Check the below NCERT MCQ Questions for Class 12 Maths Chapter 4 Determinants with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Determinants Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

## Determinants Class 12 MCQs Questions with Answers

Determinants Class 12 MCQ Questions Question 1.
$$\left[\begin{array}{ccc} 1 & x & x^{2} \\ 1 & y & y^{2} \\ 1 & z & z^{2} \end{array}\right]$$
(a) (x – y) (y + z)(z + x)
(b) (x + y) (y – z)(z – x)
(c) (x – y) (y – z)(z + x)
(d) (x – y) (y – z) (z – x)

Answer: (d) (x – y) (y – z) (z – x)

Determinants Class 12 MCQ Question 2.
The value of the determinant
$$\left[\begin{array}{ccc} 3 & 1 & 7 \\ 5 & 0 & 2 \\ 2 & 5 & 3 \end{array}\right]$$
(a) 124
(b) 125
(c) 134
(d) 144

MCQ Of Determinants Class 12 Question 3.
If a, b, c are in A.P. then the determinant
$$\left[\begin{array}{ccc} x+2 & x+3 & x+2a \\ x+3 & x+4 & x+2b \\ x+4 & x+5 & x+2c \end{array}\right]$$
(a) 1
(b) x
(c) 0
(d) 2x

Class 12 Maths Chapter 4 MCQ Question 4.
If w is a non-real root of the equation x² – 1 = 0. then
$$\left[\begin{array}{ccc} 1 & ω & ω^{2} \\ ω & ω^{2} & 1 \\ ω^{2} & 1 & ω \end{array}\right]$$ =
(a) 0
(b) 1
(c) ω
(d) ω²

Determinants MCQ Class 12 Question 5.
If Δ = $$\left[\begin{array}{cc} 10 & 2 \\ 30 & 6 \end{array}\right]$$ then A =
(a) 0
(b) 10
(c) 12
(d) 60

MCQ On Determinants Class 12 Question 6.
If 7 and 2 are two roots of the equation $$\left[\begin{array}{ccc} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \end{array}\right]$$ then the third root is
(a) -9
(b) 14
(c) $$\frac{1}{2}$$
(d) None of these

Determinants MCQs Class 12 Question 7.
If $$\left[\begin{array}{cc} x & 2 \\ 18 & x \end{array}\right]$$ = $$\left[\begin{array}{cc} 6 & 2 \\ 18 & 6 \end{array}\right]$$ x is equal to
(a) 6
(b) ±6
(c) -1
(d) -6

Determinants MCQs With Answers Class 12 Question 8.
$$\left[\begin{array}{ccc} 1 & a & a^{2}-bc \\ 1 & b & b^{2}-ca \\ 1 & c & c^{2}-ab \end{array}\right]$$ is equal to
(a) abc
(b) ab + bc + ca
(c) 0
(d) (a – b)(b – c)(c – a)

Determinant MCQ Class 12 Question 9.
A = $$\left[\begin{array}{ll} \alpha & q \\ q & \alpha \end{array}\right]$$ |A³| = 125 then α =
(a) ±3
(b) ±2
(c) ±5
(d) 0

Class 12 Determinants MCQ Question 10.
If a ≠ 0 and $$\left[\begin{array}{ccc} 1+a & 1 & 1 \\ 1 & 1+a & 1 \\ 1 & 1 & 1+a \end{array}\right]$$ = 0 then a =
(a) a = -3
(b) a = 0
(c) a = 1
(d) a = 3

MCQ Questions On Determinants Class 12 Question 11.
If x > 0 and x ≠ 1. y > 0. and y ≠ 1, z > 0 and z ≠ 1 then
$$\left[\begin{array}{ccc} 1 & log_{x}y & log_{x}z \\ log_{y}x & 1 & log_{y}z \\ log_{z}x & log_{z}y & 1 \end{array}\right]$$ is equal to
(a) 1
(b) -1
(c) 0
(d) None of these

Determinants MCQs Class 12 Question 12.
$$\left[\begin{array}{ccc} y+z & z & x \\ y & z+x & y \\ z & z & x+y \end{array}\right]$$ is equal to
(a) 6xyz
(b) xyz
(c) 4xyz
(d) xy + yz + zx

MCQ Of Chapter 4 Maths Class 12 Question 13.
If $$\left[\begin{array}{cc} 2 & 4 \\ 5 & 1 \end{array}\right]$$ = $$\left[\begin{array}{cc} 2x & 4 \\ 6 & x \end{array}\right]$$ then the value of x is
(a) ±2
(b) ±$$\frac{1}{3}$$
(c) ±√3
(d) ± (0.5)

MCQs On Determinants Class 12 Question 14.
If $$\left[\begin{array}{cc} 2x & 5 \\ 8 & x \end{array}\right]$$ = $$\left[\begin{array}{cc} 6 & -2 \\ 7 & 3 \end{array}\right]$$ then the value of x is
(a) 3
(b) ±3
(c) ±6
(d) 6

MCQ Determinants Class 12 Question 15.
The value of determinant $$\left[\begin{array}{ccc} a-b & b+c & a \\ b-c & c+a & b \\ c-a & a+b & c \end{array}\right]$$
(a) a³ + b³ + c ³
(b) 3bc
(c) a³ + b³ + c³ – 3abc
(d) None of these

Answer: (c) a³ + b³ + c³ – 3abc

MCQ On Determinants Class 12 With Solutions Question 16.
The area of a triangle with vertices (-3, 0) (3, 0) and (0, k) is 9 sq. units. The value of k will be
(a) 9
(b) 3
(c) -9
(d) 6

Class 12 Maths Ch 4 MCQ Question 17.
The determinant $$\left[\begin{array}{ccc} b^{2}-ab & b-c & bc-ac \\ ab-a^{2} & a-b & b^{2}-ab \\ bc-ac & c-a & ab-a^{2} \end{array}\right]$$ equals
(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

Ch 4 Maths Class 12 MCQ Question 18.
The number of distinct real roots of $$\left[\begin{array}{ccc} sin x & cos x & cos x \\ cos x & sin x & cos x \\ cos x & cos x & sin x \end{array}\right]$$ = 0 in the interval –$$\frac{π}{4}$$ ≤ x ≤ $$\frac{π}{4}$$ is
(a) 0
(b) 2
(c) 1
(d) 3

Chapter 4 Maths Class 12 MCQ Question 19.
If A, B and C are angles of a triangle, then the determinant
$$\left[\begin{array}{ccc} -1 & cos C & cos B \\ cos C & -1 & cos A \\ cos B & cos A & -1 \end{array}\right]$$
(a) 0
(b) -1
(c) 1
(d) None of these

MCQ On Matrices And Determinants Class 12 Question 20.
Let f(t) = $$\left[\begin{array}{ccc} cot t & t & 1 \\ 2 sin t & t & 2t \\ sin t & t & t \end{array}\right]$$ then $$_{t→0}^{lim}$$ $$\frac{f(t)}{t^2}$$ is equal to
(a) 0
(b) -1
(c) 2
(d) 3

Question 21.
The maximum value of $$\left[\begin{array}{ccc} 1 & 1 & 1 \\ 1 & 1+sin θ & 1 \\ 1+cos θ & 1 & 1 \end{array}\right]$$ is (θ is real number)
(a) $$\frac{1}{2}$$
(b) $$\frac{√3}{2}$$
(c) $$\frac{2√3}{4}$$
(d) √2

Answer: (a) $$\frac{1}{2}$$

Question 22.
If f(x) = $$\left[\begin{array}{ccc} 0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0 \end{array}\right]$$ then
(a) f(a) = 0
(b) f(b) = 0
(c) f(0) = 0
(d) f(1) = 0

Question 23.
If A = $$\left[\begin{array}{ccc} 2 & \lambda & -3 \\ 0 & 2 & 5 \\ 1 & 1 & 3 \end{array}\right]$$ then A-1 exists if
(a) λ = 2
(b) λ ≠ 2
(c) λ ≠ -2
(d) None of these

Question 24.
If A and B are invertible matrices, then which of the following is not correct?
(b) det (a)-1 = [det (a)]-1
(c) (AB)-1 = B-1A-1
(d) (A + B)-1 = B-1 + A-1

Answer: (d) (A + B)-1 = B-1 + A-1

Question 25.
If x, y, z are all different from zero and
$$\left[\begin{array}{ccc} 1+x & 1 & 1 \\ 1 & 1+y & 1 \\ 1 & 1 & 1+z \end{array}\right]$$ = 0, then value of x-1 + y-1 + z-1 is
(a) xyz
(b) x-1y-1z-1
(c) -x – y – z
(d) -1

Question 26.
The value of the determinant $$\left[\begin{array}{ccc} x & x+y & x+2y \\ x+2y & x & x+y \\ x+y & x+2y & x \end{array}\right]$$ is
(a) 9x² (x + y)
(b) 9y² (x + y)
(c) 3y² (x + y)
(d) 7x² (x + y)

Answer: (b) 9y² (x + y)

Question 27.
There are two values of a which makes determinant
Δ = $$\left[\begin{array}{ccc} 1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2a \end{array}\right]$$ = 86, then sum of these number is
(a) 4
(b) 5
(c) -4
(d) 9

Question 28.
Evaluate the determinant Δ = $$\left|\begin{array}{cc} log_{3}512 & log_{4}3 \\ log_{3}8 & log_{4}9 \end{array}\right|$$
(a) $$\frac{15}{2}$$
(b) 12
(c) $$\frac{14}{3}$$
(d) 6

Answer: (a) $$\frac{15}{2}$$

Question 29.
$$\left|\begin{array}{cc} x & -7 \\ x & 5 x+1 \end{array}\right|$$
(a) 3x² + 4
(b) x(5x + 8)
(c) 3x + 4x²
(d) x(3x + 4)

Question 30.
$$\left|\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \alpha \end{array}\right|$$
(a) 0
(b) 1
(c) 2
(d) 3

Question 31.
$$\left|\begin{array}{ll} \cos 15^{\circ} & \sin 15^{\circ} \\ \sin 75^{\circ} & \cos 75^{\circ} \end{array}\right|$$
(a) 0
(b) 5
(c) 3
(d) 7

Question 32.
$$\left|\begin{array}{cc} a+i b & c+i d \\ -c+i d & a-i b \end{array}\right|$$
(a) (a + b)²
(b) (a + b + c + d)²
(c) (a² + b² – c² – d²)
(d) a² + b² + c² + a²

Answer: (d) a² + b² + c² + a²

Question 33.
If $$\left|\begin{array}{lll} b+c & c+a & a+b \\ c+a & a+b & b+c \\ a+b & b+c & c+a \end{array}\right|$$ = $$k\left|\begin{array}{lll} a & b & c \\ b & c & a \\ c & a & b \end{array}\right|$$ then k =
(a) 0
(b) 1
(c) 2
(d) 3

Question 34.
If $$\left|\begin{array}{ccc} a-b-c & 2 a & 2 a \\ 2 b & b-c-a & 2 b \\ 2 c & 2 c & c-a-b \end{array}\right|$$ = k (a + b + c)³ then k is
(a) 0
(b) 1
(c) 2
(d) 3

Question 35.
$$\left|\begin{array}{lll} a+1 & a+2 & a+4 \\ a+3 & a+5 & a+8 \\ a+7 & a+10 & a+14 \end{array}\right|$$ =
(a) 2
(b) -2
(c) 4
(d) -4

Question 36.
If abc ≠ 0 and $$\left|\begin{array}{ccc} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \end{array}\right|$$ = 0 then $$\frac{1}{a}$$ + $$\frac{1}{b}$$ + $$\frac{1}{c}$$ =
(a) 1
(b) 2
(c) -1
(d) -3

Question 37.
$$\left|\begin{array}{ccc} 2 x y & x^{2} & y^{2} \\ x^{2} & y^{2} & 2 x y \\ y^{2} & 2 x y & x^{2} \end{array}\right|$$ =
(a) (x³ + y³)²
(b) (x² + y²)³
(c) -(x² + y²)³
(d) -(x³ + y³)²

Question 38.
$$\left|\begin{array}{ccc} b^{2} c^{2} & b c & b+c \\ c^{2} a^{2} & c a & c+a \\ a^{2} b^{2} & a b & a+b \end{array}\right|$$ =
(a) a7 + b7 + c7
(b) (a + b + c)7
(c) (a² + b² + c²) (a5 + b5 + c5)
(d) 0

Question 39.
If a, b, c are cube roots of unity, then
$$\left|\begin{array}{lll} e^{a} & e^{2 a} & e^{3 a}-1 \\ e^{b} & e^{2 b} & e^{3 b}-1 \\ e^{c} & e^{2 c} & e^{3 c}-1 \end{array}\right|$$ =
(a) 0
(b) e
(c) e²
(d) e³

Question 40.
The value of
$$\left|\begin{array}{ccc} \cos (\alpha+\beta) & -\sin (\alpha+\beta) & \cos 2 \beta \\ \sin \alpha & \cos \alpha & \sin \beta \\ -\cos \alpha & \sin \alpha & \cos \beta \end{array}\right|$$
is independent of
(a) α
(b) β
(c) α.β
(d) None of these

Question 41.
If x is a complex root of the equation
$$\left|\begin{array}{lll} 1 & x & x \\ x & 1 & x \\ x & x & 1 \end{array}\right|$$ + $$\left|\begin{array}{ccc} 1-x & 1 & 1 \\ 1 & 1-x & 1 \\ 1 & 1 & 1-x \end{array}\right|$$ = 0
then x2007 + x-2007 =
(a) 1
(b) -1
(c) -2
(d) 2

Question 42.
$$\left|\begin{array}{lll} b-c & c-a & a-b \\ c-a & a-b & b-c \\ a-b & b-c & c-a \end{array}\right|$$ =
(a) 0
(b) 1
(c) 2
(d) 3

Question 43.
Let Δ = $$\left|\begin{array}{ccc} x & y & z \\ x^{2} & y^{2} & z^{2} \\ x^{3} & y^{3} & z^{3} \end{array}\right|$$ then the value of Δ is
(a) (x – y) (y- z)(z – x)
(b) xyz
(c) x² + y² + z²)²
(d) xyz (x – y)(y – z) (z – x)

Answer: (d) xyz (x – y)(y – z) (z – x)

Question 44.
The value of the determinant $$\left|\begin{array}{ccc} \alpha & \beta & \gamma \\ \alpha^{2} & \beta^{2} & \gamma^{2} \\ \beta+\gamma & \gamma+\alpha & \alpha+\beta \end{array}\right|$$
(a) (α + β)(β + γ)(γ + α)
(b) (α – β)(β – γ) (γ – α) (α + β + γ)
(c) (α + β + γ)² (α – β – γ)²
(d) αβγ (α + β + γ)