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 May 29, 2023 by Teachoo

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

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)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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