CBSE Class 12 Mathematics Determinants MCQs Set A

Question: For 3 × 3 matrices M and N, which of the following statement(s) is (are) not correct ?
(a) T N M N is symmetric or skew-symmetric, according as M is symmetric or skew-symmetric
(b) MN – NM is is symmetric for all symmetric matrices M and N
(c) M N is symmetric for all symmetric matrices M and N
(d) (adj M) (adj N) = adj (MN) for all invertible matrices M and N

Answer: c,d

Question: If ω is a cube root of unity and △ (Image 80) then △2 is equal to:
(a) −ω
(b) ω
(c) 1
(d) ω2

Answer: b

Question: If the system of linear equations x + 2ay + az = 0 x + 3by + bz = 0, x +3cy + cz = 0 has a non-zero solution, then a,b,c ?
(a) Are in AP.
(b) Are in G.P.
(c) Are in H.P.
(d) Satisfy

Answer: c

Question: If the value of a third order determinant is 11, then the value of the square of the determinant formed by the cofactors will be:
(a) 11
(b) 121
(c) 1331
(d) 14641

Answer: d

Question: Let M be a 2 × 2 symmetric matrix with integer entries. Then, M is invertible, if:
(a) the first column of M is the transpose of the second row of M
(b) the second row of M is the transpose of the first column of M
(c) M is a diagonal matrix with non-zero entries in the main diagonal
(d) the product of entries in the main diagonal of M is not the square of an integer.

Answer: c,d

Question: If the system of equations x+ ay= 0, az+y = 0 and ax+ z + = 0 has infinite solutions, then the value of a is
(a) 0
(b) – 1
(c) 1
(d) no real values

Answer: c

Question: The equations x+ y + z = 6, x + 2y +3z =10, x+2y +mz = n give infinite number of values of the triplet (x, y, z) if:
(a) m = 3, n ∈ R
(b) m = 3, n ≠ 10
(c) m = 3, n = 10
(d) None of these

Answer: c

Question: The three lines ax + by + c = 0, bx + cy + a = 0, cx + ay + b = 0 are concurrent only when:
(a) a + b + c = 0
(b) a2 + b2 + c2 = ab + bc + ca
(c) a3 + b3 + c3 = ab + bc + ca
(d) None of these

Answer: a,b

Question: If the system of equations x + 2y − 3z =1, (k + 3)z = 3, (2k +1)x + z = 0 is inconsistent, then the value of k is:
(a) –3
(b) 1/2
(c) 0
(d) 2

Answer: a

Assertion and Reason

Note: Read the Assertion (A) and Reason (R) carefully to mark the correct option out of the options given below:
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
e. If assertion is false but reason is true.

Question: Let A be a 2×2 matrix with non-zero entries and let A2 =I
where I is 2×2 identity matrix. Define Tr (A) = sum of diagonal elements of A and |A| = determinant of matrix A:
Assertion: Tr (A) =0
Reason: |A|=1.

Answer: b

Question: Let A be a 2×2matrix
Assertion: adj(adjA) = A
Reason: |adjA| = |A|

Answer: b

Question: Assertion: If A∈Mn(R), A ≠ O with det (A) = 0, then det
(Adj A) = 0
Reason: For (R), A∈Mn det (Adj A) = (det 1 )n An-1
Answer: a

Question: Consider the system of equations x − 2y + 3z = −1,
x − 3y + 4z =1 and −x + y − 2z = k

Answer: a