity Learn provides videos, notes, NCERT textbook solutions, other practice book solutions and assignments that help you learn the concepts and to memorise the concepts for entrance exams and board exams. Most important, Infinity learn provide instant doubt support by subject experts.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Explain the first principle of Mathematical Induction in Chapter 4 of NCERT Exemplar Solutions for Class 11 Maths.\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The first principle of Mathematical Induction states that both the base step and inductive step are true, for all natural numbers. Many kinds of problems that are based on this concept are available in the NCERT textbook of Class 11. Exercise-wise problems and their solutions are also available which helps students to score well in the annual exam.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Why is the NCERT Exemplar Solutions for Class 11 Maths Chapter 4 PDF important from the exam point of view?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The NCERT Exemplar Solutions for Class 11 Maths Chapter 4 gives better concepts about the induction and deduction techniques with the help of which equations and statements are proved. With the help of solutions students get clear knowledge about the principle and applications of Mathematical Induction. These solutions will increase the confidence level among students who are preparing for the Class 11 exams.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Why Opt for Infinity Learn?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"In this chapter Infinity Learn provides videos, notes, NCERT textbook solutions, other practice book solutions and assignments that help you learn the concepts and to memorise the concepts for entrance exams and board exams. Most important, Infinity learn provide instant doubt support by subject experts.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>NCERT Exemplar Solutions for Class 11 Maths Chapter 4, Principle of Mathematical Induction, is covered in detail through the NCERT [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"NCERT Exemplar Solutions for Class 11 Maths Chapter 4","_yoast_wpseo_title":"NCERT Exemplar Solutions for Class 11 Maths Chapter 4","_yoast_wpseo_metadesc":"The NCERT Exemplar Solutions for Class 11 Maths Chapter 4 helps students learn about applications and principles of mathematical 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