MCQ Questions for Class 12 Biology with Answers were prepared based on the latest exam pattern. And the order of B is . Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Vector Algebra MCQs Pdf with Answers to know their preparation level. Answers of all CBSE Class 12 Maths MCQs Multiple Choice Questions with Answers provided here with detailed solutions so that you can easily understand the logic behind each answer. Free Question Bank for JEE Main & Advanced Mathematics Determinants & Matrices Expansion of determinants, Solution of equation in the form of determinants and properties of determinants Question 2. NCERT Solutions, NCERT Exemplars, Revison Notes, Free Videos, CBSE Papers, MCQ Tests & more. Learn Chapter 4 Determinants of Class 12 free with solutions of all NCERT Questions for CBSE Maths . Based on CBSE and NCERT guidelines. Akash Mandhan. Determinants Important Questions for CBSE Class 12 Maths Expansion of Determinants. Practice MCQ Questions for Class 10 Maths With Answers for 2020 Board Exams. Maths Class 12 NCERT Solutions are written by considering the marking scheme. All chapter wise RS Aggarwal Class 12 Exercise Questions with Solutions to help you to revise the complete Syllabus … Here you will find Chapter Wise NCERT MCQ Questions for Class 12 Maths with Answers PDF Free Download based on the important concepts and topics given in the textbook. Please keep a pen and paper ready for rough work but keep your books away. Previous Years Examination Questions. Question 6. To assist you with that, we are here with notes. Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 4 Determinants. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. 1 Mark Questions. The important questions are taken as per the syllabus of CBSE board. Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 7 Integrals. Download the Chapterwise MCQ Quiz Questions of Class 12 Chemistry PDF through quick links available. Get Free RD Sharma Class 12 Solutions Chapter 6 Ex 6.1. CBSE recommends NCERT books and most of the questions in … Then, (a) C is empty (b) B has as many elements as C (c) A = B È C (d) B has twice as many elements as C [IIT JEE 1981] Maths MCQs for IIT-JEE | Matrix and Determinants MCQ Practice Test Answer keys: 1. a 2. a 3. Here you can get free RD Sharma Solutions for Class 12 Maths of Chapter 6 Determinants Exercise 6.2.All RD Sharma Book Solutions are given here exercise wise for Determinants. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Integrals MCQs Pdf with Answers to know their preparation level. Class 12 Maths Determinant – Get here the Notes for Class 12 Maths Determinant. These questions are strictly based on the latest CBSE pattern prescribed by the Board for Class 12th Mathematics Examination 2020. Here you will find Chapter Wise NCERT MCQ Questions for Class 12 Maths with Answers PDF Free Download based on the important concepts and topics given in the textbook. CBSE recommends NCERT books and most of the questions in … Practicing questions from RD Sharma Mathematics Solutions for Class 12 … There is no substitute for consistent practice whether one wants to understand a concept thoroughly or one wants to score better. B 7. Also, get the Mastery unavailable. Free PDF download of RS Aggarwal Solutions for Class 12 for Maths Book solved by expert teachers on Vedantu.com as per NCERT (CBSE) guidelines. There are around 3-5 solved test papers in each chapter. These Questions with solution are prepared by our team of expert teachers who are teaching grade in CBSE schools for years. The matrices and determinants questions from the previous years of JEE Main are present in this page along with the detailed solution for each question. CBSE recommends NCERT books and most of the questions in … Important Questions for Class 12 Maths Chapter 3 matrices are provided here. Find K if D (K, 0) is a point such that area of, Using properties of determinants, prove that, © 2020 myCBSEguide | CBSE Papers & NCERT Solutions, {tex}\left| {\begin{array}{*{20}{c}} {1 – x}&2&3 \\ 0&{2 – x}&0 \\ 0&2&{3 – x} \end{array}} \right| = 0{/tex}, {tex}\left| {\begin{array}{*{20}{c}} {2\cos x}&1&0 \\ 1&{2\cos x}&1 \\ 0&1&{2\cos x} \end{array}} \right|{/tex}, {tex}\left| {\begin{array}{*{20}{c}} 1&4&{20} \\ 1&{ – 2}&5 \\ 1&{2x}&{5{x^2}} \end{array}} \right| = 0{/tex}, {tex}{\text{2 }} \times {\text{ 2}}{/tex}, {tex}\begin{vmatrix}2x&5\\8&x\end{vmatrix}=\begin{vmatrix}6&5\\8&3\end{vmatrix}{/tex}, {tex}A = \left[ {\begin{array}{*{20}{c}} 2&3 \\ 1&4 \end{array}} \right]. Every year you will get at least 1 - 3 questions in JEE Main and other exams, directly and indirectly, the concept of this chapter will be involved in many other chapters, like integral and differential calculus. MCQ Questions for Class 12 Chemistry with Answers were prepared based on the latest exam pattern. Determinants Class 12 […] 3. Students can solve NCERT Class 12 Business Studies Financial Management MCQs Pdf with Answers to know their preparation level. myCBSEguide has just released Chapter Wise Question Answers for class 12 Maths. JEE examiner ask question on every topic. myCBSEguide has just released Chapter Wise Question Answers for class 12 Maths. Ended on Jun 13, 2020. Question 5. Check the below NCERT MCQ Questions for Class 12 Biology Chapter 11 Biotechnology: Principles and Processes with Answers Pdf free download. A 9. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. The solved questions answers in this Test: Matrices & Determinants (Competition Level) quiz give you a good mix of easy questions and tough questions. Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 12 Linear Programming. \left [\begin {array} {ccc} 1 & x & x^ {2} \\ 1 & y & y^ {2} \\ 1 & z & z^ {2} \end {array}\right] (a) (x – y) (y + z) (z + x) (b) (x + y) (y – z) (z – x) (c) (x – y) (y – z) (z + x) (d) (x – y) (y – z) (z – x) Answer. StudiesToday.com brings here the biggest collection of Class 12 MCQ based online tests for CBSE Class 12 2020 exams to help you prepare properly and get highest rank in exams. If elements of a row (or a column) in a determinant can be expressed as the sum of two or more elements, then the given determinant can be expressed as the ________ of two or more determinants. Students can solve NCERT Class 12 Maths Linear Programming MCQs Pdf with Answers to know their preparation level. Matrices and determinants quiz questions and answers PDF, rectangular matrix quiz, column matrix quiz, multiplication of matrix quiz, homogeneous linear equations quiz, symmetric matrix quizzes for colleges offering online degree programs. Invertible functions: Relations and functions. Download latest questions with multiple choice answers for Class 12 Matrices and Determinants in pdf free or read online in online reader free. However, cracking the MCQ Questions for Class 12 Maths still needs a lot of critical thinking. Multiple Choice Questions (MCQ) for Determinants - CBSE Class 12-science Mathematics on Topperlearning. CBSE Class 12th Mathematics Chapter 4 - Determinants Question 10- Find the value of A -1 if: Using A -1 , solve the system of linear equations x - 2y = 10, 2x - y - z = 8 and - 2y + z = 7. Determinants Class 12 Maths RD Sharma Solutions are extremely helpful while doing your homwork or while preparing for the exam. We have provided Biotechnology: Principles and Processes Class 12 Biology MCQs Questions with Answers to help students understand the concept very well. We have Provided Reproduction in Plants Class 7 Science MCQs Questions with Answers to help students understand the concept very well. There will be total 10 MCQ in this test. CBSE Question Papers 12th Mathematics Chapter 4. If the equations a(y + z) = x, b(z + x) = y and c (x + y) = z, where a ¹ –1, b ¹ – 1, c ¹ –1 admit non-trivial solution, then (1 + a) –1 + (1 + b) –1 + (1 + c) –1 is (a) 2 (b) 1 (c) 1/2 (d) None of these. Question 1. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 10 Vector Algebra. Check the below NCERT MCQ Questions for Class 7 Science Chapter 12 Reproduction in Plants with Answers Pdf free download. NCERT Solutions, NCERT Exemplars, Revison Notes, Free Videos, CBSE Papers, MCQ Tests & more. Multiple choice questions and answers on Matrices and Determinants quiz answers PDF 1 to learn math certificate online course. Class 12 English MCQs Questions with Answers Flamingo, Vistas. Every year you will get at least 1 - 3 questions in JEE Main and other exams, directly and indirectly, the concept of this chapter will be involved in many other chapters, like integral and differential calculus. Determinants Class 12 Maths MCQs Pdf. English Mathematics. Practicing these CBSE NCERT MCQ Questions of Class 12 English with Answers Pdf of Flamingo, Vistas will guide students to do a quick revision for all the concepts present in each chapter and prepare for final exams. NCERT Solutions For Class 12 Maths Chapter 4 Determinants are available at BYJU’S which are given by our expert faculty. We have taken care of every single concept given in CBSE Class 12 Mathematics syllabus and questions are framed as per the latest marking scheme and blue print issued by CBSE for class 12. NCERT Solutions class 12 Maths Exercise 4.6 Class 12 Maths book solutions are available in PDF format for free download. 1. Here, the important questions for class 12 chapter 4 determinants are given here with solutions. D 10. Question 3. NCERT Solutions, NCERT Exemplars, Revison Notes, Free Videos, CBSE Papers, MCQ Tests & more. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number. RD Sharma Solutions are helpful in the preparation of several school level, graduate and undergraduate level competitive exams. Class 12 Maths HOTs - Matrices Determinants Questions Database for chapter Application of Derivatives.Based on CBSE and NCERT guidelines. NCERT Solutions For Class 12 Maths Chapter 4 Determinants are available at BYJU’S which are given by our expert faculty. We cannot multiply through a row by 0. with value –1. We wish the knowledge shed above regarding the Class 12 Maths MCQ Questions has been useful to you in some or the other way. The step by step solutions for all the questions enlisted under the chapter and each solution has been explained using suitable examples or formulas. Download latest MCQs for Class 12 all subjects in pdf free Let C be the subset of A consisting of all determinants. Ended on Oct 11, 2020. Answer: (d) (x – y) (y – z) (z – x) Question 1. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Register for online coaching for IIT JEE (Mains & Advanced), NEET, Engineering and Medical entrance exams. Matrices Class 12 […] Students who are looking for Multiple Choice Type Questions (MCQs) for all subjects can download from here. Students can practise these questions for the board examination to score well. Matrices and Determinants: In Mathematics, one of the interesting, easiest and important topic is Matrices and Determinants. Remember, we generally want to “correct” columns from left to right, so we will attack the position containing the 1 later. All Chapter 6 - Determinants Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. Multiplying a determinant by k means multiplying the elements of only one row (or one column) by ________. CBSE papers with answers and Determinants for chapter 4 Determinants class 12th Mathematics includes practice question papers with 10-12 questions in each test paper. Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 3 Matrices. Maths MCQ Questions for Class 12 with Answers Pdf Download. Then the equation of line AB is. These MCQ's are extremely critical for all CBSE students to score better marks. C. GENERAL MCQS Current Affairs General Knowledge Everyday Science Arithmetic/Mathematics Computer/IT English (Vocab&Grammar) MCQs SCIENCE MCQS General Science Biology Chemistry Physics Mathematics Statistics Medical Science NCERT Exemplar Class 12 Maths is very important resource for students preparing for XII Board Examination. To solve the system of linear equations and to find the inverse of a matrix, the determinants play an important role. Questions are expected in the various sections of the question paper corresponding to (i) Very Short Answer Type (VSA) Questions: 1 Mark, (ii) Short Answer Type (SA) Questions: 2 Marks, (iii) Long Answer Type I (LA-I) Questions: 4 Marks, and Harendra Lega. Important Questions for Class 12 Maths Class 12 Maths NCERT Solutions Home Page Algebra, coordinate geometry, You should have to have six to seven years question paper of jee mains and advanced both students so that you will get to know about the question level and paper pattern. Download free printable worksheets for CBSE Class 12 Matrices & Determinants with important topic wise questions, students must practice the NCERT Class 12 Matrices & Determinants worksheets, question banks, workbooks and exercises with solutions which will help them in revision of important concepts Class 12 Matrices & Determinants. Matrices and Determinants MCQs Sheet 1. Important 6 marks Questions for CBSE Class 12 Maths; Class 12 Chapter 4 Determinants Important Questions with Solutions. Students might perceive Multiple Choice Questions of Class 12 Maths as unchallenging and feel relaxed as they don’t have to answer lengthy answers. Kerala Syllabus 9th Standard Physics Solutions Guide, Kerala Syllabus 9th Standard Biology Solutions Guide, Chapter 2 Inverse Trigonometric Functions MCQs, Chapter 5 Continuity and Differentiability MCQs, Chapter 6 Application of Derivatives MCQs, Chapter 11 Three Dimensional Geometry MCQs, NCERT Solutions for Class 8 English Honeydew Chapter 9 The Great Stone Face 1, NCERT Solutions for Class 8 English Honeydew Chapter 8 A Short Monsoon Diary, NCERT Solutions for Class 8 English Honeydew Chapter 7 A Visit to Cambridge, NCERT Solutions for Class 8 English Honeydew Chapter 6 This is Jody’s Fawn, NCERT Solutions for Class 8 English Honeydew Chapter 5 The Summit Within, NCERT Solutions for Class 8 English Honeydew Chapter 4 Bepin Choudhury’s Lapse of Memory, NCERT Solutions for Class 8 English Honeydew Chapter 3 Glimpses of the Past, NCERT Solutions for Class 8 English Honeydew Chapter 2 The Tsunami, NCERT Solutions for Class 8 English Honeydew Chapter 1 The Best Christmas Present in the World, Ekarthak Shabd in Hindi | एकार्थक शब्द की परिभाषा एवं उनके भेद और उदाहरण (हिन्दी व्याकरण), Tatsam Tadbhav Shabd in Hindi | तत्सम तद्भव शब्द की परिभाषा एवं उनके भेद और उदाहरण (हिन्दी व्याकरण), Shabd Vichar in Hindi | शब्द विचार की परिभाषा एवं उनके भेद और उदाहरण (हिन्दी व्याकरण), Kriya Visheshan in Hindi | क्रिया विशेषण की परिभाषा एवं उनके भेद और उदाहरण (हिन्दी व्याकरण), Paryayvachi Shabd in Hindi | पर्यायवाची शब्द की परिभाषा एवं उनके भेद और उदाहरण (हिन्दी व्याकरण), Anek Shabdon Ke Liye Ek Shabd in Hindi | अनेक शब्दों के लिए एक शब्द की परिभाषा एवं उनके भेद और उदाहरण (हिन्दी व्याकरण). Class 12 math (India) Course summary; Relations and functions. Practicing NCERT Online Maths Objective Questions For Class 12 Pdf Answers is one of the best ways to prepare for the CBSE Class 12 board exam. Business Studies MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. 30 Most Expected Questions - Determinants ( Part - 02 ) Nov 9, 2020 • 1h 51m . 2. Question 4. About vaibhav chauhan Education is the process of facilitating learning, or the acquisition of knowledge, skills, values, beliefs, and habits. The solutions are given in a step-by-step procedure so that students can understand in an easy and a better way. There chapter wise Practice Questions with complete solutions are available for download in myCBSEguide website and mobile app. Realtime Solving - CBSE 2021 Sample Paper: Part A. There chapter wise Practice Questions with complete solutions are available for download in myCBSEguide website and mobile app. Composite functions: Relations and functions Intro to inverse functions: Relations and functions Verifying inverse functions by composition: Relations and functions. Download here the NCERT Solutions for class 12 Maths chapter 4 Determinants all exercises with miscellaneous exercise in Hindi Medium and English Medium in PDF for the new academic session 2020-2021. Question from very important topics are covered by NCERT Exemplar Class 12.You also get idea about the type of questions and method to answer in your class 12th … These Worksheets for Grade 12 Matrices & Determinants, class … Important Questions Class 12 Mathematics Determinants. We have provided Alcohols, Phenols and Ethers Class 12 Chemistry MCQs Questions with Answers to help students understand the concept very well. Matrices and Determinants Multiple Choice Questions (MCQs) Page-1. UP board solutions for class 12 Maths Chapter 4 are same as the NCERT Sols for 12th Maths Chapter 4. 1. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. Register online for Maths tuition on Vedantu.com to score more marks in CBSE board examination. ANSWERS: MATRICES AND DETERMINANTS QUIZ 6. Multiple Choice Questions have been coming in Class 12 Matrices and Determinants exams, thus do MCQs to test understanding of important topics in the chapters. Here we have provided NCERT Exemplar Problems Solutions along with NCERT Exemplar Problems Class 12.. Download Now . Multiple choice questions help to develop understanding of all key points of chapter. You can prepare effectively for the Class 12 Maths Exam as they help you be familiar with the kind of questions appearing in the exam. There chapter wise Practice Questions with complete solutions are available for download in myCBSEguide website and mobile app. 1. Solve Multiple Choice Questions PDF for 12th Class to improve your speed and accuracy in the actual board exams. These Questions with solution are prepared by our team of expert teachers who are teaching grade in CBSE … CBSE Class 12 Chapter 3 Matrices Extra Questions. The step by step solutions for all the questions enlisted under the chapter and each solution has been explained using suitable examples or formulas. Pages: 1 | 2. 12th Class Maths Objective Questions prevailing here will help you with this and aids you in achieving more marks in the exam. Free PDF Download of CBSE Business Studies Multiple Choice Questions for Class 12 with Answers Chapter 9 Financial Management. Mathematics → Matrices & Determinants MCQs. Practice these important problems, which are asked in the previous year board examination. This is possible only when you have the best CBSE Class 12 Maths study material and a smart preparation plan. However, cracking the MCQ Questions for Class 12 Maths still needs a lot of critical thinking. Matrices and Determinants carry a total of 12-13 marks in the CBSE Class XII Board Examination. Students can solve NCERT Class 12 Maths Linear Programming MCQs Pdf with Answers to know their preparation level. 2019 - 2020. If A is a matrix, then the determinant of a matrix A is generally represented using det (A) or |A|. Students might perceive Multiple Choice Questions of Class 12 Maths as unchallenging and feel relaxed as they don’t have to answer lengthy answers. This contains 30 Multiple Choice Questions for JEE Test: Matrices & Determinants (Competition Level) (mcq) to study with solutions a complete question bank. MCQ Questions for Class 7 Science with Answers were prepared based on the latest exam pattern. ... Hindi Mathematics. Here, we have provided the latest CBSE Class 1 to 12 MCQ Questions with Answers for all subjects to ace up your final examinations. NCERT Solutions class 12 Maths Exercise 4.5 Class 12 Maths book solutions are available in PDF format for free download. Important Questions Class 12 Maths Chapter 4 Determinants; Determinant of a Matrix . Tags # accountancy solutions. TN 12th Standard EM - Maths Application of Matrices and Determinants - Practice Test - Questions Practice Test. Download CBSE Class 12 Chemistry The Solid State MCQs in pdf, Chemistry chapter wise Multiple Choice Questions free, Q.1 Chottky defect defines imperfection in the lattice structure ofOption:(a) solid (b) gas(c) liquid (d) plasmaAnswer=AQ.2 An AB2 type structure is found inOption:(a) NaCl (b) CaF2(c) Al2O3 (d) N2OAnswer=BQ.3 An element (atomic mass 100 g/mol) having bcc Important Questions Class 12 Mathematics Determinants. myCBSEguide | CBSE Papers & NCERT Solutions. NCERT Exemplar Class 12 Maths is very important resource for students preparing for XII Board Examination. (Section 8.1: Matrices and Determinants) 8.12 We now want a “0” to replace the “4” in the bottom left. These Questions with solution are prepared by our team of expert teachers who are teaching grade in CBSE … UP Board students are also using following NCERT Textbooks for new session, so class 12 … Students can solve NCERT Class 12 Maths Determinants MCQs Pdf with Answers to know their preparation level. There are around 4-5 set of solved Chapter 4 Mathematics Extra Questions from each and every chapter. NCERT Solutions, NCERT Exemplars, Revison Notes, Free Videos, CBSE Papers, MCQ Tests & more. This questions will really help you in Preparation and Development of your Skills. We will learn. If you have any queries left answered feel free to reach us and we will get back to you. Check the below NCERT MCQ Questions for Class 12 Chemistry Chapter 11 Alcohols, Phenols and Ethers with Answers Pdf free download. Save my name, email, and website in this browser for the next time I comment. How to Create Worksheets using Test Generator? These ncert book chapter wise questions and answers are very helpful for CBSE board exam. Important 6 Marks Questions for Class 12 Maths CBSE Board. Candidates who are ambitious to qualify the Class 12 with good score can check this article for Notes. In order to score well try practicing the list of Multiple Choice Type Questions provided in the links below. What a determinant is, and its difference from matrix; Finding determinant for 2 x 2 and 3 x 3 matrix; Finding Area of Triangle using Determinant; Finding Equation of line using Determinants (We use Area of Triangle formula); Finding Minors and Cofactors of Determinant myCBSEguide has just released Chapter Wise Question Answers for class 12 Maths. If the order of matrix A is . 12th Class Maths Objective Questions prevailing here will help you with this and aids you in achieving more marks in the exam. Determinants Class 12 MCQs Questions with Answers. The following quizzes are from Matrices, Determinants, their properties & key facts. CBSE Maths notes, CBSE physics notes, CBSE chemistry notes. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Now, let us discuss how to find the determinant of 2×2 matrix and 3×3 matrix. Download MCQs for Class 12 all subjects, for important topics for all chapters in Class 12 all subjects based on CBSE and NCERT pattern. Matrices - Class 12 - IMP MCQs Solving. So Cover all the topic of NCERT Mathematics Class 10, 11, 12 glowing. English Mathematics. This test is Rated positive by 85% students preparing for JEE.This MCQ test is related to JEE syllabus, prepared by JEE teachers. Students can solve NCERT Class 12 Maths Matrices MCQs Pdf with Answers to know their preparation level. Furthermore, access the Chapter Wise MCQs of Class 12 Maths and prepare the topics and subtopics in it. NCERT MCQ's for class 9 to 12. So here are a few important 6 marks questions, which is a part of 12th maths important 10 marks questions for students, who aim to secure good percentage: Question 1- In answering a question on a multiple-choice test, a student either knows the answer or guesses. Subscribe and get the complete access of 12th Standard EM - Maths Multiple Choice One Mark Questions Online Test Pack and score high marks Let P (x, y) be any point on AB. Find the value of x for which the matrix A=\left [\begin {array} {ccc} 3-x & 2 & 2 \\ 2 & 4-x & 1 \\ -2 & -4 & -1-x \end {array}\right] is singular. Answers of all CBSE Class 12 Maths MCQs Multiple Choice Questions with Answers provided here with detailed solutions so that you can easily understand the logic behind each answer. Inverse trigonometric functions. Download Now . Oct 01,2020 - Test: Properties Of Determinants | 10 Questions MCQ Test has questions of JEE preparation. … According to the question, we have to evaluate. Class XII Maths Chapter 4 solutions is given here. NCERT Solutions for Class 11; CBSE Class 11 Notes; CBSE Sample Papers for Class 11; CBSE Guide for Class 10. Matrices and Determinants: In Mathematics, one of the interesting, easiest and important topic is Matrices and Determinants. Download here the NCERT Solutions for class 12 Maths chapter 4 Determinants all exercises with miscellaneous exercise in Hindi Medium and English Medium in PDF for the new academic session 2020-2021. Exercise 6.1 Class 12 Maths RD Sharma Solutions were prepared according to CBSE Guidelines {/tex}, {tex}A = \left[ {\begin{array}{*{20}{c}} 1&2 \\ 4&8 \end{array}} \right]{/tex}, {tex}2 \left| \begin{array} { r r } { 7 } & { – 2 } \\ { – 10 } & { 5 } \end{array} \right|{/tex}, {tex}\left| {\begin{array}{*{20}{c}} {\cos \alpha \cos \beta }&{\cos \alpha \sin \beta }&{ – \sin \alpha } \\ { – \sin \beta }&{\cos \beta }&0 \\ {\sin \alpha \cos \beta }&{\sin \alpha \sin \beta }&{\cos \alpha } \end{array}} \right|{/tex}, {tex} \left[ \begin{array} { c c c } { 1 } & { – 2 } & { 3 } \\ { 0 } & { – 1 } & { 4 } \\ { – 2 } & { 2 } & { 1 } \end{array} \right]{/tex}, {tex}A = \left[ {\begin{array}{*{20}{c}} 3&{ – 4} \\ { – 1}&2 \end{array}} \right],{/tex}, {tex} \left| \begin{array} { c c c } { b + c } & { c + a } & { a + b } \\ { q + r } & { r + p } & { p + q } \\ { y + z } & { z + x } & { x + y } \end{array} \right| = 2 \left| \begin{array} { c c c } { a } & { b } & { c } \\ { p } & { q } & { r } \\ { x } & { y } & { z } \end{array} \right|{/tex}, {tex}A = \left[ {\begin{array}{*{20}{c}} 1&{ – 1}&1 \\ 1&{ – 2}&{ – 2} \\ 2&1&3 \end{array}} \right]{/tex}, {tex}B = \left[ {\begin{array}{*{20}{c}} { – 4}&4&4 \\ { – 7}&1&3 \\ 5&{ – 3}&{ – 1} \end{array}} \right]{/tex}, {tex}\left| {\begin{array}{*{20}{c}} {1 – x}&2&3 \\ 0&{2 – x}&0 \\ 0&2&{3 – x} \end{array}} \right| = 0 \Rightarrow {/tex}, {tex} \left| {\begin{array}{*{20}{c}} {2\cos x}&1&0 \\ 1&{2\cos x}&1 \\ 0&1&{2\cos x} \end{array}} \right|{/tex}, {tex}\left| {\begin{array}{*{20}{c}} {2\cos \frac{\pi }{3}}&1&0 \\ 1&{2\cos \frac{\pi }{3}}&1 \\ 0&1&{2\cos \frac{\pi }{3}} \end{array}} \right| \\ {/tex}, {tex}\Rightarrow \left| {\begin{array}{*{20}{c}} {2.\frac{1}{2}}&1&0 \\ 1&{2.\frac{1}{2}}&1 \\ 0&1&{2.\frac{1}{2}} \end{array}} \right| \\{/tex}, {tex}\Rightarrow \left| {\begin{array}{*{20}{c}} 1&1&0 \\ 1&1&1 \\ 0&1&1 \end{array}} \right| {/tex}, {tex} \Rightarrow 1(0) – 1(1) = – 1 \\{/tex}, {tex}\left| {\begin{array}{*{20}{c}} 1&4&{20} \\ 0&{ – 6}&{ – 15} \\ 0&{2x – 4}&{5{x^2} – 20} \end{array}} \right| = 0{/tex}, {tex}adjA = \left[ {\begin{array}{*{20}{c}} 4&{ – 3} \\ { – 1}&2 \end{array}} \right]{/tex}, {tex}\left| A \right| = \left| {\begin{array}{*{20}{c}} 1&2 \\ 4&8 \end{array}} \right|{/tex}, {tex}2 \left| \begin{array} { r r } { 7 } & { – 2 } \\ { – 10 } & { 5 } \end{array} \right| = 2 [ 35 – ( 20 ) ]{/tex}, {tex}\Delta = \left| {\begin{array}{*{20}{c}} {\cos \alpha \cos \beta }&{\cos \alpha \sin \beta }&{ – \sin \alpha } \\ { – \sin \beta }&{\cos \beta }&0 \\ {\sin \alpha \cos \beta }&{\sin \alpha \sin \beta }&{\cos \alpha } \end{array}} \right|{/tex}, {tex}= \cos \alpha \cos \beta \left( {\cos \alpha \cos \beta – 0} \right) {/tex}, {tex}- \cos \alpha \sin \beta \left( { – \cos \alpha \sin \beta – 0} \right) {/tex}, {tex}- \sin \alpha \left( { – \sin \alpha {{\sin }^2}\beta – \sin \alpha {{\cos }^2}\beta } \right){/tex}, {tex}= {\cos ^2}\alpha {\cos ^2}\beta + {\cos ^2}\alpha {\sin ^2}\beta {/tex}, {tex}+ {\sin ^2}\alpha \left( {{{\sin }^2}\beta + {{\cos }^2}\beta } \right){/tex}, {tex}= {\cos ^2}\alpha \left( {{{\cos }^2}\beta + {{\sin }^2}\beta } \right){/tex}, {tex} + {\sin ^2}\alpha \left( {{{\sin }^2}\beta + {{\cos }^2}\beta } \right){/tex}, {tex}= {\cos ^2}\alpha + {\sin ^2}\alpha{/tex}, {tex}\Delta = \frac{1}{2}\left| {\begin{array}{*{20}{c}} {{x_1}}&{{y_1}}&1 \\ {{x_2}}&{{y_2}}&1 \\ {{x_3}}&{{y_3}}&1 \end{array}} \right|{/tex}, {tex}= \frac{1}{2}\left| {\begin{array}{*{20}{c}} 3&8&1 \\ { – 4}&2&1 \\ 5&1&1 \end{array}} \right|{/tex}, {tex} = \frac{1}{2}\left[ {3\left( {2 – 1} \right) – 8\left( { – 4 – 5} \right) + 1\left( { – 4 + 10} \right)} \right]{/tex}, {tex} = \frac{1}{2}\left[ {3 + 72 – 14} \right] = \frac{{61}}{2}{/tex}, {tex}\frac{1}{2}\left| {\begin{array}{*{20}{c}} 0&0&1 \\ 1&3&1 \\ x&y&1 \end{array}} \right| = 0{/tex}, {tex}\frac{1}{2}\left| {\begin{array}{*{20}{c}} 1&3&1 \\ 0&0&1 \\ K&0&1 \end{array}} \right| = \pm 3{/tex}, {tex} |A|=\left| \begin{array} { c c c } { 1 } & { – 2 } & { 3 } \\ { 0 } & { – 1 } & { 4 } \\ { – 2 } & { 2 } & { 1 } \end{array} \right|{/tex}, {tex} A _ { 11 } = ( – 1 ) ^ { 1 + 1 } \left| \begin{array} { c c } { – 1 } & { 4 } \\ { 2 } & { 1 } \end{array} \right| = ( – 1 – 8 ) = – 9{/tex}, {tex} A _ { 12 } = ( – 1 ) ^ { 1 } + 2 \left| \begin{array} { c c } { 0 } & { 4 } \\ { – 2 } & { 1 } \end{array} \right| = – ( 0 + 8 ) = – 8{/tex}, {tex} A _ { 13 } = ( – 1 ) ^ { 1 + 3 } \left| \begin{array} { c c } { 0 } & { -1 } \\ { – 2 } & { 2 } \end{array} \right| = ( 0 – 2 ) = – 2{/tex}, {tex} A _ { 21 } = ( – 1 ) ^ { 2 + 1 } \left| \begin{array} { c c } { – 2 } & { 3 } \\ { 2 } & { 1 } \end{array} \right| = – ( – 2 – 6 ) = 8{/tex}, {tex} A _ { 22 } = ( – 1 ) ^ { 2 + 2 } \left| \begin{array} { c c } { 1 } & { 3 } \\ { – 2 } & { 1 } \end{array} \right| = ( 1 + 6 ) = 7{/tex}, {tex} A _ { 23 } = ( – 1 ) ^ { 2 + 3 } \left| \begin{array} { c c } { 1 } & { – 2 } \\ { – 2 } & { 2 } \end{array} \right| = – ( 2 – 4 ) = 2{/tex}, {tex} A _ { 31 } = ( – 1 ) ^ { 3 + 1 } \left| \begin{array} { c c } { – 2 } & { 3 } \\ { – 1 } & { 4 } \end{array} \right| = ( – 8 + 3 ) = – 5{/tex}, {tex} A _ { 32 } = ( – 1 ) ^ { 3 + 2 } \left| \begin{array} { l l } { 1 } & { 3 } \\ { 0 } & { 4 } \end{array} \right| = – ( 4 – 0 ) = – 4{/tex}, {tex} A _ { 33 } = ( – 1 ) ^ { 3 +3 } \left| \begin{array} { c c } { 1 } & { – 2 } \\ { 0 } & { – 1 } \end{array} \right| = ( – 1 – 0 ) = – 1{/tex}, {tex} \left[ \begin{array} { l l l } { A _ { 11 } } & { A _ { 21 } } & { A _ { 31 } } \\ { A _ { 12 } } & { A _ { 22 } } & { A _ { 32 } } \\ { A _ { 13 } } & { A _ { 23 } } & { A _ { 33 } } \end{array} \right] = \left[ \begin{array} { c c c } { – 9 } & { 8 } & { – 5 } \\ { – 8 } & { 7 } & { – 4 } \\ { – 2 } & { 2 } & { – 1 } \end{array} \right]{/tex}, {tex} A ^ { -1 } = \frac { 1 } { | A | } \text { adj } A = \frac { 1 } { 1 } \left[ \begin{array} { c c c } { – 9 } & { 8 } & { – 5 } \\ { – 8 } & { 7 } & { – 4 } \\ { – 2 } & { 2 } & { – 1 } \end{array} \right]{/tex}, {tex} \left[ \begin{array} { c c c } { – 9 } & { 8 } & { – 5 } \\ { – 8 } & { 7 } & { – 4 } \\ { – 2 } & { 2 } & { – 1 } \end{array} \right]’ = \left[ \begin{array} { c c c } { – 9 } & { – 8 } & { – 2 } \\ { 8 } & { 7 } & { 2 } \\ { – 5 } & { – 4 } & { – 1 } \end{array} \right]{/tex}, {tex}adjA = \left[ {\begin{array}{*{20}{c}} 2&4 \\ 1&3 \end{array}} \right]{/tex}, {tex}{A^{ – 1}} = \frac{1}{{\left| A \right|}}\left( {adjA} \right){/tex}, {tex}= \frac{1}{2}\left[ {\begin{array}{*{20}{c}} 2&4 \\ 1&3 \end{array}} \right]{/tex}, {tex}= \left[ {\begin{array}{*{20}{c}} 1&2 \\ {\frac{1}{2}}&{\frac{3}{2}} \end{array}} \right]{/tex}, {tex}B = \left[ {\begin{array}{*{20}{c}} 1&2 \\ {\frac{1}{2}}&{\frac{3}{2}} \end{array}} \right]{/tex}, {tex} \left| \begin{array} { c c c c } { b + c } & { c + a } & { a + b } \\ { q + r } & { r + p } & { p + q } \\ { y + z } & { z + x } & { x + y } \end{array} \right| = 2 \left| \begin{array} { l l l } { a } & { b } & { c } \\ { p } & { q } & { r } \\ { x } & { y } & { z } \end{array} \right|{/tex}, {tex}\left| \begin{array} { c c c } { b + c } & { c + a } & { a + b } \\ { q + r } & { r + p } & { p + q } \\ { y + z } & { z + x } & { x + y } \end{array} \right|{/tex}, {tex}\Delta = \left| \begin{array} { c c c } { 2 ( a + b + c ) } & { c + a } & { a + b } \\ { 2 ( p + q + r ) } & { r + p } & { p + q } \\ { 2 ( x + y + z ) } & { z + x } & { x + y } \end{array} \right|{/tex}, {tex}\Delta = 2\left| {\begin{array}{*{20}{c}} {a + b + c}&{c + a}&{a + b} \\ {p + q + r}&{r + p}&{p + q} \\ {x + y + z}&{z + x}&{x + y} \end{array}} \right|{/tex}, {tex}\Delta = 2 \left| \begin{array} { c c c } { a + b + c } & { – b } & { – c } \\ { p + q + r } & { – q } & { – r } \\ { x + y + z } & { – y } & { – z } \end{array} \right|{/tex}, {tex}C_1\rightarrow C_1+C_2+C_3,we\ get,{/tex}, {tex}\Delta = 2 \left| \begin{array} { c c c } { a } & { – b } & { – c } \\ { p } & { – q } & { – r } \\ { x } & { – y } & { – z } \end{array} \right|{/tex}, {tex}\Delta = 2 \left| \begin{array} { l l l } { a } & { b } & { c } \\ { p } & { q } & { r } \\ { x } & { y } & { z } \end{array} \right|{/tex}, {tex}A = \left[ {\begin{array}{*{20}{c}} 1&{ – 1}&1 \\ 1&{ – 2}&{ – 2} \\ 2&1&3 \end{array}} \right]X = \left[ {\begin{array}{*{20}{c}} x \\ y \\ z \end{array}} \right]C = \left[ {\begin{array}{*{20}{c}} 4 \\ 9 \\ 1 \end{array}} \right]{/tex}, {tex}AB = \left[ {\begin{array}{*{20}{c}} 1&{ – 1}&1 \\ 1&{ – 2}&{ – 2} \\ 2&1&3 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} { – 4}&4&4 \\ { – 7}&1&3 \\ 5&{ – 3}&{ – 1} \end{array}} \right]{/tex}, {tex} = \left[ {\begin{array}{*{20}{c}} 8&0&0 \\ 0&8&0 \\ 0&0&8 \end{array}} \right]{/tex}, {tex}{A^{ – 1}} = \frac{1}{8}B\left[ \begin{gathered} \because {A^{ – 1}}AB = 8{A^{ – 1}}I \hfill \\ B = 8{A^{ – 1}} \hfill \\ \end{gathered} \right]{/tex}, {tex} = \frac{1}{8}\left[ {\begin{array}{*{20}{c}} { – 4}&4&4 \\ { – 7}&1&3 \\ 5&{ – 3}&{ – 1} \end{array}} \right]{/tex}, {tex}\left[ {\begin{array}{*{20}{c}} x \\ y \\ z \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 3 \\ { – 2} \\ { – 1} \end{array}} \right]{/tex}, CBSE Class 12 Chapter 3 Matrices Extra Questions, Class 12 Maths Inverse Trigonometric Functions Important Questions, Chapter 12 Probability Class 12 Mathematics Important Questions, CBSE Class 12 Mathematics Vector Algebra Extra Questions, Differential Equations Class 12 Mathematics Extra Questions, Integrals Class 12 Mathematics Chapter 7 Important Questions, Continuity and Differentiability Class 12 Mathematics Extra Question, Relations and Functions Extra Questions for Class 12 Mathematics, Free Online Test Series for CBSE Students, Case Study based Questions Class 10 Mathematics, CBSE Class 10 English Sample Paper 2020-21, How to add Subjective Questions in Online Tests, The Best Mobile App for CBSE and NCERT Syllabus.