TOP 100+ Determinants Class 12 MCQ Questions And Answers

These Determinants Class 12 MCQ Questions And Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Determinants Class 12 MCQ Questions And Answers will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.

Determinants Class 12 MCQ Questions And Answers

1. If  then the value of x is

(A) 3

(B) ±3

(C) ±6

(D) 6

Answer: ±6


2. If a ≠ 0 and  = 0 then a =

(A) a = -3

(B) a = 0

(C) a = 1

(D) a = 3

Answer: a = -3


3. The number of distinct real roots of  = 0 in the interval –π/4 ≤ x ≤ π/4 is

(A) 0

(B) 2

(C) 1

(D) 3

Answer: 1


4. The value of the determinant  is

(A) 9x² (x + y)

(B) 9y² (x + y)

(C) 3y² (x + y)

(D) 7x² (x + y)

Answer: 9y² (x + y)


5. If abc ≠ 0 and  = 0 then 1/a + 1/b + 1/c =

(A) 1

(B) 2

(C) -1

(D) -3

Answer: -1


6. Let Δ =  then the value of Δ is

(A) (x – y) (y- z)(z – x)

(B) xyz

(C) x² + y² + z²)²

(D) xyz (x – y)(y – z) (z – x)

Answer: xyz (x – y)(y – z) (z – x)


7. If 7 and 2 are two roots of the equation  then the third root is

(A) -9

(B) 14

(C) 12

(D) None of these

Answer: -9


8. Let f(t) =  is equal to

(A) 0

(B) -1

(C) 2

(D) 3

Answer: 0


9. 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

Answer: -6, 6


10. 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)


11. The value of  is independent of

(A) α

(B) β

(C) α, β

(D) none of these

Answer: α


12. 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


13. 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


14. 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


15. 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


16. 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


17. 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


18. 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


19. 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


20. 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


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