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Class 12 Maths Chapter 4: Determinants MCQs with answers

10 multiple-choice questions on Determinants, each with its answer and the reason, written from the NCERT chapter. For the CBSE board and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
The value of the determinant |[[5, −3], [2, 4]]| is
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Answer: (c) 26

|[[5, −3], [2, 4]]| = 5(4) − (−3)(2) = 20 + 6 = 26. Taking +6 as −6 gives 14.

Question 2
The value of |A| for A = [[3, 0, 2], [1, 4, 0], [−2, 1, 5]] is
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Answer: (c) 78

Expand along R₁ (it has a zero): |A| = 3(4·5 − 0·1) − 0 + 2(1·1 − 4·(−2)) = 3(20) + 2(9) = 60 + 18 = 78.

Question 3
If |[[x, 4], [3, x]]| = |[[5, 2], [7, 4]]| and x > 0, then x is
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Answer: (a) 3√2

x2 − 12 = 20 − 14 = 6, so x2 = 18 and, as x > 0, x = √18 = 3√2.

Question 4
A is a square matrix of order 3 with |A| = 4. Then |2A| is
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Answer: (d) 32

For order n, |kA| = kⁿ|A|. Here n = 3, so |2A| = 23 × 4 = 32. Writing 2|A| gives 8; 22|A| gives 16.

Question 5
The area of the triangle with vertices (1, 2), (4, −1) and (6, 5), in square units, is
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Answer: (d) 12

Area = 12|1(−1 − 5) + 4(5 − 2) + 6(2 − (−1))| = 12|−6 + 12 + 18| = 12(24) = 12. Leaving out the half gives 24.

Question 6
In the determinant |[[4, −1, 2], [3, 5, 0], [−2, 6, 1]]|, the minor M₃₂ of the element 6 is
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Answer: (a) −6

Delete row 3 and column 2: M₃₂ = |[[4, 2], [3, 0]]| = 4(0) − 2(3) = −6. The cofactor A₃₂ = (−1)5(−6) = 6 is the distractor.

Question 7
In the determinant |[[2, 7, −3], [1, 0, 4], [5, −2, 6]]|, the cofactor A₂₃ of the element 4 is
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Answer: (d) 39

M₂₃ = |[[2, 7], [5, −2]]| = −4 − 35 = −39, and A₂₃ = (−1)2+3 M₂₃ = −(−39) = 39.

Question 8
The adjoint of A = [[6, −2], [5, 3]] is
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Answer: (b) [[3, 2], [−5, 6]]

For a 2 × 2 matrix, interchange a₁₁ and a₂₂ and change the signs of a₁₂ and a₂₁: adj A = [[3, 2], [−5, 6]]. [[3, −5], [2, 6]] is the cofactor matrix, not its transpose.

Question 9
The matrix [[k, 6], [3, 2]] is singular when k is
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Answer: (c) 9

Singular means the determinant is 0: 2k − 18 = 0, so k = 9.

Question 10
The system x + 2y = 3, 2x + 4y = 7 is
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Answer: (a) inconsistent, as it has no solution

Doubling the first equation gives 2x + 4y = 6, which cannot also equal 7. No (x, y) satisfies both, so the system is inconsistent.

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