{"id":5147,"date":"2026-05-21T10:03:50","date_gmt":"2026-05-21T10:03:50","guid":{"rendered":"https:\/\/diznr.com\/?p=5147"},"modified":"2026-05-22T05:20:57","modified_gmt":"2026-05-22T05:20:57","slug":"mathematics-12-notes-part4-pdf","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/mathematics-12-notes-part4-pdf\/","title":{"rendered":"Mathematics 12 Notes Part4.pdf"},"content":{"rendered":"<div id=\"pl-5147\" class=\"panel-layout\">\n<div id=\"pg-5147-0\" class=\"panel-grid panel-no-style\">\n<div id=\"pgc-5147-0-0\" class=\"panel-grid-cell\" data-weight=\"1\">\n<div id=\"panel-5147-0-0-0\" class=\"so-panel widget widget_black-studio-tinymce widget_black_studio_tinymce panel-first-child panel-last-child\" data-index=\"0\" data-style=\"{&quot;background_image_attachment&quot;:false,&quot;background_display&quot;:&quot;tile&quot;}\">\n<div class=\"textwidget\">CBSE Class 12 Maths Chapter Notes are available here. Students can read these notes for exam preparation. These notes have been created after a thorough research by a subject expert and are written in simple language for easy understanding of the students. Maths Notes has been extensively compiled by the teachers having experience of around 25 years and after studying the exam papers of last ten years. Moreover, they are all designed with the subject material of the latest academic year so that any difference in the syllabus can also be accounted for. NCERT Class 12 Maths Notes are very useful and important, as it is necessary that all the questions are answered in an efficient manner. By studying from these NCERT Maths Notes for Class 12 and employing sample papers, students will not face any difficulty in reducing any stress before the exam as they will be thoroughly prepared for their board exams. These CBSE maths notes for class 12 will serve the purpose and help them prepare for board exams as well as competitive exams. The revision notes provided are of great importance for the students preparing for IIT-JEE. The revision notes also contain previous year questions which will help the students to get an idea of \u200b\u200bthe type of questions asked in the exam and also help the students to manage their time to solve the questions. This will improve the understanding of the students.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"pg-5147-1\" class=\"panel-grid panel-no-style\">\n<div id=\"pgc-5147-1-0\" class=\"panel-grid-cell\" data-weight=\"1\">\n<div id=\"panel-5147-1-0-1\" class=\"so-panel widget widget_black-studio-tinymce widget_black_studio_tinymce panel-last-child\" data-index=\"2\" data-style=\"{&quot;background_image_attachment&quot;:false,&quot;background_display&quot;:&quot;tile&quot;}\">\n<div class=\"textwidget\">\n<p>It looks like you want to upload a file. Go ahead and upload <strong data-start=\"61\" data-end=\"96\">Mathematics 12 Notes Part 4.pdf<\/strong>, and I&#8217;ll help you with whatever you need!<\/p>\n<h3 class=\"LC20lb MBeuO DKV0Md\">maths-notes-class-12-pdf<\/h3>\n<p><a href=\"https:\/\/drive.google.com\/open?id=15JytlbNtNUqeBIUAFcCjRX3l5aJqJcVc\" target=\"_blank\" rel=\"noopener noreferrer\"><b>Download Chapter-Notes\u00a0 PDF<\/b><\/a><\/p>\n<h3 class=\"_root_obrnh_1 _heading1_obrnh_38 _bold_obrnh_18 _none_obrnh_14 _title_b08mc_1\">CBSE Class 12 Maths Notes Chapter 4 Determinants PDF Download<\/h3>\n<p><a href=\"https:\/\/static.pw.live\/5eb393ee95fab7468a79d189\/GLOBAL_CMS_BLOGS\/f36253bd-0236-4097-8eac-ac363149a11c.pdf\" target=\"_blank\" rel=\"noopener\"><strong>CBSE Class 12 Maths Notes Chapter 4 Determinants PDF<\/strong><\/a><\/p>\n<h3 data-section-id=\"cjb8zy\" data-start=\"300\" data-end=\"326\"><span role=\"text\"><strong data-start=\"304\" data-end=\"326\">1. About the Notes<\/strong><\/span><\/h3>\n<ul data-start=\"327\" data-end=\"600\">\n<li data-section-id=\"170xdfj\" data-start=\"327\" data-end=\"344\"><strong data-start=\"329\" data-end=\"339\">Class:<\/strong> 12<\/li>\n<li data-section-id=\"1sp8xj9\" data-start=\"345\" data-end=\"410\"><strong data-start=\"347\" data-end=\"356\">Part:<\/strong> 4 (Usually covers final chapters in NCERT syllabus)<\/li>\n<li data-section-id=\"1tgtxcf\" data-start=\"411\" data-end=\"491\"><strong data-start=\"413\" data-end=\"425\">Purpose:<\/strong> Quick revision, problem-solving practice, and formula reference<\/li>\n<li data-section-id=\"iktza2\" data-start=\"492\" data-end=\"600\"><strong data-start=\"494\" data-end=\"507\">Audience:<\/strong> Class 12 students preparing for board exams, JEE Main\/Advanced, or other competitive exams<\/li>\n<\/ul>\n<h3 data-section-id=\"gnu9f4\" data-start=\"607\" data-end=\"644\"><span role=\"text\"><strong data-start=\"611\" data-end=\"644\">2. Typical Contents of Part 4<\/strong><\/span><\/h3>\n<h4 data-start=\"646\" data-end=\"682\"><span role=\"text\"><strong data-start=\"651\" data-end=\"682\">A. Probability (Chapter 13)<\/strong><\/span><\/h4>\n<ul data-start=\"683\" data-end=\"855\">\n<li data-section-id=\"x2u16k\" data-start=\"683\" data-end=\"727\">Random experiments, sample space, events<\/li>\n<li data-section-id=\"2s49v7\" data-start=\"728\" data-end=\"753\">Probability of events<\/li>\n<li data-section-id=\"1uylkij\" data-start=\"754\" data-end=\"781\">Conditional probability<\/li>\n<li data-section-id=\"1a8trtd\" data-start=\"782\" data-end=\"804\">Independent events<\/li>\n<li data-section-id=\"exlh2p\" data-start=\"805\" data-end=\"823\">Bayes\u2019 theorem<\/li>\n<li data-section-id=\"1asoo6v\" data-start=\"824\" data-end=\"855\">Solved examples &amp; exercises<\/li>\n<\/ul>\n<h4 data-start=\"857\" data-end=\"900\"><span role=\"text\"><strong data-start=\"862\" data-end=\"900\">B. Linear Programming (Chapter 12)<\/strong><\/span><\/h4>\n<ul data-start=\"901\" data-end=\"1068\">\n<li data-section-id=\"i73t9z\" data-start=\"901\" data-end=\"932\">Introduction to LP problems<\/li>\n<li data-section-id=\"mexv0w\" data-start=\"933\" data-end=\"961\">Mathematical formulation<\/li>\n<li data-section-id=\"1s6bxm4\" data-start=\"962\" data-end=\"994\">Graphical method of solution<\/li>\n<li data-section-id=\"10cact3\" data-start=\"995\" data-end=\"1029\">Feasible region, corner points<\/li>\n<li data-section-id=\"2wpl9\" data-start=\"1030\" data-end=\"1068\">Optimization of objective function<\/li>\n<\/ul>\n<h4 data-start=\"1070\" data-end=\"1106\"><span role=\"text\"><strong data-start=\"1075\" data-end=\"1106\">C. Applications of Calculus<\/strong><\/span><\/h4>\n<ol data-start=\"1107\" data-end=\"1411\">\n<li data-section-id=\"14n0d2u\" data-start=\"1107\" data-end=\"1238\"><strong data-start=\"1110\" data-end=\"1152\">Integration Applications (if included)<\/strong>\n<ul data-start=\"1156\" data-end=\"1238\">\n<li data-section-id=\"gm2wfn\" data-start=\"1156\" data-end=\"1177\">Area under curves<\/li>\n<li data-section-id=\"12wjj8l\" data-start=\"1181\" data-end=\"1215\">Volume of solids of revolution<\/li>\n<li data-section-id=\"1n6crsk\" data-start=\"1219\" data-end=\"1238\">Solved examples<\/li>\n<\/ul>\n<\/li>\n<li data-section-id=\"czfd08\" data-start=\"1240\" data-end=\"1411\"><strong data-start=\"1243\" data-end=\"1295\">Differential Equations (if included in syllabus)<\/strong>\n<ul data-start=\"1299\" data-end=\"1411\">\n<li data-section-id=\"4wqcuc\" data-start=\"1299\" data-end=\"1338\">Formation of differential equations<\/li>\n<li data-section-id=\"it1r08\" data-start=\"1342\" data-end=\"1375\">Solving first-order equations<\/li>\n<li data-section-id=\"udk06a\" data-start=\"1379\" data-end=\"1411\">Applications in growth\/decay<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<h4 data-start=\"1413\" data-end=\"1445\"><span role=\"text\"><strong data-start=\"1418\" data-end=\"1445\">D. Vector &amp; 3D Geometry<\/strong><\/span><\/h4>\n<ul data-start=\"1446\" data-end=\"1607\">\n<li data-section-id=\"i6ctlm\" data-start=\"1446\" data-end=\"1478\">Direction ratios and cosines<\/li>\n<li data-section-id=\"fvjb2q\" data-start=\"1479\" data-end=\"1515\">Equation of a line &amp; plane in 3D<\/li>\n<li data-section-id=\"5y8z6g\" data-start=\"1516\" data-end=\"1550\">Angle between two lines\/planes<\/li>\n<li data-section-id=\"8omiue\" data-start=\"1551\" data-end=\"1607\">Distance between points, line to plane, line to line<\/li>\n<\/ul>\n<h3 data-section-id=\"5iab7z\" data-start=\"1614\" data-end=\"1646\"><span role=\"text\"><strong data-start=\"1618\" data-end=\"1646\">3. Features of the Notes<\/strong><\/span><\/h3>\n<ul data-start=\"1647\" data-end=\"1845\">\n<li data-section-id=\"a1sf1r\" data-start=\"1647\" data-end=\"1698\">Chapter-wise summary of formulas and key points<\/li>\n<li data-section-id=\"1uys9vz\" data-start=\"1699\" data-end=\"1731\">Step-by-step solved examples<\/li>\n<li data-section-id=\"1cxi2u4\" data-start=\"1732\" data-end=\"1765\">Important diagrams and graphs<\/li>\n<li data-section-id=\"1e3wb6h\" data-start=\"1766\" data-end=\"1806\">Tips for board and competitive exams<\/li>\n<li data-section-id=\"1sjs8tx\" data-start=\"1807\" data-end=\"1845\">Quick revision tables for formulas<\/li>\n<\/ul>\n<h3 data-section-id=\"dwwow7\" data-start=\"1852\" data-end=\"1893\"><span role=\"text\"><strong data-start=\"1856\" data-end=\"1893\">4. How to Use the PDF Effectively<\/strong><\/span><\/h3>\n<ol data-start=\"1894\" data-end=\"2247\">\n<li data-section-id=\"1sxv07a\" data-start=\"1894\" data-end=\"1955\"><strong data-start=\"1897\" data-end=\"1916\">Go chapter-wise<\/strong>, first revising theory and formulas.<\/li>\n<li data-section-id=\"g5w8ht\" data-start=\"1956\" data-end=\"2018\"><strong data-start=\"1959\" data-end=\"1987\">Practice solved examples<\/strong> before attempting exercises.<\/li>\n<li data-section-id=\"1j1cshu\" data-start=\"2019\" data-end=\"2081\"><strong data-start=\"2022\" data-end=\"2046\">Make a formula sheet<\/strong> for quick revision before exams.<\/li>\n<li data-section-id=\"gy05kh\" data-start=\"2082\" data-end=\"2172\">Solve <strong data-start=\"2091\" data-end=\"2118\">previous year questions<\/strong> for topics like Probability and Linear Programming.<\/li>\n<li data-section-id=\"j7c71n\" data-start=\"2173\" data-end=\"2247\">Use diagrams and graphs wherever applicable for visual understanding.<\/li>\n<\/ol>\n<h2><a href=\"https:\/\/autotutor.com.au\/_formula_sheets\/Maths%20Notes%20for%20Class%2012%20chapter%204%20Determinants.pdf\" target=\"_blank\" rel=\"noopener\">Mathematics 12 Notes Part4.pdf<\/a><\/h2>\n<h2 id=\"_KecPatKCDILsseMPv8aOgAw_49\" class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/media.geeksforgeeks.org\/wp-content\/uploads\/20240410123458\/CBSE-Class-12th-Math-Notes.pdf\" target=\"_blank\" rel=\"noopener\">CBSE Class 12th Math Notes PDF<\/a><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>CBSE Class 12 Maths Chapter Notes are available here. Students can read these notes for exam preparation. These notes have been created after a thorough research by a subject expert and are written in simple language for easy understanding of the students. Maths Notes has been extensively compiled by the teachers having experience of around [&hellip;]<\/p>\n","protected":false},"author":64,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1200],"tags":[227,228,229,230,231,232,234,235,236,237],"class_list":["post-5147","post","type-post","status-publish","format-standard","hentry","category-mathematics-12-notes-part4","tag-class-12-maths-ncert-solutions","tag-class-12-maths-solutions","tag-ex-7-2-class-12","tag-math-class-12","tag-math-class-12-notes","tag-math-class-12-notes-pdf","tag-ncert-class-12-maths","tag-rd-sharma-class-12","tag-rd-sharma-class-12-solutions","tag-teachoo-class-12"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/5147","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/users\/64"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=5147"}],"version-history":[{"count":2,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/5147\/revisions"}],"predecessor-version":[{"id":11446,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/5147\/revisions\/11446"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=5147"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=5147"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=5147"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}