CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

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Question 8 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by

if [8(2a+b a-2b 5c-d 4c+3d)] = [8(4 -3 11 24)], then value of a + b − c + 2d is :

(a) 8  (b) 10
(c) 4  (d) −8

This question is inspired from Example 5 - Chapter 3 Class 12   - Matrices

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Transcript

Question 8 if [■8(2𝑎+𝑏&𝑎−2𝑏@5𝑐−𝑑&4𝑐+3𝑑)] = [■8(4&−3@11&24)], then value of a + b − c + 2d is : (a) 8 (b) 10 (c) 4 (d) −8 Since matrices are equal. Their corresponding elements are equal 2a + b = 4 5c – d = 11 a – 2b = – 3 4c + 3d = 24 Solving these equations Since matrices are equal. Their corresponding elements are equal 2a + b = 4 5c – d = 11 a – 2b = – 3 4c + 3d = 24 Solving these equations Solving (1) 2a + b = 4 b = 4 – 2a Putting value of b in (3) a – 2b = – 3 Putting b = 4 – 2a a – 2(4 – 2a) = -3 a – 8 + 4a = -3 a + 4a = -3 + 8 5a = 5 a = 5/5 a = 1 From (1) 2a + b = 4 Putting a = 1 2(1) + b = 4 2 + b = 4 b = 4 – 2 b = 2 From (2) 5c – d = 11 5c = 11 + d 5c – 11 = d d = 5c – 11 Solving (4) 4c + 3d = 24 Putting d = 5c – 11 4c + 3(5c – 11) = 24 4c + 15c – 33 = 24 19c – 33 = 24 19c = 24 + 33 19c = 57 c = 57/19 c = 3 Now, d = 5c – 11 Putting c = 3 d = 5(3) – 11 d = 15 – 11 d = 4 Hence, a = 1, b = 2, c = 3 and d = 4 Thus, a + b − c + 2d = 1 + 2 − 3 + 2(4) = 8 So, the correct answer is (a)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.