{"id":9366,"date":"2018-02-09T16:46:14","date_gmt":"2018-02-09T11:16:14","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/?p=9366"},"modified":"2018-03-17T09:56:25","modified_gmt":"2018-03-17T04:26:25","slug":"binomial-theorem-class-11-notes-mathematics","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/binomial-theorem-class-11-notes-mathematics\/","title":{"rendered":"Binomial Theorem class 11 Notes Mathematics"},"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' ><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/binomial-theorem-class-11-notes-mathematics\/#CBSE_Guide_Binomial_Theorem_class_11_Notes\" >CBSE Guide Binomial Theorem class 11 Notes<\/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\/binomial-theorem-class-11-notes-mathematics\/#Binomial_Theorem_class_11_Notes_Mathematics\" >Binomial Theorem class 11 Notes Mathematics<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/binomial-theorem-class-11-notes-mathematics\/#Download_Revision_Notes_as_PDF\" >Download Revision Notes as PDF<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/binomial-theorem-class-11-notes-mathematics\/#The_Binomial_Theorem_class_11_Notes\" >The Binomial Theorem class 11 Notes<\/a><\/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\/binomial-theorem-class-11-notes-mathematics\/#CBSE_Class-11_Revision_Notes_and_Key_Points\" >CBSE Class-11 Revision Notes and Key Points<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>CBSE Mathematics Chapter 8 Binomial Theorem class 11 Notes Mathematics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Binomial Theorem class 11 Notes Mathematics latest chapter wise notes for quick preparation of CBSE exams and school based annual examinations. Class 11 Mathematics notes on Chapter 8 Binomial Theorem class 11 Notes Mathematics are also available for download in CBSE Guide website.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Guide_Binomial_Theorem_class_11_Notes\"><\/span>CBSE Guide Binomial Theorem class 11 Notes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>CBSE guide notes are the comprehensive notes which covers the latest syllabus of CBSE and NCERT. It includes all the topics given in NCERT class 11 Mathematics text book. Users can download CBSE guide quick revision notes from myCBSEguide mobile app and my CBSE guide website.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Binomial_Theorem_class_11_Notes_Mathematics\"><\/span>Binomial Theorem class 11 Notes Mathematics<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Download CBSE class 11th revision notes for Chapter 8 Binomial Theorem class 11 Notes Mathematics in PDF format for free. Download revision notes for Binomial Theorem class 11 Notes Mathematics and score high in exams. These are the Binomial Theorem class 11 Notes Mathematics prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the best tips recommended by teachers during exam days.<\/p>\n<h1 style=\"text-align: center\"><span class=\"ez-toc-section\" id=\"Download_Revision_Notes_as_PDF\"><\/span><a href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-11-chemistry\/1356\/cbse-revision-notes\/7\/\">Download Revision Notes as PDF<\/a><span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p style=\"text-align: center\"><strong>CBSE Class 11 Mathematics<br \/>\nRevision Notes<br \/>\nChapter-8<br \/>\nBinomial Theorem class 11 Notes Mathematics<br \/>\n<\/strong><\/p>\n<p><strong>\u00a0\u00a0 1. \u00a0Binomial Theorem for Positive Integral Indices <\/strong><\/p>\n<p><strong>\u00a0\u00a0 2. \u00a0General and Middle Terms<\/strong><\/p>\n<ul>\n<li><strong>Binomial Theorem<\/strong>: The expansion of a binomial for any positive integral n is given by Binomial Theorem, which is<br \/>\n<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\left( a+b \\right)}^{n}}{{=}^{n}}{{C}_{0}}{{a}^{n}}{{+}^{n}}{{C}_{1}}{{a}^{n-1}}b{{+}^{n}}{{C}_{2}}{{a}^{n-2}}{{b}^{2}}\" \/><\/span><\/span><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?+....+^{n}{{C}_{n-1}}a{{b}^{n-1}}{{+}^{n}}{{C}_{n}}{{b}^{n}}.\" \/><\/span><\/span><\/li>\n<li>The coefficients of the expansions are arranged in an array. This array is called <em>Pascal\u2019s triangle.<\/em><\/li>\n<li>The general term of an expansion <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?~~{{\\left( \\text{a }+~\\text{b} \\right)}^{n}}\\ \\ is\\ {{T}_{r+1}}\\ \\ {{=}^{n}}{{C}_{r}}{{a}^{n-r}}.{{b}^{r}}\" \/><\/span><\/span><\/li>\n<li>The general term of an expansion <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\left( {a - b} \\right)^n} = {\\left( { - 1} \\right)^r}{.^n}{{\\rm{C}}_r}.{a^{n - r}}.{b^r}\" \/><\/span><\/span><\/li>\n<li>The general term of <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\left( {1 + x} \\right)^n}{ = ^n}{{\\rm{C}}_r}.{x^r}\" \/><\/span><\/span><\/li>\n<li>The general term of <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\left( {1 - x} \\right)^n} = {\\left( { - 1} \\right)^r}{.^n}{{\\rm{C}}_r}.{x^r}\" \/><\/span><\/span><\/li>\n<li>In the expansion <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\left( \\text{a }+\\text{ b} \\right)}^{n}}\" \/><\/span><\/span>, if n is even, then the middle term is the\u00a0 <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\left( \\frac{n}{2}+1 \\right)}^{th}}\" \/><\/span><\/span>term. If n is odd, then the middle terms are <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\left( \\frac{n}{2}+1 \\right)}^{th}}\" \/><\/span><\/span>and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\left( \\frac{n+1}{2}+1 \\right)}^{th}}\" \/><\/span><\/span>\u00a0terms.<\/li>\n<li><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{r^{th}}\" \/><\/span><\/span>\u00a0term from the end in <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\left( {a + b} \\right)^n} = {\\left( {n + 2 - r} \\right)^{th}}\" \/><\/span><\/span>\u00a0term fromt he beginning.<\/li>\n<li>Method to prove Binomial Theorem:<\/li>\n<\/ul>\n<p>(a) Principle of Mathematical Induction.<\/p>\n<p>(b) Combinatorial Method.<\/p>\n<ul>\n<li>Factorial notation:<br \/>\n(i) <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?n! = 1 \\times 2 \\times 3 \\times 4....... \\times n;\" \/><\/span><\/span>\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?0! = 1\" \/><\/span><\/span><br \/>\n(ii) <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{^n{{\\rm{C}}_r} = {{n!} \\over {r!\\left( {n - r} \\right)!}}}\" \/><\/span><\/span><br \/>\n(iii) <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?^n{{\\rm{C}}_r}{ = ^n}{{\\rm{C}}_{n - r}}\" \/><\/span><\/span><br \/>\n(iv) <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?^n{{\\rm{C}}_r}{ + ^n}{{\\rm{C}}_{r - 1}}{ = ^{n + 1}}{{\\rm{C}}_r}\" \/><\/span><\/span><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"The_Binomial_Theorem_class_11_Notes\"><\/span>The Binomial Theorem class 11 Notes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>CBSE Revision notes (PDF Download) Free<\/li>\n<li>CBSE Revision notes for Class 11 Mathematics PDF<\/li>\n<li>CBSE Revision notes Class 11 Mathematics \u2013 CBSE<\/li>\n<li>CBSE Revisions notes and Key Points Class 11 Mathematics<\/li>\n<li>Summary of the NCERT books all chapters in Mathematics class 11<\/li>\n<li>Short notes for CBSE class 11th Mathematics<\/li>\n<li>Key notes and chapter summary of Mathematics class 11<\/li>\n<li>Quick revision notes for CBSE exams<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Class-11_Revision_Notes_and_Key_Points\"><\/span><strong>CBSE Class-11 Revision Notes and Key Points<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Binomial Theorem class 11 Notes Mathematics. CBSE quick revision note for class-11 Mathematics, Physics, Chemistry, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.<\/p>\n<ul>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-physics\/1340\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Physics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-chemistry\/1356\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Chemistry<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-mathematics\/1371\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Mathematics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-biology\/1388\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Biology<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-accountancy\/1411\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Accountancy<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-economics\/1423\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Economics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-business-studies\/1740\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Business Studies<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-computer-science\/1852\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Computer Science<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-informatics-practices\/1874\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Informatics Practices<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-geography\/1864\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Geography<\/a><\/li>\n<\/ul>\n<p>To download Binomial Theorem class 11 Notes, sample paper for class 11 Chemistry, Physics, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n<ul>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/sets-class-11-notes-mathematics\/\">Sets class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/relations-functions-class-11-notes-mathematics\/\">Relations And Functions class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/trigonometric-functions-class-11-notes-mathematics\/\">Trigonometric Functions class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/principles-mathematical-induction-class-11-notes-mathematics\/\">Principles Of Mathematical Induction class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/\">Complex Numbers And Quadratic Equations class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/linear-inequalities-class-11-notes-mathematics\/\">Linear Inequalities class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/permutations-combinations-class-11-notes-mathematics\/\">Permutations And Combinations class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/binomial-theorem-class-11-notes-mathematics\/\">Binomial Theorem class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/sequences-and-series-class-11-notes-mathematics\/\">Sequences And Series class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/straight-lines-class-11-notes-mathematics\/\">Straight Lines class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/conic-sections-class-11-notes-mathematics\/\">Conic Sections class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/limits-and-derivatives-class-11-notes-mathematics\/\">Limits And Derivatives class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/mathematical-reasoning-class-11-notes-mathematics\/\">Mathematical Reasoning class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/statistics-class-11-notes-mathematics\/\">Statistics class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/probability-class-11-notes-mathematics\/\">Probability class 11 Notes Mathematics<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>CBSE Mathematics Chapter 8 Binomial Theorem class 11 Notes Mathematics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Binomial Theorem class 11 Notes Mathematics latest chapter wise notes for quick preparation of CBSE exams and school based annual examinations. Class 11 Mathematics notes on &#8230; <a title=\"Binomial Theorem class 11 Notes Mathematics\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/binomial-theorem-class-11-notes-mathematics\/\" aria-label=\"More on Binomial Theorem class 11 Notes Mathematics\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":9298,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,456],"tags":[579,457,150,461,426,240],"class_list":["post-9366","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse-class-11","category-revision-notes","tag-binomial-theorem","tag-cbse-notes","tag-cbse-notes-and-key-points","tag-mathematics-notes","tag-quick-revision","tag-quick-revision-notes"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Binomial Theorem class 11 Notes Mathematics | myCBSEguide<\/title>\n<meta name=\"description\" content=\"Binomial Theorem class 11 Notes Mathematics Chapter 8 in PDF format for free download. 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