{"id":60217,"date":"2022-01-29T17:34:44","date_gmt":"2022-01-29T12:04:44","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=60217"},"modified":"2022-06-16T10:22:41","modified_gmt":"2022-06-16T04:52:41","slug":"study-materials-ncert-exemplar-solutions-class-11-maths-chapter-8-binomial-theorem","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-8-binomial-theorem\/","title":{"rendered":"NCERT Exemplar Solutions for Class 11 Maths Chapter 8 &#8211; Binomial Theorem"},"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-8-binomial-theorem\/#NCERT_Exemplar_Solutions_for_Class_11_Maths_Chapter_8-_Binomial_Theorem\" title=\"NCERT Exemplar Solutions for Class 11 Maths Chapter 8- Binomial Theorem\">NCERT Exemplar Solutions for Class 11 Maths Chapter 8- Binomial Theorem<\/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-8-binomial-theorem\/#Frequently_Asked_Questions\" title=\"Frequently Asked Questions\">Frequently Asked Questions<\/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'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-8-binomial-theorem\/#Explain_the_concept_of_the_Binomial_Theorem_covered_in_Chapter_8_of_NCERT_Exemplar_Solutions_for_Class_11_Maths\" title=\"Explain the concept of the Binomial Theorem covered in Chapter 8 of NCERT Exemplar Solutions for Class 11 Maths.\">Explain the concept of the Binomial Theorem covered in Chapter 8 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-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-8-binomial-theorem\/#Will_the_NCERT_Exemplar_Solutions_for_Class_11_Maths_Chapter_8_help_students_to_understand_the_concepts_which_are_important_from_the_exam_perspective\" title=\"Will the NCERT Exemplar Solutions for Class 11 Maths Chapter 8 help students to understand the concepts which are important from the exam perspective?\">Will the NCERT Exemplar Solutions for Class 11 Maths Chapter 8 help students to understand the concepts which are important from the exam perspective?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-8-binomial-theorem\/#In_the_Binomial_Theorem_explain_the_properties_of_positive_integers_covered_in_the_NCERT_Exemplar_Solutions_for_Class_11_Maths_Chapter_8\" title=\"In the Binomial Theorem, explain the properties of positive integers covered in the NCERT Exemplar Solutions for Class 11 Maths Chapter 8?\">In the Binomial Theorem, explain the properties of positive integers covered in the NCERT Exemplar Solutions for Class 11 Maths Chapter 8?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-8-binomial-theorem\/#Why_Opt_for_Infinity_Learn\" title=\"Why Opt for Infinity Learn?\">Why Opt for Infinity Learn?<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-8-binomial-theorem\/#Infinity_Learn_App\" title=\"Infinity Learn App\">Infinity Learn App<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><span style=\"font-size: 12pt;\"><span style=\"font-weight: 400;\">Subject specialists have created NCERT Exemplar Solutions for Class 11 Maths Chapter 8- Binomial Theorem, <\/span><span style=\"font-weight: 400;\">which includes thorough solutions for reference. All of the unsolved questions from the textbook&#8217;s exercises are answered here. The NCERT Exemplar Solutions for Class 11 provide useful solutions for improving conceptual knowledge and help in entrance examinations like <strong><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/jee\" target=\"_blank\" rel=\"noopener\">JEE mains and advanced<\/a><\/span><\/strong>.<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Exemplar Solutions for Class 11. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 11 pupils perform well in upcoming competitive exams.<\/span><\/p>\n<p><span style=\"font-size: 12pt;\"><span style=\"font-weight: 400;\">The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.<\/span><span style=\"font-weight: 400;\"> <\/span><\/span><\/p>\n<p><span style=\"font-size: 12pt;\">\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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underline;\">terms and conditions<\/a> and <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/privacy\" style=\"text-decoration: underline;\">privacy policy<\/a>.<\/p>\n<p><input type=\"button\" style=\"cursor:pointer;width:auto;\" class=\"il_otp_submit\" value=\"Get OTP\" onclick=\"sendCF7OTP(this, otp_phone.value, user_name.value)\"><\/p>\n<div class=\"form-submit-btn-div\" style=\"display:none;\">\n<input type=\"submit\" value=\"Download PDF\" class=\"wpcf7-form-control has-spinner wpcf7-submit download-pdf-submit\" \/>\n<\/div>\n<\/div>\n<div class=\"wpcf7-response-output\" aria-hidden=\"true\"><\/div><\/form><\/div>\n\t\t\t\t\t<span class=\"pdf-link hidden\" data-pdf=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/securepdfs\/2022\/01\/Class11_Maths_Chapter8DE-8.pdf\"><\/span>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t<div class=\"bg-overlay\"><\/div>\n\t\t<\/div>\n\t\t<a href=\"\/surge\/?pdfemb-serveurl=https%3A%2F%2Finfinitylearn.com%2Fsurge%2Fwp-content%2Fuploads%2Fsecurepdfs%2F2022%2F01%2FClass11_Maths_Chapter8DE-8.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=\"5206d781f2\" data-disablerightclick=\"on\" data-toolbar=\"top\" data-toolbar-fixed=\"on\">Class11_Maths_Chapter8(DE-8)<br\/><\/a><\/span><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">Following are the topics and subtopics explained in the Chapter 8 Binomial Theorem of <strong><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/\" target=\"_blank\" rel=\"noopener\">NCERT Exemplar Solutions<\/a><\/span><\/strong> for Class 11:<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">8.1 Introduction to Binomial Theorem <\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">8.2 Binomial Theorem for Positive Integral Indices <\/span><\/p>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400; font-size: 12pt;\">Pascal\u2019s Triangle<\/span><\/p>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400; font-size: 12pt;\">8.2.1 Binomial theorem for any positive integer n, <\/span><\/p>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400; font-size: 12pt;\">8.2.2 Some special cases<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">8.3 General and Middle Terms <\/span><\/p>\n<p><span style=\"font-size: 12pt;\">The number of questions in the exercises is as follows:<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">Exercise 8.1 Solutions 14 Questions<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">Exercise 8.2 Solutions 12 Questions<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400; font-size: 12pt;\">Miscellaneous Exercise On Chapter 8 Solutions 10 Questions<\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Exemplar_Solutions_for_Class_11_Maths_Chapter_8-_Binomial_Theorem\"><\/span><span style=\"font-size: 12pt; color: #0000ff;\"><b>NCERT Exemplar Solutions for Class 11 Maths Chapter 8- Binomial Theorem<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">The chapter Binomial Theorem is found in the unit Algebra, and it accounts for 30 of the total 80 points. This chapter has three exercises, including a miscellaneous exercise. <\/span><\/p>\n<p><span style=\"font-weight: 400; font-size: 12pt;\">As a result, a student who thoroughly understands the eighth chapter of Class 11, the Binomial Theorem, will be well-versed in the history of the Binomial Theorem, the statement and proof of the Binomial Theorem for positive integral indices, Pascal&#8217;s triangle, the General and Middle Terms in Binomial Expansion, and simple applications of the Binomial Theorem.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Frequently_Asked_Questions\"><\/span><strong><span style=\"font-size: 12pt;\">Frequently Asked Questions<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\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_concept_of_the_Binomial_Theorem_covered_in_Chapter_8_of_NCERT_Exemplar_Solutions_for_Class_11_Maths\"><\/span>Explain the concept of the Binomial Theorem covered in Chapter 8 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 method of algebraically extending the power of sums of two or more binomials is known as the Binomial Theorem. Binomial coefficients are the coefficients of binomial terms that are involved in the expansion process. The definitions of concepts that are relevant for the tests are included in the chapter's introduction. Students can now use the NCERT Exemplar Solutions, which are available in PDF format, to study and keep up to current on the latest CBSE syllabus.\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=\"Will_the_NCERT_Exemplar_Solutions_for_Class_11_Maths_Chapter_8_help_students_to_understand_the_concepts_which_are_important_from_the_exam_perspective\"><\/span>Will the NCERT Exemplar Solutions for Class 11 Maths Chapter 8 help students to understand the concepts which are important from the exam perspective?<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\tBefore tackling the exercise-by-exercise questions, students can refer to the examples in the NCERT textbook to better grasp the expansion technique. Each problem in the solutions is solved in a step-by-step manner to assist students in better grasping the ideas. Students will be well-versed in the approach of solving these problems and will do well on the exam if they use the solutions PDF.\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=\"In_the_Binomial_Theorem_explain_the_properties_of_positive_integers_covered_in_the_NCERT_Exemplar_Solutions_for_Class_11_Maths_Chapter_8\"><\/span>In the Binomial Theorem, explain the properties of positive integers covered in the NCERT Exemplar Solutions for Class 11 Maths Chapter 8?<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\tPositive integers have more than ten qualities, which students can master with the NCERT Exemplar Solutions for Class 11 Maths Chapter 8. These features are critical for grasping the concept of effectively solving equations. The yearly test question paper would focus on chapters that are straightforward for pupils yet difficult to solve. If students want to get good grades, they should go over the NCERT Exemplar Solutions for this purpose.\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 concept of the Binomial Theorem covered in Chapter 8 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 method of algebraically extending the power of sums of two or more binomials is known as the Binomial Theorem. Binomial coefficients are the coefficients of binomial terms that are involved in the expansion process. The definitions of concepts that are relevant for the tests are included in the chapter's introduction. Students can now use the NCERT Exemplar Solutions, which are available in PDF format, to study and keep up to current on the latest CBSE syllabus.\"\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\": \"Will the NCERT Exemplar Solutions for Class 11 Maths Chapter 8 help students to understand the concepts which are important from the exam perspective?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Before tackling the exercise-by-exercise questions, students can refer to the examples in the NCERT textbook to better grasp the expansion technique. Each problem in the solutions is solved in a step-by-step manner to assist students in better grasping the ideas. Students will be well-versed in the approach of solving these problems and will do well on the exam if they use the solutions PDF.\"\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\": \"In the Binomial Theorem, explain the properties of positive integers covered in the NCERT Exemplar Solutions for Class 11 Maths Chapter 8?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Positive integers have more than ten qualities, which students can master with the NCERT Exemplar Solutions for Class 11 Maths Chapter 8. These features are critical for grasping the concept of effectively solving equations. The yearly test question paper would focus on chapters that are straightforward for pupils yet difficult to solve. If students want to get good grades, they should go over the NCERT Exemplar Solutions for this purpose.\"\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<h3><span class=\"ez-toc-section\" id=\"Infinity_Learn_App\"><\/span><strong><span style=\"color: #0000ff;\">Infinity Learn App<\/span><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Now you can find answers to all your subject queries &amp; prepare for your Exams on our <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/play.google.com\/store\/apps\/details?id=com.infinitylearn.learn\" target=\"_blank\" rel=\"noopener\">Learning App<\/a><\/span> &#8211; Infinity Learn.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Subject specialists have created NCERT Exemplar Solutions for Class 11 Maths Chapter 8- Binomial Theorem, which includes thorough solutions for [&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 8","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Subject specialists have created NCERT Exemplar Solutions for Class 11 Maths Chapter 8- Binomial Theorem, which includes thorough solutions for reference.","custom_permalink":"study-materials\/ncert-exemplar-solutions\/class-11\/maths\/chapter-8-binomial-theorem\/"},"categories":[107,113,105],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - 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