CBSE Class 12 Mathematics Determinants Worksheet
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Question 1.
Question 2.
Question 3.
Find x, if ⎢1 2 x
1 1 1
2 1 −1⎥ is singular
(a) 1
(b) 2
(c) 3
(d) 4
Question 4.
Find the value of x for which the matrix A= ⎢3−x 2 2
2 4-x 1
−2 −4 −1−x⎥ is singular.
(a) 0, 1
(b) 1, 3
(c) 0, 3
(d) 3, 2
Question 5.
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
Question 7.
The number of distinct real roots of ∣sin x cos x cos x
Cos x sin x cos x
Cos x cos x sin x ∣=0
in the interval −Ï€4≤x≤Ï€4 is
(a) 0
(b) 2
(c) 1
(d) 3
Question 8.
(a) 0
(b) -1
(c) 2
(d) 3
Question 9.
Question 10.
The value of the determinant ∣x x + y x +2y
x+2y x x + y
x+ y x+2y x ∣ is
(a) 9x2 (x + y)
(b) 9y2 (x + y)
(c) 3y2 (x + y)
(d) 7x2 (x + y)
Question 11.
For what value of x, matrix [6−x 4
3−x 1] is a singularmatrix?
(a) 1
(b) 2
(c) -1
(d) -2
Question 12.
Compute (AB)-1, If
Question 13.
Question 14.
Question 15.
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
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
Question 18.
Find the minor of the element of second row and third column in the following determinant
⎢2 -3 5
6 0 4
1 5 −7⎥
(a) 13
(b) 4
(c) 5
(d) 0
Question 19. If Δ=∣5 3 8
2 0 1
1 2 3 ∣, then write the minor of the element a23.
(a) 7
(b) -7
(c) 4
(d) 8
Question 20.
If a, b, c are the roots of the equation x3 – 3x2 + 3x + 7 = 0, then the value of
∣2bc−a2 c 2 b2
c 2 2ac – b 2 a2
b 2 a2 2ab− c2 ∣ is
(a) 9
(b) 27
(c) 81
(d) 0
Question 21.
Question 22.
If 4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1, then z = ________
(a) 1
(b) 3
(c) -2
(d) 2
Question 23.
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
Question 24.
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
Question 25.
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
Question 26.
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, 125
(b) -1, 15
(c) -6, 175
(d) 6, −125
Question 27.
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
Question 28.
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
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