if [8(2a+b a-2b 5c-d 4c+3d)] = [8(4 -3 11 24)], then value of a + b β c + 2d is :
(a) 8Β (b) 10
(c) 4Β (d) β8
This question is inspired from Example 5 - Chapter 3 Class 12 Β - Matrices
Last updated at Sept. 4, 2021 by
This question is inspired from Example 5 - Chapter 3 Class 12 Β - Matrices
Transcript
Question 8 if [β 8(2π+π&πβ2π@5πβπ&4π+3π)] = [β 8(4&β3@11&24)], then value of a + b β c + 2d is : (a) 8 (b) 10 (c) 4 (d) β8 Since matrices are equal. Their corresponding elements are equal 2a + b = 4 5c β d = 11 a β 2b = β 3 4c + 3d = 24 Solving these equations Since matrices are equal. Their corresponding elements are equal 2a + b = 4 5c β d = 11 a β 2b = β 3 4c + 3d = 24 Solving these equations Solving (1) 2a + b = 4 b = 4 β 2a Putting value of b in (3) a β 2b = β 3 Putting b = 4 β 2a a β 2(4 β 2a) = -3 a β 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 β 2 b = 2 From (2) 5c β d = 11 5c = 11 + d 5c β 11 = d d = 5c β 11 Solving (4) 4c + 3d = 24 Putting d = 5c β 11 4c + 3(5c β 11) = 24 4c + 15c β 33 = 24 19c β 33 = 24 19c = 24 + 33 19c = 57 c = 57/19 c = 3 Now, d = 5c β 11 Putting c = 3 d = 5(3) β 11 d = 15 β 11 d = 4 Hence, a = 1, b = 2, c = 3 and d = 4 Thus, a + b β c + 2d = 1 + 2 β 3 + 2(4) = 8 So, the correct answer is (a)
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CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)
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