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
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
Answer
Answer: (c) 134
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
Answer
Answer: (c) 0
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
Answer
Answer: (a) 0
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
Answer
Answer: (a) 0
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
Answer
Answer: (a) -9
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
Answer
Answer: (b) ±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)
Answer
Answer: (c) 0
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
Answer
Answer: (a) ±3
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
Answer
Answer: (a) 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
Answer
Answer: (c) 0
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
Answer
Answer: (c) 4xyz
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)
Answer
Answer: (c) ±√3
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
Answer
Answer: (c) ±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
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
Answer
Answer: (b) 3
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
Answer
Answer: (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
Answer
Answer: (c) 1
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
Answer
Answer: (a) 0
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
Answer
Answer: (a) 0
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
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
Answer
Answer: (c) f(0) = 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
Answer
Answer: (d) None of these
Question 24.
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 = B-1A-1
(d) (A + B)-1 = B-1 + A-1
Answer
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
Answer
Answer: (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
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
Answer
Answer: (c) -4
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
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)
Answer
Answer: (b) x(5x + 8)
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
Answer
Answer: (b) 1
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
Answer
Answer: (a) 0
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
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
Answer
Answer: (c) 2
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
Answer
Answer: (b) 1
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
Answer
Answer: (b) -2
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
Answer
Answer: (c) -1
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
Answer
Answer: (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
Answer
Answer: (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
Answer
Answer: (a) 0
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
Answer
Answer: (a) α
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
Answer
Answer: (c) -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
Answer
Answer: (a) 0
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
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
Answer: (b) (α – β)(β – γ) (γ – α) (α + β + γ)
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