Stay in touch with our site for more information on MCQ Questions of various subjects for different classes. Get Free RD Sharma Class 12 Solutions Chapter 6 Ex 6.1. Check the below NCERT MCQ Questions for Class 12 Biology Chapter 11 Biotechnology: Principles and Processes with Answers Pdf free download. Answer: (d) (x – y) (y – z) (z – x) 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. Multiple choice questions and answers on Matrices and Determinants quiz answers PDF 1 to learn math certificate online course. There will be total 10 MCQ in this test. 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. Register for online coaching for IIT JEE (Mains & Advanced), NEET, Engineering and Medical entrance exams. These Questions with solution are prepared by our team of expert teachers who are teaching grade in CBSE … Composite functions: Relations and functions Intro to inverse functions: Relations and functions Verifying inverse functions by composition: Relations and functions. Here we have provided NCERT Exemplar Problems Solutions along with NCERT Exemplar Problems Class 12.. 2. Free PDF download of Important Questions for CBSE Class 12 Maths Chapter 5 - Continuity and Differentiability prepared by expert Maths teachers from latest edition of CBSE(NCERT) books. Determinants Class 12 Maths MCQs Pdf. According to the question,we have to use properties of determinants to prove that. To solve the system of linear equations and to find the inverse of a matrix, the determinants play an important role. Here, the important questions for class 12 chapter 4 determinants are given here with solutions. 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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 ANSWERS: MATRICES AND DETERMINANTS QUIZ 6. Class XII Maths Chapter 4 solutions is given here. 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. Check the below NCERT MCQ Questions for Class 7 Science Chapter 12 Reproduction in Plants with Answers Pdf free download. Students can solve NCERT Class 12 Business Studies Financial Management MCQs Pdf with Answers to know their preparation level. If you have any queries left answered feel free to reach us and we will get back to you. 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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. Remember, we generally want to “correct” columns from left to right, so we will attack the position containing the 1 later. Let C be the subset of A consisting of all determinants. NCERT Solutions class 12 Maths Exercise 4.3 Class 12 Maths book solutions are available in PDF format for free download. Class 12 Maths Determinant – Get here the Notes for Class 12 Maths Determinant. 12th Class Maths Objective Questions prevailing here will help you with this and aids you in achieving more marks in the exam. 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. Learn Chapter 4 Determinants of Class 12 free with solutions of all NCERT Questions for CBSE Maths . These Questions with solution are prepared by our team of expert teachers who are teaching grade in CBSE schools for years. Question 3. 12th Class Maths Objective Questions prevailing here will help you with this and aids you in achieving more marks in the exam. Important Questions Class 12 Mathematics Determinants. Realtime Solving - CBSE 2021 Sample Paper: Part A. The step by step solutions for all the questions enlisted under the chapter and each solution has been explained using suitable examples or formulas. CBSE Class 12 Chapter 3 Matrices Extra Questions. The following quizzes are from Matrices, Determinants, their properties & key facts. Question 1. CBSE recommends NCERT books and most of the questions in … These Questions with solution are prepared by our team of expert teachers who are teaching grade in CBSE … myCBSEguide | CBSE Papers & NCERT Solutions. Subscribe and get the complete access of 12th Standard EM - Maths Multiple Choice One Mark Questions Online Test Pack and score high marks If A is a matrix, then the determinant of a matrix A is generally represented using det (A) or |A|. 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. The solved questions answers in this Test: Matrices & Determinants (Competition Level) quiz give you a good mix of easy questions and tough questions. NCERT Exemplar Class 12 Maths is very important resource for students preparing for XII Board Examination. However, cracking the MCQ Questions for Class 12 Maths still needs a lot of critical thinking. Register online for Maths tuition on Vedantu.com to score more marks in CBSE board examination. 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Important Questions for Class 12 Maths Chapter 3 matrices are provided here. \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. D 10. Here we have provided NCERT Exemplar Problems Solutions along with NCERT Exemplar Problems Class 12.. So Cover all the topic of NCERT Mathematics Class 10, 11, 12 glowing. 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. NCERT Solutions For Class 12 Maths Chapter 4 Determinants are available at BYJU’S which are given by our expert faculty. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. … Determinants Class 12 […] Matrices and Determinants Multiple Choice Questions (MCQs) Page-1. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. The important questions are taken as per the syllabus of CBSE board. 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. NCERT Solutions, NCERT Exemplars, Revison Notes, Free Videos, CBSE Papers, MCQ Tests & more. {/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. 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