JEE MATHS UNIT 3
QUIZ NO 1
TOTAL QUESTIONS = 20
1. If A is a 2x2 matrix with det(A) = 5, then det(3A) is
A. 15
B. 45
C. 25
D. 75
2. The determinant of a singular matrix is
A. 1
B. 0
C. infinity
D. -1
3. If A and B are two matrices such that AB = BA = I, then B is
A. inverse of A
B. transpose of A
C. adjoint of A
D. none of these
4. The determinant of the matrix [[2, 3], [1, 4]] is
A. 5
B. 8
C. 7
D. 2
5. The rank of a 3x3 identity matrix is
A. 0
B. 1
C. 2
D. 3
6. If A is a square matrix, then adjoint(adj(A)) is equal to
A. A
B. A^2
C. adj(A)
D. det(A) * A
7. The value of the determinant of [[1, 0, 0], [0, 2, 0], [0, 0, 3]] is
A. 1
B. 6
C. 5
D. 3
8. If A is a 3x3 matrix with det(A) = 4, then det(A^T) is
A. 4
B. -4
C. 0
D. 1
9. The determinant of [[1, 2], [3, 4]] is
A. -2
B. -1
C. 0
D. 1
10. A square matrix A is invertible if and only if
A. det(A) = 0
B. det(A) ≠ 0
C. adj(A) = 0
D. adj(A) ≠ 0
11. The inverse of the matrix [[1, 1], [1, -1]] is
A. [[1, 1], [-1, 1]]
B. [[1, -1], [1, 1]]
C. [[1/2, 1/2], [-1/2, 1/2]]
D. none of these
12. The trace of a matrix is the
A. sum of diagonal elements
B. product of diagonal elements
C. determinant of the matrix
D. sum of all elements
13. The determinant of a skew-symmetric matrix of odd order is always
A. positive
B. negative
C. zero
D. one
14. If A is a square matrix, then det(kA), where k is a scalar, is
A. k * det(A)
B. k^2 * det(A)
C. k^n * det(A)
D. det(A)/k
15. 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/B)
16. The adjoint of [[2, 3], [4, 5]] is
A. [[5, -3], [-4, 2]]
B. [[5, -4], [-3, 2]]
C. [[5, 4], [3, 2]]
D. [[2, -4], [3, 5]]
17. A matrix is said to be singular if
A. det(A) ≠ 0
B. adj(A) = 0
C. det(A) = 0
D. trace(A) = 0
18. The determinant of a diagonal matrix is equal to
A. 0
B. the sum of diagonal elements
C. the product of diagonal elements
D. 1
19. If A = [[1, 2], [3, 4]], then adj(A) is
A. [[4, -2], [-3, 1]]
B. [[4, -3], [-2, 1]]
C. [[1, -2], [-3, 4]]
D. [[4, -3], [2, -1]]
20. The value of det(A^T A) for any square matrix A is
A. negative
B. zero
C. positive
D. none of these
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