☰
GkSeries.com

NCERT Solutions for class 12 Maths | Chapter 4 - Determinants

Free download in PDF Class 12 Maths Chapter 4 Determinants Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries. These will help the students for preparation of their examination./p>

Go To Download Page
(1) Find the minor of 6 and cofactor of 4 respectively in the determinant Δ= Class 12 Maths Determinants
[A] 6, 6
[B] 6, -6
[C] -6, -6
[D] -6, 6
Answer: -6, 6
(2) The value of the determinant Class 12 Maths Determinants
[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: (α – β)(β – γ)(γ – α)(α + β + γ)
(3) The value of is independent of Class 12 Maths Determinants
[A] α
[B] β
[C] α, β
[D] none of these
Answer: α
(4) 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: 15.5 sq. units
(5) 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: 40/7
(6) 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: a1b2 = a2b1
(7) 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: 35 sq. units
(8) 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: 1
(9) 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: x = -1, y = -3, z = 2
(10) 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 – b = 2
(11) If 4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1, then z = ________
[A] 1
[B] 3
[C] -2
[D] 2
Answer: 2
(12) 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: 2 : 1 : -2
(13) 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
(14)
[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 – b)(b – c)(c – a)(a2 + b2 + c2)
(15) 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: y = 2x
(16) The area of the triangle whose vertices are A(5, 4), B(-2, 4) and C(2, -6) is
[A] 15 square units.
[B] 25 square units.
[C] 35 square units.
[D] 45 square units.
Answer: 35 square units.
(17) Determinant of the 1 x 1 matrix [- 3] is
[A] 3
[B] - 3
[C] 0
[D] none of these
Answer: - 3
(18) If the equations (a + 1)3 x + (a + 2)3 y = (a + 3)3 (a + 1) x + (a + 2) y = a + 3 and x + y = 1 are consistent, then
[A] a = - 1
[B] a = - 2
[C] a = - 3
[D] none of these.
Answer: a = - 2
(19) If A is a square matrix of order 2, then det (adj A) is equal to
[A] 1
[B] det A
[C] (det A)2
[D] none of these
Answer: det A
(20) 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: 5

Chapters

Click Here to Read more questions