{"id":68991,"date":"2021-08-24T11:01:00","date_gmt":"2021-08-24T05:31:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=68991"},"modified":"2021-08-31T18:34:34","modified_gmt":"2021-08-31T13:04:34","slug":"rd-sharma-solutions-class-12-maths-chapter-3-exercise-3-3","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-3-exercise-3-3\/","title":{"rendered":"RD Sharma Solutions For Class 12 Maths Exercise 3.3 Chapter 3 Binary Operations (Updated for 2021-22)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-118245\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-3-Exercise-3.3.png\" alt=\"RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-3-Exercise-3.3.png 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-3-Exercise-3.3-768x432.png 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3: <\/strong><span style=\"font-size: inherit; background-color: initial;\">The identity elements for binary operations are explained in the third exercise in Chapter 3. The <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> Exercise 3.3 are provided in easy-to-understand language, which increases students&#8217; grasping ability.\u00a0Students can refer to <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-12-solutions\/\"><strong>RD Sharma Solutions Class 12 Maths<\/strong><\/a> Chapter 3 Binary Operations Exercise 3.3 PDF, which is available here, for more understanding on the concepts covered in this exercise.<\/span><\/p>\n<div id=\"text-body\">\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-69e7674737823\" 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-69e7674737823\"><\/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-3-3\/#download-rd-sharma-solutions-class-12-maths-chapter-3-exercise-33-pdf\" title=\"Download RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3 PDF\">Download RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3 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-3-3\/#access-rd-sharma-solutions-for-class-12-maths-chapter-3-%e2%80%93-binary-operations-exercise-33-questions-with-solution\" title=\"Access RD Sharma Solutions For Class 12 Maths Chapter 3 \u2013 Binary Operations Exercise 3.3 Questions With Solution\">Access RD Sharma Solutions For Class 12 Maths Chapter 3 \u2013 Binary Operations Exercise 3.3 Questions With Solution<\/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-3-3\/#faqs-on-rd-sharma-solutions-for-class-12-maths-chapter-3-exercise-33\" title=\"FAQs on RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.3\">FAQs on RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.3<\/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-3-3\/#how-many-questions-are-there-in-rd-sharma-solutions-for-class-12-maths-chapter-3-exercise-33\" title=\"How many questions are there in RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.3?\">How many questions are there in RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.3?<\/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-3-3\/#is-rd-sharma-solutions-for-class-12-maths-chapter-3-exercise-33-for-free\" title=\"Is RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.3 for free?\">Is RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.3 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-3-3\/#where-can-i-download-rd-sharma-solutions-class-12-maths-chapter-3-exercise-33-free-pdf\" title=\"Where can I download RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3 free PDF?\">Where can I download RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3 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-33-pdf\"><\/span>Download RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3 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-3ex-3.3.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-3ex-3.3.pdf\">RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3<\/a><\/p>\n<p><span style=\"font-size: inherit; background-color: initial;\"> Before designing textbook <strong>RD Sharma Solutions<\/strong> in accordance with the CBSE board&#8217;s prescribed syllabus, Kopykitab&#8217;s team of experts do extensive research on each topic.<\/span><\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-rd-sharma-solutions-for-class-12-maths-chapter-3-%e2%80%93-binary-operations-exercise-33-questions-with-solution\"><\/span>Access RD Sharma Solutions For Class 12 Maths Chapter 3 \u2013 Binary Operations Exercise 3.3 Questions With Solution<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>1. Find the identity element in the set I<sup>+<\/sup>\u00a0of all positive integers defined by a * b = a + b for all a, b \u2208 I<sup>+<\/sup>.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Let e be the identity element in I<sup>+<\/sup>\u00a0with respect to * such that<\/p>\n<p>a * e = a = e * a, \u2200 a \u2208 I<sup>+<\/sup><\/p>\n<p>a * e = a and e * a = a, \u2200 a \u2208 I<sup>+<\/sup><\/p>\n<p>a + e = a and e + a = a, \u2200 a \u2208 I<sup>+<\/sup><\/p>\n<p>e = 0, \u2200 a \u2208 I<sup>+<\/sup><\/p>\n<p>Thus, 0 is the identity element in I<sup>+<\/sup>\u00a0with respect to *.<\/p>\n<p><strong>2. Find the identity element in the set of all rational numbers except \u2013 1 with respect to * defined by a * b = a + b + ab<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Let e be the identity element in I<sup>+<\/sup>\u00a0with respect to * such that<\/p>\n<p>a * e = a = e * a, \u2200 a \u2208 Q \u2013 {-1}<\/p>\n<p>a * e = a and e * a = a, \u2200 a \u2208 Q \u2013 {-1}<\/p>\n<p>a + e + ae = a and e + a + ea = a, \u2200 a \u2208 Q \u2013 {-1}<\/p>\n<p>e + ae = 0 and e + ea = 0, \u2200 a \u2208 Q \u2013 {-1}<\/p>\n<p>e (1 + a) = 0 and e (1 + a) = 0, \u2200 a \u2208 Q \u2013 {-1}<\/p>\n<p>e = 0, \u2200 a \u2208 Q \u2013 {-1} [because a not equal to -1]<\/p>\n<p>Thus, 0 is the identity element in Q \u2013 {-1} with respect to *.<\/p>\n<p><strong>Binary Operations Ex 3.3 Q3<\/strong><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8651\/16214481042_57a3499fa8_o.gif\" alt=\"RD Sharma Class 12 Solutions Chapter 3 Binary Operations Ex 3.3 Q3\" width=\"433\" height=\"221\" \/><br \/><strong>Binary Operations Ex 3.3 Q4<\/strong><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8606\/16189398956_8ee6744736_o.gif\" alt=\"RD Sharma Class 12 Solutions Free online Chapter 3 Binary Operations Ex 3.3 Q4\" width=\"447\" height=\"199\" \/><\/p>\n<p>We have provided complete details of RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3. 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-for-class-12-maths-chapter-3-exercise-33\"><\/span>FAQs on RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1629801445036\" 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-for-class-12-maths-chapter-3-exercise-33\"><\/span>How many questions are there in RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.3?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>There are a total of 4 questions in RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.3.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629801488516\" 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-33-for-free\"><\/span>Is RD Sharma Solutions for Class 12 Maths Chapter 3 Exercise 3.3 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 3.3 for free.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629801503796\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-download-rd-sharma-solutions-class-12-maths-chapter-3-exercise-33-free-pdf\"><\/span>Where can I download RD Sharma Solutions Class 12 Maths Chapter 3 Exercise 3.3 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 3.3 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 3.3: The identity elements for binary operations are explained in the third exercise in Chapter 3. The RD Sharma Solutions for Class 12 Chapter 3 Exercise 3.3 are provided in easy-to-understand language, which increases students&#8217; grasping ability.\u00a0Students can refer to RD Sharma Solutions Class 12 Maths &#8230; <a title=\"RD Sharma Solutions For Class 12 Maths Exercise 3.3 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-3-3\/\" aria-label=\"More on RD Sharma Solutions For Class 12 Maths Exercise 3.3 Chapter 3 Binary Operations (Updated for 2021-22)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":118245,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3429,73223,73664,4388,76720,76723],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68991"}],"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=68991"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68991\/revisions"}],"predecessor-version":[{"id":121965,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68991\/revisions\/121965"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/118245"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=68991"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=68991"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=68991"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}