Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 4 Determinants. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Determinants MCQs Pdf with Answers to know their preparation level. https://www.cbselabs.com/maths-mcqs-for-class-12-with-answers-chapter-4/
Determinants Class 12 Maths MCQs Pdf
Determinants Class 12 MCQ Questions Question 1.
Answer:
(b) \(\left[\begin{array}{cc}
4 & -2 \\
-3 & 1
\end{array}\right]\)
Determinants MCQs With Answers Question 2.
Answer:
(b) \(\left[\begin{array}{ccc}
15 & 6 & -15 \\
0 & -3 & 0 \\
-10 & 0 & 5
\end{array}\right]\)
MCQ Of Determinants Class 12 Question 3.
Find x, if \(\left[\begin{array}{ccc}
1 & 2 & x \\
1 & 1 & 1 \\
2 & 1 & -1
\end{array}\right]\) is singular
(a) 1
(b) 2
(c) 3
(d) 4
Answer:
(d) 4
Determinants Class 12 MCQ Question 4.
Find the value of x for which the matrix \(A=\left[\begin{array}{ccc}
3-x & 2 & 2 \\
2 & 4-x & 1 \\
-2 & -4 & -1-x
\end{array}\right]\) is singular.
(a) 0, 1
(b) 1, 3
(c) 0, 3
(d) 3, 2
Answer:
(c) 0, 3
Class 12 Maths Chapter 4 MCQ Question 5.
Answer:
(b) \(-\frac{25}{13}\)
Determinants MCQs Class 12 Question 6.
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:
(b) 3
Class 12 Determinants MCQ Question 7.
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 \(-\frac{\pi}{4} \leq x \leq \frac{\pi}{4}\) is
(a) 0
(b) 2
(c) 1
(d) 3
Answer:
(c) 1
MCQ On Determinants Class 12 Pdf Download Question 8.
(a) 0
(b) -1
(c) 2
(d) 3
Answer:
(a) 0
MCQ Of Chapter 4 Maths Class 12 Question 9.
Answer:
(a) \(\frac{1}{2}\)
Determinants MCQs With Answers Pdf Question 10.
The value of the determinant \(\left|\begin{array}{ccc}
x & x+y & x+2 y \\
x+2 y & x & x+y \\
x+y & x+2 y & x
\end{array}\right|\) is
(a) 9x2 (x + y)
(b) 9y2 (x + y)
(c) 3y2 (x + y)
(d) 7x2 (x + y)
Answer:
(b) 9y2 (x + y)
Matrices And Determinants Class 12 MCQ Question 11.
For what value of x, matrix \(\left[\begin{array}{ll}
6-x & 4 \\
3-x & 1
\end{array}\right]\) is a singularmatrix?
(a) 1
(b) 2
(c) -1
(d) -2
Answer:
(b) 2
MCQ Determinants Class 12 Question 12.
Compute (AB)-1, If
Answer:
(a) \(\frac{1}{19}\left[\begin{array}{ccc}
16 & 12 & 1 \\
21 & 11 & -7 \\
10 & -2 & 3
\end{array}\right]\)
MCQ Questions On Determinants Class 12 Question 13.
Answer:
(a) A-1
Determinants MCQs Question 14.
Answer:
(a) \(\frac{1}{11}\left[\begin{array}{cc}
14 & 5 \\
5 & 1
\end{array}\right]\)
MCQs Of Determinants Class 12 Question 15.
Answer:
(b) \(\frac{1}{17}\left[\begin{array}{cc}
4 & 3 \\
-3 & 2
\end{array}\right]\)
MCQs On Determinants Class 12 Question 16.
If the points (3, -2), (x, 2), (8, 8) are collinear, then find the value of x.
(a) 2
(b) 3
(c) 4
(d) 5
Answer:
(d) 5
MCQs On Matrices And Determinants Question 17.
Using determinants, find the equation of the line joining the points (1, 2) and (3, 6).
(a) y = 2x
(b) x = 3y
(c) y = x
(d) 4x – y = 5
Answer:
(a) y = 2x
MCQ On Determinants Class 12 With Solutions Question 18.
Find the minor of the element of second row and third column in the following determinant \(\left[\begin{array}{ccc}
2 & -3 & 5 \\
6 & 0 & 4 \\
1 & 5 & -7
\end{array}\right]\)
(a) 13
(b) 4
(c) 5
(d) 0
Answer:
(a) 13
Determinants MCQ Class 12 Question 19.
If \(\Delta=\left|\begin{array}{lll}
5 & 3 & 8 \\
2 & 0 & 1 \\
1 & 2 & 3
\end{array}\right|\), then write the minor of the element a23.
(a) 7
(b) -7
(c) 4
(d) 8
Answer:
(a) 7
Matrices And Determinants MCQs Question 20.
If a, b, c are the roots of the equation x3 – 3x2 + 3x + 7 = 0, then the value of \(\left|\begin{array}{ccc}
2 b c-a^{2} & c^{2} & b^{2} \\
c^{2} & 2 a c-b^{2} & a^{2} \\
b^{2} & a^{2} & 2 a b-c^{2}
\end{array}\right|\) is
(a) 9
(b) 27
(c) 81
(d) 0
Answer:
(d) 0
Question 21.
If \(\left|\begin{array}{ccc}
1+a^{2} x & \left(1+b^{2}\right) x & \left(1+c^{2}\right) x \\
\left(1+a^{2}\right) x & 1+b^{2} x & \left(1+c^{2}\right) x \\
\left(1+a^{2}\right) x & \left(1+B^{2}\right) x & 1+c^{2} x
\end{array}\right|\), then f(x) is apolynomial of degree
(a) 2
(b) 3
(c) 0
(d) 1
Answer:
(a) 2
Question 22.
\(\left|\begin{array}{lll}
a^{2} & 2 a b & b^{2} \\
b^{2} & a^{2} & 2 a b \\
2 a b & b^{2} & a^{2}
\end{array}\right|\) is equal to
(a) a3 – b3
(b) a3 + b3
(c) (a3 – b3)2
(d) (a3 + b3)2
Answer:
(d) (a3 + b3)2
Question 23.
If α, β, γ are in A.P., then \(\left|\begin{array}{ccc}
x-3 & x-4 & x-\alpha \\
x-2 & x-3 & x-\beta \\
x-1 & x-2 & x-\gamma
\end{array}\right|=\)
(a) 0
(b) (x – 2)(x – 3)(x – 4)
(c) (x – α)(x – β)(x – γ)
(d) αβγ (α – β)(β – γ)2
Answer:
(a) 0
Question 24.
\(\left|\begin{array}{ccc}
1 & a^{2}+b c & a^{3} \\
1 & b^{2}+c a & b^{3} \\
1 & c^{2}+a b & c^{3}
\end{array}\right|\)
(a) -(a – b)(b – c)(c – a)(a2 + b2 + c2)
(b) (a – b)(b – c)(c – a)
(c) (a2 + b2 + c2)
(d) (a – b)(b – c)(c – a)(a2 + b2 + c2)
Answer:
(a) -(a – b)(b – c)(c – a)(a2 + b2 + c2)
Question 25.
Evaluate the determinant \(\Delta=\left|\begin{array}{ll}
\log _{3} 512 & \log _{4} 3 \\
\log _{3} 8 & \log _{4} 9
\end{array}\right|\)
(a) \(\frac { 15 }{ 2 }\)
(b) 12
(c) \(\frac { 14 }{ 3 }\)
(d) 6
Answer:
(a) \(\frac { 15 }{ 2 }\)
Question 26.
\(\left|\begin{array}{cc}
x & -7 \\
x & 5 x+1
\end{array}\right|\)
(a) 3x2 + 4
(b) x(5x + 8)
(c) 3x + 4x2
(d) x(3x + 4)
Answer:
(b) x(5x + 8)
Question 27.
\(\left|\begin{array}{cc}
\cos 15^{\circ} & \sin 15^{\circ} \\
\sin 75^{\circ} & \cos 75^{\circ}
\end{array}\right|\)
(a) 0
(b) 5
(c) 3
(d) 7
Answer:
(a) 0
Question 28.
Answer:
(b) 1
Question 29.
Answer:
(c) -1
Question 30.
Answer:
(a) \(\left[\begin{array}{cc}
4 & 2 \\
-1 & 1
\end{array}\right]\)
Question 31.
If for the non-singular matrix A, A2 = I, then find A-1.
(a) A
(b) I
(c) O
(d) None of these
Answer:
(a) A
Question 32.
If the equation a(y + z) = x, b(z + x) = y, c(x + y) = z have non-trivial solutions then the value of \(\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}\) is
(a) 1
(b) 2
(c) -1
(d) -2
Answer:
(b) 2
Question 33.
A non-trivial solution of the system of equations x + λy + 2z = 0, 2x + λz = 0, 2λx – 2y + 3z = 0 is given by x : y : z =
(a) 1 : 2 : -2
(b) 1 : -2 : 2
(c) 2 : 1 : 2
(d) 2 : 1 : -2
Answer:
(d) 2 : 1 : -2
Question 34.
If 4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1, then z = ________
(a) 1
(b) 3
(c) -2
(d) 2
Answer:
(d) 2
Question 35.
If the equations 2x + 3y + z = 0, 3x + y – 2z = 0 and ax + 2y – bz = 0 has non-trivial solution, then
(a) a – b = 2
(b) a + b + 1 = 0
(c) a + b = 3
(d) a – b – 8 = 0
Answer:
(a) a – b = 2
Question 36.
Solve the following system of equations x – y + z = 4, x – 2y + 2z = 9 and 2x + y + 3z = 1.
(a) x = -4, y = -3, z = 2
(b) x = -1, y = -3, z = 2
(c) x = 2, y = 4, z = 6
(d) x = 3, y = 6, z = 9
Answer:
(b) x = -1, y = -3, z = 2
Question 37.
If the system of equations x + ky – z = 0, 3x – ky – z = 0 & x – 3y + z = 0 has non-zero solution, then k is equal to
(a) -1
(b) 0
(c) 1
(d) 2
Answer:
(c) 1
Question 38.
If the system of equations 2x + 3y + 5 = 0, x + ky + 5 = 0, kx – 12y – 14 = 0 has non-trivial solution, then the value of k is
(a) -2, \(\frac{12}{5}\)
(b) -1, \(\frac{1}{5}\)
(c) -6, \(\frac{17}{5}\)
(d) 6, \(-\frac{12}{5}\)
Answer:
(c) -6, \(\frac{17}{5}\)
Question 39.
If \(\left|\begin{array}{cc}
2 x & 5 \\
8 & x
\end{array}\right|=\left|\begin{array}{cc}
6 & -2 \\
7 & 3
\end{array}\right|\), then the value of x is
(a) 3
(b) ±3
(c) ±6
(d) 6
Answer:
(c) ±6
Question 40.
\(\left|\begin{array}{ccc}
(b+c)^{2} & a^{2} & b c \\
(c+a)^{2} & b^{2} & c a \\
(a+b)^{2} & c^{2} & a b
\end{array}\right|=\)
(a) (a – b)(b – c)(c – a)(a2 + b2 + c2)
(b) -(a – b)(b – c)(c – a)
(c) (a – b)(b – c)(c – a)(a + b + c)(a2 + b2 + c2)
(d) 0
Answer:
(c) (a – b)(b – c)(c – a)(a + b + c)(a2 + b2 + c2)
Question 41.
Find the area of the triangle with vertices P(4, 5), Q(4, -2) and R(-6, 2).
(a) 21 sq. units
(b) 35 sq. units
(c) 30 sq. units
(d) 40 sq. units
Answer:
(b) 35 sq. units
Question 42.
If the points (a1, b1), (a2, b2) and(a1 + a2, b1 + b2) are collinear, then
(a) a1b2 = a2b1
(b) a1 + a2 = b1 + b2
(c) a2b2 = a1b1
(d) a1 + b1 = a2 + b2
Answer:
(a) a1b2 = a2b1
Question 43.
If the points (2, -3), (k, -1) and (0, 4) are collinear, then find the value of 4k.
(a) 4
(b) 7/140
(c) 47
(d) 40/7
Answer:
(d) 40/7
Question 44.
Find the area of the triangle whose vertices are (-2, 6), (3, -6) and (1, 5).
(a) 30 sq. units
(b) 35 sq. units
(c) 40 sq. units
(d) 15.5 sq. units
Answer:
(d) 15.5 sq. units
Question 45.
\(\left|\begin{array}{ccc}
2 x y & x^{2} & y^{2} \\
x^{2} & y^{2} & 2 x y \\
y^{2} & 2 x y & x^{2}
\end{array}\right|=\)
(a) (x3 + y3)2
(b) (x2 + y2)3
(c) -(x2 + y2)3
(d) -(x3 + y3)2
Answer:
(d) -(x3 + y3)2
Question 46.
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:
(a) α
Question 47.
Let \(\Delta=\left|\begin{array}{ccc}
x & y & z \\
x^{2} & y^{2} & z^{2} \\
x^{3} & y^{3} & z^{3}
\end{array}\right|\), then the value of ∆ 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 48.
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)
Question 49.
Using properties of determinants, \(\left|\begin{array}{ccc}
1 & a & a^{2}-b c \\
1 & b & b^{2}-c a \\
1 & c & c^{2}-a b
\end{array}\right|=\)
(a) 0
(b) 1
(c) 2
(d) 3
Answer:
(a) 0
Question 50.
Find the minor of 6 and cofactor of 4 respectively in the determinant \(\Delta=\left|\begin{array}{lll}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{array}\right|\)
(a) 6, 6
(b) 6, -6
(c) -6, -6
(d) -6, 6
Answer:
(d) -6, 6
We hope the given Maths MCQs for Class 12 with Answers Chapter 4 Determinants will help you. If you have any query regarding CBSE Class 12 Maths Determinants MCQs Pdf, drop a comment below and we will get back to you at the earliest.