# MCQ Questions for Class 12 Maths Chapter 4 Determinants with Answers - Learn Hool

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

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)

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

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

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

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

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

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

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)

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

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

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

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

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)

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

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

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

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

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

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

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

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

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|) = (kleft|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)

Answer: (b) (α – β)(β – γ) (γ – α) (α + β + γ)

We hope the given NCERT MCQ Questions for Class 12 Maths Chapter 4 Determinants with Answers Pdf free download will help you. If you have any queries regarding Determinants CBSE Class 12 Maths MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.

@ Designed By : Vikas Copyright 2023 @ LearnHool.In