# MCQs For NCERT Class 12 Mathematics Chapter 4 Determinants

Please refer to the MCQ Questions for Class 12 Mathematics Chapter 4 Determinants with Answers. The following Determinants Class 12 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 12. Our experts have designed MCQ Questions for Class 12 Mathematics with Answers for all chapters in your NCERT Class 12 Mathematics book.

## Determinants Class 12 MCQ Questions with Answers

See below Determinants Class 12 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

Question. If the area of a triangle with vertices (-3, 0), (3, 0) and (0, k) is 9 sq units. Then, the value of k will be
(a) 9
(b) 3
(c) -9
(d) 6

B

Question: If α,β,Y ∈ R, then the determinant

(a) independent of α, β and y
(b) dependent on α β , and y
(c) independent of α,β
(d) independent of α,y

A

Question:

(a) 4
(b) 6
(c) 7
(d) 8

C

Question:

polynomial of degree
(a) 2
(b) 3
(c) atmost 2
(d) atmost 3

C

Question: The determinant Δ=

divisible by
(a) x
(b) x2
(c) x3
(d) x4

(A,B,C,D)

Question: Let f(x)=

where the symbols have their usual meanings. The f (x ) is divisible by
(a) n2 +n + 1
(b) (n + 1)!
(c) n!
(d) None of these

(A,C)

Question:

(a) Re(z) = 4
(b) lm (z) = 0
(c) Re(z) = – 4
(d) lm (z) = – 1

(B,C)

Question: The determinant Δ =

equal to zero, if
(a) a, b, c  are in AP
(b) a, b, c are in GP
(c) a, b, c  are in HP
(d) α is the root of ax2+ 2bx +c 2=0

(B,D)

Question:

(B,C)

Question:

(a) 1
(b) – 1
(c) 0
(d) p+ q+ r

(A,C)

Question:

(a)1
(b) 2
(c) – 2
(d) None of these

(B,C)

Question: The equation

=0 has
(a) exactly two distinct roots
(b) one pair of equal real roots
(c) modulus of each root 1
(d) three pairs of equal roots .

(B,C,D)

Question:

(a) x
(b) y
(c) n
(d) z .

(A,B,C,D)

Question:  Suppose x, y, z  are positive and none of x, y, z is 1. If

independent of
(a) x
(b) y
(c) y and z only
(d) z   40 .

(A,B,D)

Question: If D=

for xy ≠ 0, then D is divisible by
(a) both x and y
(b) x but not y
(c) y but not x
(d) niether x nor y

A

Question:  Let a, b and c be any real numbers. Suppose that there are real numbers x, y and z not all zero such that x = cy+ bz, y =az+cx and z=bx+ay.  Then, a2+ b2+ c2 +2 is equal to
(a) 1
(b) 2
(c) – 1
(d) 0

A

Question:  Let a, b  and  c be such that (b +c)≠ 0.If

then the value of n is
(a) zero
(b) any even integer
(c) any odd integer
(d) any integer

C

Question: If a2+b2+c2=-2 and

then f (x) is a polynomial of degree
(a) 0
(b) 1
(c) 2
(d) 3

C

Question. The determinant

a) abc (b – c)(c – a)(a – b)
(b) (b – c)(c – a)(a – b)
(c) (a + b + c)(b – c)(c – a)(a – b)
(d) None of these

D

Question.

(a) 3
(b) ± 3
(c) ± 6
(d) 6

C

Question.

(a) a3 + b3 + c3
(b) 3bc
(c) a3 + b3 + c3 – 3abc
(d) None of these

D

Question. The number of distinct real roots of

(a) 0
(b) 2
(c) 1
(d) 3

C

Question. If x, y and z are all different from zero and

then the value of x-1 + y-1 + z-1 is
(a) xyz
(b) x-1 y-1 z-1
(c) -x – y – z
(d) -1

D

Question.

(a) 9x2 (x + y)
(b) 9y2 (x + y)
(c) 3y2 (x + y)
(d) 7x2 (x + y)

B

Question. The maximum value of

(a) 1/2
(b) √3/2
(c) √2
(d) 2√3/4

A

Question.

(a) f(a) = 0
(b) f(b) = 0
(c) f(0) = 0
(d) f (1) = 0

C

Question. If A, B and C are angles of a triangle, then the determinant

(a) 0
(b) -1
(c) 1
(d) None of these

A

Question.

(a) 0
(b) -1
(c) 2
(d) 3

A

Question.

(a) λ = 2
(b) λ ≠ 2
(c) λ ≠ -2
(d) None of these

D

Question. If A and B are invertible matrices, then which of the following is not correct?
(a) adj A = |A| · A-1
(b) det (A)-1 = [det (A)]-1
(c) (AB)-1
(d) (A + B)-1 = B-1+ A-1

D

Question. If there are two values of a which makes determinant,

(a) 4
(b) 5
(c) – 4
(d) 9

C

True/False

Question.

True

Question. |adj A| =| A|2, where A is a square matrix of order two.

False

Question. |A-1| ≠ |A|-1, where A is a non-singular matrix.

False

Question. (A3)-1 = (A-1)3. where A is a square matrix and |A| ≠ 0.

True

Question.

False

Question.

True

Question. If A and B are matrices of order 3 and | A| = 5, |B| = 3, then |3AB| = 27 x 5 x 3 = 405.

True

Question. If the value of a third order determinant is 12, then the value of the determinant formed by replacing each element by its cofactor will be 144.

True

Question.

splits into exactly k determinants of order 3, each element of which contains only one term, then the value of k is 8.

True

Question.

True

Question.

True

Consider the determinant

Mij denotes the minor of an element in ith row and jth column and Cij denotes the cofactor of an element in ith row and jth column. Question:  The value of q· M12– y·M22+ m· M 32 is
(a) 0
(b) –Δ
(c) Δ
(d) Δ

B

Question: The value of x· C21+ y· C22 + z·C23 is
(a) 0
(b) –Δ
(c) Δ
(d) Δ2

C

Question:  The value of p· C21+ q· C22+ r· C 23 is
(a) 0
(b) –Δ
(c) Δ
(d) Δ2

A

A3 x3  determinant has its entries as either 1 or – 1. The number of such determinants is 29= 512. We wil call a 3x 3 ´ determinant with entires 1 or – 1 as minus special, if product of elements of any rows or any columns is – 1 for example

Question:  The minimum value of a 3×3  minus special determinant is
(a) – 6
(b) – 4
(c) – 2
(d) 0

B

Question:  The number of n x n  minus special determinants must be
(a) 2n – 1
(b) 2(n-1)2
(c) 13n2-37n+26/2
(d) 2

B

Question:  The number of 3×3  minus special determinants must be
(a) 10
(b) 12
(c) 16
(d) 18

C

Each of these questions contains two statements : Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.
(a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
(b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
(c) Statement I is true; Statement II is false.
(d) Statement I is false; Statement II is true.

Question: Statement I

then coefficient of x in f (x ) is zero.

A

Question: Let x, y, z are three integers lying between 1 and 9 such that x51 y41 , and z31 are three digit numbers.

Statement I The value of the determinant

Statement II The value of a determinant is zero, if the entries in any two rows (or columns) of the determinant are correspondingly proportional.

D

Question:

A

Question: