JEE MATHS UNIT 3
QUIZ NO 4
TOTAL QUESTIONS = 20
1. The determinant of [[1, 2], [3, 4]] is
A. -2
B. 2
C. 1
D. 4
2. If A is a 2x2 matrix with det(A) = 3, then det(2A) is
A. 6
B. 12
C. 9
D. 18
3. The adjoint of the matrix [[2, 3], [1, 4]] is
A. [[4, -3], [-1, 2]]
B. [[4, 3], [1, 2]]
C. [[-4, 3], [-1, 2]]
D. [[2, -1], [-3, 4]]
4. If A and B are square matrices of the same order, then det(AB) is
A. det(A) + det(B)
B. det(A) * det(B)
C. det(A) - det(B)
D. det(A)/det(B)
5. The rank of the matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]] is
A. 1
B. 2
C. 3
D. 0
6. If A is a square matrix, then det(A^T) is equal to
A. det(A)
B. det(A)^2
C. -det(A)
D. 1/det(A)
7. The trace of the matrix [[1, 0, 0], [0, 2, 0], [0, 0, 3]] is
A. 6
B. 5
C. 1
D. 3
8. The determinant of a skew-symmetric matrix of odd order is always
A. 0
B. positive
C. negative
D. non-zero
9. 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
10. The inverse of the matrix [[2, 3], [1, 4]] is
A. [[4, -3], [-1, 2]]
B. [[2, -1], [-3, 4]]
C. [[1, -3], [-2, 4]]
D. none of these
11. A matrix A is singular if
A. det(A) ≠ 0
B. det(A) = 0
C. trace(A) = 0
D. adj(A) = 0
12. If A is a 2x2 matrix and det(A) = 7, then det(adj(A)) is
A. 49
B. 7
C. 1
D. 0
13. The determinant of the identity matrix of order n is
A. n
B. 0
C. 1
D. -1
14. If A = [[1, 2], [3, 4]], then adj(A) is
A. [[4, -2], [-3, 1]]
B. [[-4, 2], [3, -1]]
C. [[2, -1], [-3, 4]]
D. [[4, 3], [2, 1]]
15. The rank of the zero matrix of order 3x3 is
A. 1
B. 3
C. 0
D. undefined
16. If A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]], then det(A) is
A. 0
B. 9
C. 3
D. 15
17. If A and B are invertible matrices, then (AB)^-1 is
A. A^-1 * B^-1
B. B^-1 * A^-1
C. A^-1 * adj(B)
D. adj(A) * B^-1
18. The determinant of [[0, 1], [-1, 0]] is
A. -1
B. 0
C. 1
D. 2
19. If A is a diagonal matrix with diagonal elements 2, 3, and 5, then det(A) is
A. 30
B. 10
C. 0
D. 15
20. If A is a 2x2 matrix and det(A) = -3, then det(2A) is
A. -6
B. -12
C. -9
D. -18
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