{"id":1066,"date":"2021-12-17T16:27:42","date_gmt":"2021-12-17T10:57:42","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=1066"},"modified":"2024-05-16T13:00:01","modified_gmt":"2024-05-16T07:30:01","slug":"study-materials-ncert-solutions-class-12-maths-chapter-1-relations-and-function","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-1-relations-and-function\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions"},"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-solutions\/class-12\/maths\/chapter-1-relations-and-function\/#NCERT_Solutions_for_Class_12_Maths_Chapter_1_Relations_and_Functions\" title=\"NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions\">NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-1-relations-and-function\/#Relation_And_Function_Class_12_PDF\" title=\"Relation And Function Class 12 PDF\">Relation And Function Class 12 PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-1-relations-and-function\/#Topics_Covered_in_Relation_And_Functions_Class_12_NCERT_Solutions\" title=\"Topics Covered in Relation And Functions Class 12 NCERT Solutions\">Topics Covered in Relation And Functions Class 12 NCERT Solutions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-1-relations-and-function\/#Key_Features_of_NCERT_Solutions_class_12_Maths_ch_1\" title=\"Key Features of NCERT Solutions class 12 Maths ch 1\">Key Features of NCERT Solutions class 12 Maths ch 1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-1-relations-and-function\/#FAQs_on_NCERT_Solutions_12th_CBSE_Maths_Solutions\" title=\"FAQs on NCERT Solutions 12th CBSE Maths Solutions\">FAQs on NCERT Solutions 12th CBSE Maths Solutions<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-1-relations-and-function\/#What_are_the_concepts_explained_in_NCERT_Solutions_in_this_chapter\" title=\"What are the concepts explained in NCERT Solutions in this chapter?\">What are the concepts explained in NCERT Solutions in this chapter?<\/a><\/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-solutions\/class-12\/maths\/chapter-1-relations-and-function\/#What_are_the_key_features_of_these_NCERT_Solutions\" title=\"What are the key features of these NCERT Solutions?\">What are the key features of these NCERT Solutions?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-1-relations-and-function\/#Are_these_NCERT_Solutions_enough_to_prepare_for_the_first_term_exams\" title=\"Are these NCERT Solutions enough to prepare for the first term exams?\">Are these NCERT Solutions enough to prepare for the first term exams?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><strong>NCERT Solutions for Class 12 Maths Chapter 1<\/strong>, Relations and Functions, offer comprehensive answers to all chapter-related questions in the CBSE syllabus 2024-25. With a step-by-step approach, students grasp concepts effectively. Mastering both basics and advanced sections is crucial. Practicing these class 12 maths chapter 1 solutions enhances exam readiness, making even complex questions seem simple. Access the class 12 maths <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/\"><strong>NCERT solutions<\/strong><\/a> pdf via the provided link to sharpen math skills.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_12_Maths_Chapter_1_Relations_and_Functions\"><\/span>NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In this class 12 chapter 1, students study different relations and equivalence relations, the composition of functions, invertible functions, and binary operations. Students can use the class 12 relations and functions for any quick reference to comprehend complex topics.<\/p>\n<p><strong>The main features of this chapter are as follows:<\/strong><\/p>\n<ul>\n<li>Empty relation<\/li>\n<li>Universal relation<\/li>\n<li>Reflexive relation<\/li>\n<li>Symmetric relation<\/li>\n<li>Transitive relation<\/li>\n<li>Equivalence relation<\/li>\n<li>A function f : X \u2192 Y is one-one (or injective) if f (x1) = f(x2) \u21d2 x1 = x2\u2200 x1, x2\u2208 X.<\/li>\n<li>A function f : X \u2192 Y is onto (or surjective) if given any y \u2208 Y, \u2203 x \u2208 X such that f(x) = y.<\/li>\n<li>A function f: X \u2192 Y is one-one and onto (or bijective) if f is one-one and onto.<\/li>\n<li>A function f: X \u2192 Y is invertible if f is one-one and onto.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Relation_And_Function_Class_12_PDF\"><\/span>Relation And Function Class 12 PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"auto\">\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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wpcf7-validates-as-required wpcf7-validates-as-number\" aria-required=\"true\" aria-invalid=\"false\" \/><\/span><\/p>\n<p><span style=\"display:none;\"><span class=\"wpcf7-form-control-wrap current-page-url\"><input type=\"text\" name=\"current-page-url\" value=\"https:\/\/_:443\/surge\/wp-json\/wp\/v2\/posts\/1066\" size=\"40\" class=\"wpcf7-form-control wpcf7dtx-dynamictext wpcf7-dynamictext\" aria-invalid=\"false\" \/><\/span><\/span><\/p>\n<style>.wpcf7-list-item{margin: 0 0.5em 0 0!important;}<\/style>\n<p class=\"title\" style=\"color: #6e6e6e;font-size:14px;font-weight:400;text-decoration: un;\"><span class=\"wpcf7-form-control-wrap acceptance-agreement\"><span class=\"wpcf7-form-control wpcf7-acceptance\"><span class=\"wpcf7-list-item\"><input type=\"checkbox\" name=\"acceptance-agreement\" value=\"1\" aria-invalid=\"false\" checked=\"checked\" \/><\/span><\/span><\/span> I agree to the <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/terms\" style=\"text-decoration: 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\/2021\/12\/Chapter-1.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=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Chapter-1.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-toolbar=\"top\" data-toolbar-fixed=\"on\">Chapter 1<br\/><\/a><\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Topics_Covered_in_Relation_And_Functions_Class_12_NCERT_Solutions\"><\/span>Topics Covered in Relation And Functions Class 12 NCERT Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Reflexive, symmetric, transitive, and equivalence relations are examples of relations. One-to-one and onto functions, composite functions, and the inverse of a function are all examples of relation and function class 12 NCERT Solutions.<\/p>\n<div class=\"table-responsive\">\n<table class=\"table table-bordered table-striped\" cellspacing=\"0\" cellpadding=\"5\">\n<tbody>\n<tr style=\"background-color: #89cff0; color: black;\">\n<td><strong>Relations and Functions Class 12 Exercise<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-1-relations-and-function-exercise-1-1\/\" target=\"_blank\" rel=\"noopener\">Exercise 1.1 class 12 maths<\/a><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-1-relations-and-function-exercise-1-2\/\" target=\"_blank\" rel=\"noopener\">Exercise 1.2 Class 12 Maths<\/a><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-1-relations-and-function-exercise-1-3\/\" target=\"_blank\" rel=\"noopener\">Exercise 1.3 Class 12 Maths<\/a><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-1-relations-and-function-exercise-1-4\/\" target=\"_blank\" rel=\"noopener\">Exercise 1.4 Class 12 Maths<\/a><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-1-relations-and-function-exercise-miscellaneous\/\" target=\"_blank\" rel=\"noopener\">Miscellaneous Exercise on Chapter 1 Class 12<\/a><\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Key_Features_of_NCERT_Solutions_class_12_Maths_ch_1\"><\/span>Key Features of NCERT Solutions class 12 Maths ch 1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ol>\n<li>Subject experts make these NCERT exercises.<\/li>\n<li>Simple and understandable language was used.<\/li>\n<li>All questions are solved with perfect explanations.<\/li>\n<li>These NCERT Solutions are very helpful to students in their assignments and competitive exams.<\/li>\n<\/ol>\n<p><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/physics\/\">NCERT Solutions for Class 12 Physics<\/a> | <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/chemistry\/\">NCERT Solutions for Class 12 Chemistry<\/a> | <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/biology\/\">NCERT Solutions for Class 12 Biology<\/a> | <\/strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/\"><strong>NCERT Solutions for Class 12 Ma<\/strong>ths<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"FAQs_on_NCERT_Solutions_12th_CBSE_Maths_Solutions\"><\/span>FAQs on NCERT Solutions 12th CBSE Maths Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_are_the_concepts_explained_in_NCERT_Solutions_in_this_chapter\"><\/span>What are the concepts explained in NCERT Solutions in this chapter?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe concepts included in this chapter relation function class 12 are types of relations, types of functions, the composition of functions and invertible functions, and binary operations. Our subject matter expert solves the solutions to the exercise-wise problems. The main objective of providing solutions is to help students score well in their exams.\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<h3><span class=\"ez-toc-section\" id=\"What_are_the_key_features_of_these_NCERT_Solutions\"><\/span>What are the key features of these NCERT Solutions?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe NCERT 12 maths solution exercises are solved by expert faculties having vast knowledge about these concepts. Every step is explained in easy and understandable language to help students learn the method of solving complex problems effortlessly. The solutions are solved stepwise, keeping in view the marks weightage of the CBSE term I exam.\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<h3><span class=\"ez-toc-section\" id=\"Are_these_NCERT_Solutions_enough_to_prepare_for_the_first_term_exams\"><\/span>Are these NCERT Solutions enough to prepare for the first term exams?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThis chapter includes all the important topics based on the latest update of CBSE guidelines. This chapter provides four exercises, giving the students numerous problems to solve independently. The solutions are made to boost the confidence in the minds of students before appearing for the term I exams.\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\": \"What are the concepts explained in NCERT Solutions in this chapter?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The concepts included in this chapter relation function class 12 are types of relations, types of functions, the composition of functions and invertible functions, and binary operations. Our subject matter expert solves the solutions to the exercise-wise problems. The main objective of providing solutions is to help students score well in their exams.\"\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\": \"What are the key features of these NCERT Solutions?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The NCERT 12 maths solution exercises are solved by expert faculties having vast knowledge about these concepts. Every step is explained in easy and understandable language to help students learn the method of solving complex problems effortlessly. The solutions are solved stepwise, keeping in view the marks weightage of the CBSE term I exam.\"\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\": \"Are these NCERT Solutions enough to prepare for the first term exams?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"This chapter includes all the important topics based on the latest update of CBSE guidelines. This chapter provides four exercises, giving the students numerous problems to solve independently. The solutions are made to boost the confidence in the minds of students before appearing for the term I exams.\"\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","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 12 Maths Chapter 1, Relations and Functions, offer comprehensive answers to all chapter-related questions in the [&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 Solutions for Class 12 Maths Chapter 1","_yoast_wpseo_title":"Relations And Functions Class 12 NCERT Solutions Updated 2024-25","_yoast_wpseo_metadesc":"GET relation and function class 12 Chapter 1 - Relations and Functions solved by Expert Teachers as the latest 2022 NCERT(CBSE) guidelines.","custom_permalink":"study-materials\/ncert-solutions\/class-12\/maths\/chapter-1-relations-and-function\/"},"categories":[19,31],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - 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