JEE MATHS UNIT 3
QUIZ NO 3
TOTAL QUESTIONS = 20
1. The determinant of the matrix [[2, 3], [4, 6]] is
A. 12
B. 0
C. -12
D. 6
2. If A is a 2x2 matrix and det(A) = 5, then det(2A) is
A. 10
B. 20
C. 25
D. 40
3. If A and B are invertible matrices, then det(AB) is equal to
A. det(A) + det(B)
B. det(A) * det(B)
C. det(A) - det(B)
D. det(A)/det(B)
4. The determinant of an identity matrix of order n is
A. 0
B. 1
C. n
D. -1
5. The rank of a zero matrix is
A. 0
B. 1
C. undefined
D. equal to its order
6. If A is a square matrix, then det(A^T) is equal to
A. det(A)
B. -det(A)
C. 2det(A)
D. 0
7. If A is an invertible matrix, then adj(A) * A is equal to
A. 0
B. identity matrix
C. det(A)
D. A
8. The determinant of a singular matrix is
A. 1
B. 0
C. nonzero
D. undefined
9. If A is a 3x3 diagonal matrix with diagonal entries 2, 3, and 4, then det(A) is
A. 9
B. 24
C. 12
D. 20
10. The determinant of [[1, 2], [3, 4]] is
A. -2
B. 0
C. 1
D. 2
11. If A is a 2x2 matrix with det(A) = 7, then det(adj(A)) is
A. 49
B. 7
C. 1
D. 0
12. The trace of the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]] is
A. 6
B. 15
C. 45
D. 18
13. The determinant of a skew-symmetric matrix of odd order is
A. positive
B. negative
C. zero
D. undefined
14. If A is a square matrix and k is a scalar, then det(kA) is
A. k * det(A)
B. k^n * det(A)
C. k^2 * det(A)
D. det(A) / k
15. If A = [[1, 2], [3, 4]], then adj(A) is
A. [[4, -2], [-3, 1]]
B. [[-4, 2], [3, -1]]
C. [[1, -3], [-2, 4]]
D. [[4, 3], [2, 1]]
16. A square matrix A is called singular if
A. det(A) = 0
B. det(A) ≠ 0
C. adj(A) = 0
D. trace(A) = 0
17. If A and B are two matrices such that AB = BA, then det(AB) is
A. det(A) * det(B)
B. det(A) + det(B)
C. det(A) - det(B)
D. det(A) / det(B)
18. If A is a square matrix, then det(A^-1) is equal to
A. det(A)
B. 1/det(A)
C. -det(A)
D. det(A)^2
19. The determinant of [[3, 0, 0], [0, 5, 0], [0, 0, 7]] is
A. 15
B. 105
C. 35
D. 12
20. The inverse of [[1, 2], [3, 4]] is
A. [[4, -2], [-3, 1]]
B. [[-2, 1], [3, -4]]
C. [[-4, 2], [3, -1]]
D. [[2, -1], [-3, 4]]
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