# CBSE Class 12 Mathematics Determinants Worksheet

Read and download free pdf of CBSE Class 12 Mathematics Determinants Worksheet Set A. Students and teachers of Class 12 Determinants can get free printable Worksheets for Class 12 Determinants in PDF format prepared as per the latest syllabus and examination pattern in your schools. Standard 12 students should practice questions and answers given here for Determinants in Grade 12 which will help them to improve your knowledge of all important chapters and its topics. Students should also download free pdf of Class 12 Determinants Worksheets prepared as per the latest NCERT, CBSE, KVS books and syllabus issued this academic year and solve important problems provided here with solutions on daily basis to get more score in school exams and tests

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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 −π4≤x≤π4 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) 9x^{2 }(x + y)

(b) 9y^{2 }(x + y)

(c) 3y^{2 }(x + y)

(d) 7x^{2 }(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 a_{23}.

(a) 7

(b) -7

(c) 4

(d) 8

Question 20.

If a, b, c are the roots of the equation x^{3} –
3x^{2} +
3x + 7 = 0, then the value of

∣2bc−a^{2} c ^{2} b^{2}

c ^{2} 2ac – b ^{2 } a^{2 }

b ^{2} a^{2} 2ab− c^{2} ∣ 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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