{"id":68990,"date":"2021-10-12T11:21:00","date_gmt":"2021-10-12T05:51:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=68990"},"modified":"2021-10-12T18:11:19","modified_gmt":"2021-10-12T12:41:19","slug":"rd-sharma-solutions-class-12-maths-chapter-3-exercise-3-2","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-3-exercise-3-2\/","title":{"rendered":"RD Sharma Solutions For Class 12 Maths Exercise 3.2 Chapter 3 Binary Operations (Updated for 2021-22)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-118190\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-3-Exercise-3.2.png\" alt=\"RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-3-Exercise-3.2.png 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-3-Exercise-3.2-768x432.png 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2:\u00a0<\/strong>The types of binary operations are the focus of this exercise. The question in <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-12-solutions\/\"><strong>RD Sharma Solutions for Class 12<\/strong><\/a> Chapter 3 Exercise 3.2 are based on binary operations&#8217; commutativity and associativity. Students may download the free PDF of <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-3\/\"><strong>RD Sharma Solutions for Class 12 Chapter 3<\/strong><\/a>\u00a0Binary Operations Exercise 3.2 from this article.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 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\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69e77bc0aabcf\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" 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: #000000;color:#000000\" 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-69e77bc0aabcf\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-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:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-3-exercise-3-2\/#download-rd-sharma-solutions-class-12-maths-chapter-3-exercise-32-pdf\" title=\"Download RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2 PDF\">Download RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2 PDF<\/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:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-3-exercise-3-2\/#access-rd-sharma-solutions-for-binary-operations-exercise-32-class-12-maths-chapter-3-important-questions\" title=\"Access RD Sharma Solutions For Binary Operations Exercise 3.2 Class 12 Maths Chapter 3 Important Questions\">Access RD Sharma Solutions For Binary Operations Exercise 3.2 Class 12 Maths Chapter 3 Important Questions<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-3-exercise-3-2\/#faqs-on-rd-sharma-solutions-class-12-maths-chapter-3-exercise-32\" title=\"FAQs on RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2\">FAQs on RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2<\/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:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-3-exercise-3-2\/#how-many-questions-are-there-in-rd-sharma-solutions-class-12-maths-chapter-3-exercise-32\" title=\"How many questions are there in RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2?\">How many questions are there in RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-3-exercise-3-2\/#is-rd-sharma-solutions-for-class-12-maths-chapter-3-exercise-32-for-free\" title=\"Is RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.2 for free?\">Is RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.2 for free?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-3-exercise-3-2\/#where-can-i-download-rd-sharma-solutions-for-chapter-3-exercise-32-class-12-maths-free-pdf\" title=\"Where can I download RD Sharma Solutions for Chapter 3 Exercise 3.2 Class 12 Maths free PDF?\">Where can I download RD Sharma Solutions for Chapter 3 Exercise 3.2 Class 12 Maths free PDF?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-solutions-class-12-maths-chapter-3-exercise-32-pdf\"><\/span>Download RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2 PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 800px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Maths-Chapter-3-Ex-3.2-1.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Maths-Chapter-3-Ex-3.2-1.pdf\">RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2<\/a><\/p>\n<p>Students can use the <strong>RD Sharma Step Solutions<\/strong> as a primary study material to increase their speed and accuracy when solving problems. Our experts&#8217; solutions are interactive, making it simple for students to grasp the topics.\u00a0<\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-rd-sharma-solutions-for-binary-operations-exercise-32-class-12-maths-chapter-3-important-questions\"><\/span>Access RD Sharma Solutions For Binary Operations Exercise 3.2 Class 12 Maths Chapter 3 Important Questions<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>1. Let \u2018*\u2019 be a binary operation on\u00a0N\u00a0defined by a\u00a0*\u00a0b\u00a0= l.c.m. (a,\u00a0b) for all\u00a0a,\u00a0b\u00a0\u2208\u00a0N<br \/>(i) Find 2 * 4, 3 * 5, 1 * 6.<\/strong><\/p>\n<p><strong>(ii) Check the commutativity and associativity of \u2018*\u2019 on N.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118160\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/1.jpg\" alt=\"1\" width=\"394\" height=\"702\" \/><\/p>\n<p><strong>2. Determine which of the following binary operation is associative and which is commutative:<\/strong><\/p>\n<p><strong>(i) * on\u00a0N\u00a0defined by\u00a0a\u00a0*\u00a0b\u00a0= 1 for all\u00a0a,\u00a0b\u00a0\u2208\u00a0N<\/strong><\/p>\n<p><strong>(ii) * on Q defined by a * b = (a + b)\/2 for all a, b \u2208 Q<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118161\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/2.gif\" alt=\"2\" width=\"380\" height=\"278\" \/><\/p>\n<p><strong>3. Let\u00a0A\u00a0be any set containing more than one element. Let \u2018*\u2019 be a binary operation on\u00a0A defined by\u00a0a\u00a0*\u00a0b\u00a0=\u00a0b\u00a0for all\u00a0a,\u00a0b\u00a0\u2208\u00a0A\u00a0Is \u2018*\u2019 commutative or associative on\u00a0A?<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118162\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/3.gif\" alt=\"3\" width=\"396\" height=\"397\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/3.gif 396w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/3-120x120.gif 120w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><\/p>\n<p><strong>4. Check the commutativity and associativity of each of the following binary operations:<\/strong><\/p>\n<p><strong>(i) \u2018*\u2019 on\u00a0Z\u00a0defined by\u00a0a\u00a0*\u00a0b\u00a0=\u00a0a\u00a0+\u00a0b\u00a0+\u00a0a b\u00a0for all\u00a0a,\u00a0b\u00a0\u2208\u00a0Z\u00a0<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118165\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/4.gif\" alt=\"4.1\" width=\"487\" height=\"466\" \/><\/p>\n<p><strong>(ii) \u2018*\u2019 on N defined by a * b = 2<sup>ab<\/sup>\u00a0for all a,\u00a0b\u00a0\u2208 N<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118166\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/4.2.gif\" alt=\"4.2\" width=\"390\" height=\"429\" \/><\/p>\n<p><strong>(iii) \u2018*\u2019 on Q defined by a * b = a \u2013 b for all a, b \u2208 Q<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118167\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/4.3.gif\" alt=\"4.3\" width=\"438\" height=\"420\" \/><\/p>\n<p><strong>(iv) \u2018\u2299\u2019 on Q defined by a \u2299 b = a<sup>2<\/sup>\u00a0+ b<sup>2<\/sup>\u00a0for all a, b \u2208 Q<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118168\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/4.4.gif\" alt=\"4.4\" width=\"588\" height=\"448\" \/><\/p>\n<p><strong>(v) \u2018o\u2019 on Q defined by a o b = (ab\/2) for all a, b \u2208 Q<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118169\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/4.5.gif\" alt=\"4.5\" width=\"461\" height=\"507\" \/><\/p>\n<p><strong>(vi) \u2018*\u2019 on Q defined by a * b = ab<sup>2<\/sup>\u00a0for all a, b \u2208 Q<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118170\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/4.6.gif\" alt=\"4.6\" width=\"390\" height=\"412\" \/><\/p>\n<p><strong>(vii) \u2018*\u2019 on Q defined by a * b = a + a b for all a, b \u2208 Q<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118171\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/4.7-1.jpg\" alt=\"4.7\" width=\"442\" height=\"478\" \/><\/p>\n<p><strong>(viii) \u2018*\u2019 on R defined by a * b = a + b -7 for all a, b \u2208 R<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118172\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/4.8.gif\" alt=\"4.8\" width=\"438\" height=\"445\" \/><\/p>\n<p><strong>(ix) \u2018*\u2019 on Q defined by a * b = (a \u2013 b)<sup>2<\/sup>\u00a0for all a, b \u2208 Q<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118173\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/4.9.gif\" alt=\"4.9\" width=\"438\" height=\"559\" \/><\/p>\n<p><strong>(x) \u2018*\u2019 on Q defined by a * b = a b + 1 for all a, b \u2208 Q<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118174\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/4.10.gif\" alt=\"4.10\" width=\"342\" height=\"427\" \/><\/p>\n<p><strong>(xi) \u2018*\u2019 on N defined by a * b = a<sup>b<\/sup>\u00a0for all a, b \u2208 N<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118175\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/411.jpg\" alt=\"4.11\" width=\"396\" height=\"454\" \/><\/p>\n<p><strong>(xii) \u2018*\u2019 on Z defined by a * b = a \u2013 b for all a, b \u2208 Z<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118177\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/4.12.gif\" alt=\"4.12\" width=\"390\" height=\"376\" \/><\/p>\n<p><strong>(xiii) \u2018*\u2019 on Q defined by a * b = (ab\/4) for all a, b \u2208 Q<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118178\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/4.13.gif\" alt=\"4.13\" width=\"390\" height=\"418\" \/><\/p>\n<p><strong>5. If the binary operation o is defined by a0b = a + b \u2013 ab on the set Q \u2013 {-1} of all rational numbers other than 1, show that o is commutative on Q \u2013 [1].<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118179\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/5.gif\" alt=\"5\" width=\"363\" height=\"237\" \/><\/p>\n<p><strong>6. Show that the binary operation * on Z defined by a * b = 3a + 7b is not commutative?<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118180\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/6.gif\" alt=\"6\" width=\"356\" height=\"201\" \/><\/p>\n<p><strong>7. On the set Z of integers a binary operation * is defined by a 8 b = ab + 1 for all a, b \u2208 Z. Prove that * is not associative on Z.<\/strong><\/p>\n<p><img class=\"alignnone size-full wp-image-118181\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/7.gif\" alt=\"7\" width=\"391\" height=\"326\" \/><\/p>\n<p><strong>Binary Operations Ex 3.2 Q8<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7553\/16213394181_f935284877_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 3 Binary Operations Ex 3.2 Q8\" width=\"473\" height=\"475\" \/><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8628\/16214481172_6012b4a276_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 3 Binary Operations Ex 3.2 Q8-i\" width=\"460\" height=\"344\" \/><br \/><strong>Binary Operations Ex 3.2 Q9<\/strong><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8569\/16214481162_528596f11d_o.gif\" alt=\"RD Sharma Class 12 Solutions Chapter 3 Binary Operations Ex 3.2 Q9\" width=\"384\" height=\"395\" \/><br \/><strong>Binary Operations Ex 3.2 Q10<\/strong><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8609\/16215281605_386ae61137_o.gif\" alt=\"RD Sharma Class 12 Solutions Free online Chapter 3 Binary Operations Ex 3.2 Q10\" width=\"432\" height=\"459\" \/><br \/><strong>Binary Operations Ex 3.2 Q11<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7490\/16027763868_60c3c85dfa_o.gif\" alt=\"RD Sharma Class 12 Solutions Free online Chapter 3 Binary Operations Ex 3.2 Q11\" width=\"491\" height=\"315\" \/><br \/><strong>Binary Operations Ex 3.2 Q12<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7575\/15592876154_b0249efa88_o.gif\" alt=\"RD Sharma Class 12 Solutions Free online Chapter 3 Binary Operations Ex 3.2 Q12\" width=\"384\" height=\"295\" \/><br \/><strong>Binary Operations Ex 3.2 Q13<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7468\/15595428403_360a3a35d7_o.gif\" alt=\"RD Sharma Class 12 Solutions Free online Chapter 3 Binary Operations Ex 3.2 Q13\" width=\"384\" height=\"435\" \/><\/p>\n<p>We have provided complete details of RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2. If you have any queries related to <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\"><strong>CBSE<\/strong><\/a>\u00a0Class 12 Exam, feel free to ask us in the comment section below.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-solutions-class-12-maths-chapter-3-exercise-32\"><\/span>FAQs on RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1629796096498\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-many-questions-are-there-in-rd-sharma-solutions-class-12-maths-chapter-3-exercise-32\"><\/span>How many questions are there in RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>There are a total of 13 questions in RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629796219242\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-rd-sharma-solutions-for-class-12-maths-chapter-3-exercise-32-for-free\"><\/span>Is RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.2 for free?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, You can get RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.2 for free.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629796237171\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-download-rd-sharma-solutions-for-chapter-3-exercise-32-class-12-maths-free-pdf\"><\/span>Where can I download RD Sharma Solutions for Chapter 3 Exercise 3.2 Class 12 Maths free PDF?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can download RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.2 free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.2:\u00a0The types of binary operations are the focus of this exercise. The question in RD Sharma Solutions for Class 12 Chapter 3 Exercise 3.2 are based on binary operations&#8217; commutativity and associativity. Students may download the free PDF of RD Sharma Solutions for Class 12 Chapter &#8230; <a title=\"RD Sharma Solutions For Class 12 Maths Exercise 3.2 Chapter 3 Binary Operations (Updated for 2021-22)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-3-exercise-3-2\/\" aria-label=\"More on RD Sharma Solutions For Class 12 Maths Exercise 3.2 Chapter 3 Binary Operations (Updated for 2021-22)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":118190,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3429,73223,61598,73664,4388,76720,76722],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68990"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/238"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=68990"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68990\/revisions"}],"predecessor-version":[{"id":138088,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68990\/revisions\/138088"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/118190"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=68990"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=68990"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=68990"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}