NCERT Solutions for class 12 Maths | Chapter 4 - Determinants

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Questions
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)
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3 The value of Class 12 Maths Determinants is independent of
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 Class 12 Maths Determinants
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

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