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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>
(1)
Find the minor of 6 and cofactor of 4 respectively in the determinant Δ=
[A]
6, 6
[B]
6, -6
[C]
-6, -6
[D]
-6, 6
(2)
The value of the determinant
[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
[A]
α
[B]
β
[C]
α, β
[D]
none of these
(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
(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
(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
(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
(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
(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
(11)
If 4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1, then z = ________
(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
(13)
If for the non-singular matrix A, A2 = I, then find A-1.
[A]
A
[B]
I
[C]
O
[D]
None of these
[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
(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.
(17)
Determinant of the 1 x 1 matrix [- 3] is
[A]
3
[B]
- 3
[C]
0
[D]
none of these
(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.
(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
(20)
If the points (3, -2), (x, 2), (8, 8) are collinear, then find the value of x.
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