{"id":68983,"date":"2021-01-13T15:07:43","date_gmt":"2021-01-13T09:37:43","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=68983"},"modified":"2021-01-22T19:11:21","modified_gmt":"2021-01-22T13:41:21","slug":"rd-sharma-solutions-class-12-maths-chapter-2-exercise-2-5","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-2-exercise-2-5\/","title":{"rendered":"RD Sharma Solutions Class 12 Maths Chapter 2 Exercise 2.5"},"content":{"rendered":"\n<p>RD Sharma Solutions Class 12 Maths Chapter 2 Exercise 2.5: RD Sharma Solutions for Class 12, Maths Chapter 2, helps students who wish to achieve a good academic score in the exam. Solutions are expertly designed to increase students&#8217; confidence to understand the concepts covered in this chapter and how to solve problems in a short period of time.<\/p>\n<p>Our experts prepare these materials based on the Class 12 CBSE syllabus, keeping in mind the types of questions asked in the RD Sharma solution. <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-2-functions\/\">Chapter 2 Functions<\/a> explains the function and domains of functions and functions. It has four practices. Students can easily get answers to problems in RD Sharma Solutions for Class 12.<\/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-69d00cfa72a0e\" 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-69d00cfa72a0e\"><\/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-2-exercise-2-5\/#download-rd-sharma-solutions-class-12-maths-chapter-2-exercise-25-pdf\" title=\"Download RD Sharma Solutions Class 12 Maths Chapter 2 Exercise 2.5 PDF:\">Download RD Sharma Solutions Class 12 Maths Chapter 2 Exercise 2.5 PDF:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-2-exercise-2-5\/#rd-sharma-solutions-class-12-maths-chapter-2-exercise-25-important-topics-from-the-chapter\" title=\"RD Sharma Solutions Class 12 Maths Chapter 2 Exercise 2.5: Important Topics From The Chapter\">RD Sharma Solutions Class 12 Maths Chapter 2 Exercise 2.5: Important Topics From The Chapter<\/a><\/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-2-exercise-2-5\/#important-questions-from-rd-sharma-solutions-class-12-maths-chapter-2-exercise-25\" title=\"Important Questions from RD Sharma Solutions Class 12 Maths Chapter 2 Exercise 2.5\">Important Questions from RD Sharma Solutions Class 12 Maths Chapter 2 Exercise 2.5<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-solutions-class-12-maths-chapter-2-exercise-25-pdf\"><\/span>Download RD Sharma Solutions Class 12 Maths Chapter 2 Exercise 2.5 PDF:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">&nbsp;<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<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\/2020\/11\/RD-Sharma-Solutions-Class-12-Maths-Chapter-2.pdf\", \"#example1\");<\/script><\/p>\n<p>&nbsp;<\/p>\n<h2><span class=\"ez-toc-section\" id=\"rd-sharma-solutions-class-12-maths-chapter-2-exercise-25-important-topics-from-the-chapter\"><\/span>RD Sharma Solutions Class 12 Maths Chapter 2 Exercise 2.5: Important Topics From The Chapter<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Let us have a look at some of the important concepts that are discussed in this chapter.<\/p>\n<ul>\n<li>Classification of functions\n<ul>\n<li>Types of functions\n<ul>\n<li>Constant function<\/li>\n<li>Identity function<\/li>\n<li>Modulus function<\/li>\n<li>Integer function<\/li>\n<li>Exponential function<\/li>\n<li>Logarithmic function<\/li>\n<li>Reciprocal function<\/li>\n<li>Square root function<\/li>\n<\/ul>\n<\/li>\n<li>Operations on real functions<\/li>\n<li>Kinds of functions\n<ul>\n<li>One-one function<\/li>\n<li>On-to function<\/li>\n<li>Many one function<\/li>\n<li>In to function<\/li>\n<li>Bijection<\/li>\n<\/ul>\n<\/li>\n<li>Composition of functions<\/li>\n<li>Properties of the composition of functions<\/li>\n<li>Composition of real function<\/li>\n<li>Inverse of a function<\/li>\n<li>Inverse of an element<\/li>\n<li>Relation between graphs of a function and its inverse<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"important-questions-from-rd-sharma-solutions-class-12-maths-chapter-2-exercise-25\"><\/span>Important Questions from RD Sharma Solutions Class 12 Maths Chapter 2 Exercise 2.5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Question :<\/strong><\/p>\n<p class=\"TopprQuestion_question__E_F5O utils_customScrollBar\">Consider&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mrel\">:<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span>&nbsp;given by&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><\/span><\/span><\/span>. Show that&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><\/span><\/span><\/span>&nbsp;is invertible. Find the inverse&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><\/span><\/span><\/span>.<\/p>\n<p><strong>Answer :<\/strong><\/p>\n<p class=\"Solution_html__31bvW\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mord mathnormal\">e<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mord mathnormal\">e<\/span><\/span><\/span><\/span>&nbsp;test of&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mrel\">:<\/span><\/span><\/span><\/span><\/p>\n<div>Let&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span>&nbsp;and&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><\/span><\/span><\/span>&nbsp;be two elements of domain&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">R<\/span><span class=\"mclose\">)<\/span><span class=\"mpunct\">,<\/span><\/span><\/span><\/span>&nbsp;such that<\/div>\n<div><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/div>\n<div><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mrel\">\u21d2<\/span><\/span><\/span><\/span>&nbsp;&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/div>\n<div><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mrel\">\u21d2<\/span><\/span><\/span><\/span>&nbsp;&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mord mathnormal\">y<\/span><\/span><\/span><\/span><\/div>\n<div><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mrel\">\u21d2<\/span><\/span><\/span><\/span>&nbsp;&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><\/span><\/span><\/span><\/div>\n<div><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mrel amsrm\">\u2234<\/span><\/span><\/span><\/span>&nbsp;&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><\/span><\/span><\/span>&nbsp;is one-one.<\/div>\n<div>&nbsp;<\/div>\n<div><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">o<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mord mathnormal\">o<\/span><\/span><\/span><\/span>&nbsp;test for&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mrel\">:<\/span><\/span><\/span><\/span><\/div>\n<div>Let&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><\/span><\/span><\/span>&nbsp;be in the co-domain&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">R<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>, such that&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mord\">.<\/span><\/span><\/span><\/span><\/div>\n<div><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mrel\">\u21d2<\/span><\/span><\/span><\/span>&nbsp;&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><\/span><\/span><\/span><\/div>\n<div><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mrel\">\u21d2<\/span><\/span><\/span><\/span>&nbsp;&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/div>\n<div><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mrel\">\u21d2<\/span><\/span><\/span><\/span>&nbsp;&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">4<span class=\"mord mathnormal\">y<\/span><span class=\"mbin\">\u2212<\/span>3<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">\u2208<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">R<\/span><\/span><\/span><\/span>&nbsp;(Domain)<\/div>\n<div><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mrel\">\u21d2<\/span><\/span><\/span><\/span>&nbsp;&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><\/span><\/span><\/span>&nbsp;is onto.<\/div>\n<div>So,&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><\/span><\/span><\/span>&nbsp;is a bijection and hence, it is invertible.<\/div>\n<div>&nbsp;<\/div>\n<div>Now we have to find&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u22121<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">:<\/span><\/span><\/span><\/span><\/div>\n<div>Let&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u22121<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><\/span><\/span><\/span>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &#8212;- ( 1 )<\/div>\n<div><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mrel\">\u21d2<\/span><\/span><\/span><\/span>&nbsp;&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/div>\n<div><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mrel\">\u21d2<\/span><\/span><\/span><\/span>&nbsp;&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/div>\n<div><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mrel\">\u21d2<\/span><\/span><\/span><\/span>&nbsp;&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mord mathnormal\">y<\/span><\/span><\/span><\/span><\/div>\n<div><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mrel\">\u21d2<\/span><\/span><\/span><\/span>&nbsp;&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">4<span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span>3<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<div>From ( 1 ),<\/div>\n<div>So,&nbsp;<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u22121<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">4<span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span>3<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>&nbsp; &nbsp;&nbsp;<\/div>\n<div>Know more <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\">here<\/a>.<\/div>\n","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 12 Maths Chapter 2 Exercise 2.5: RD Sharma Solutions for Class 12, Maths Chapter 2, helps students who wish to achieve a good academic score in the exam. Solutions are expertly designed to increase students&#8217; confidence to understand the concepts covered in this chapter and how to solve problems in a &#8230; <a title=\"RD Sharma Solutions Class 12 Maths Chapter 2 Exercise 2.5\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-2-exercise-2-5\/\" aria-label=\"More on RD Sharma Solutions Class 12 Maths Chapter 2 Exercise 2.5\">Read more<\/a><\/p>\n","protected":false},"author":236,"featured_media":69199,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2917,73716,73411,2985,73410],"tags":[3429,62019,73664],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68983"}],"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\/236"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=68983"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68983\/revisions"}],"predecessor-version":[{"id":70718,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68983\/revisions\/70718"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/69199"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=68983"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=68983"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=68983"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}