Determinants MCQ Type Questions for ISC Class-12 Maths

Determinants MCQ Type Questions for ISC Class-12 Maths .These MCQ / Objective Type Questions is based on latest reduced syllabus according 2021-22 session on bifurcated pattern. Main motto of MCQ Type Question is cracking the next upcoming exam of council. Visit official website CISCE for detail information about ISC Board Class-12 Maths.

ISC Class-12 Maths Determinants MCQ Type Questions

Board	ISC
Class	12th (XII)
Subject	Maths
Ch-Name	Determinants
Syllabus	on bifurcated syllabus (after reduction)
Bifurcated pattern	Semester-1
Session	2021-22
Topic	MCQ / Objective Type Question

Determinants MCQ Type Questions for ISC Class-12 Maths

Question 1: A and B are invertible matrices of the same order such that |(AB)^-1| = 8, If |A| = 2, then |B| is

(a) 16
(b) 4
(c) 6
(d) 1/16

Answer: (d) 1/16

Question 2: Let A be a square matrix of order 2 × 2, then |KA| is equal to

(a) K|A|
(b) K²|A|
(c) K³|A|
(d) 2K|A|

Answer: (b) K²|A|

Question 3: 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
Answer: (b) 3

Question 4: 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: (d) 5

Question 5: 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: (a) y = 2x

Question 6:

(a) 0
(b) 5
(c) 3
(d) 7

Answer: (a) 0

Question 7: 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) A

Question 8: If A is a square matrix of order 3 and |A| = 5 then |3A| = ?

(a) 135

(b) 45

(d) 32

Answer: (a) 135

Question 9: Inverse of a matrix A exists, if

(a) | A | = 0

(b) Matrix A is non-singular

(d) A^T = A

Answer: (b) Matrix A is non-singular

Question 10: 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: (d) 2 : 1 : -2

Question 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: (d) 2

Question 12: 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) a – b = 2

Question 13: The minor M_ijof an element a_ij of a determinant is defined as the value of the determinant obtained after deleting the

(a) jth row of the determinant

(b) ith column and jth row of the determinant

(d) ith row of the determinant

Answer: (c) ith row and jth column of the determinant

Question 14: If A and B are any 2 × 2 matrices , then det. (A+B) = 0 implies

(a) det A = 0 and det B = 0

(b) det A = 0 or det B = 0

(d) None of these

Answer: (d) None of these

Question 15: 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: (b) x = -1, y = -3, z = 2

Question 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: (c) 1

Question 17: A system of linear equations AX = B is said to be inconsistent, if the system of equations has

(a) Trivial Solution

(b) Infinite Solutions

(d) Unique Solutions

Answer: (c) No Solution

Question 18: If A is a square matrix of order 3 and |A| = 7 then |A^T| =

(a) 7

(b) 21

(d) 3

Answer: (a) 7

Question 19: If A and B are invertible matrices, then which of the following is not correct?

(a) adj A = |A|.A^-1
(b) det (a)^-1 = [det (a)]^-1
(c) (AB)^-1 = B^-1A^-1
(d) (A + B)^-1 = B^-1 + A^-1

Answer: (d) (A + B)^-1 = B^-1 + A^-1

Question 20:

$math semester 1 determine isc img 2$

(a) 2
(b) -2
(c) 4
(d) -4

Answer: (b) -2

Question 21: Which of the following is correct?

(a) Determinant is a square matrix
(b) Determinant is a number associated to a matrix
(c) Determinant is a number associated to a square matrix
(d) None of these

Answer: (c) Determinant is a number associated to a square matrix

Question 22: 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: (d) 5

Question 23: 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: (a) y = 2x

Question 24: 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: (d) 2 : 1 : -2

Question 25: If 4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1, then z = …………….

(a) 1
(b) 3
(c) -2
(d) 2

Answer: (d) 2

Question 26: 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: (b) 35 sq. units

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

Answer: (d) 40/7

Question 28: If Sis the set of distinct values of ‘h’ for which the following system of linear equations:

x + y + z = 1,
x + ay + z = 1,
ax + by + z = 1
has no solution, then S is

(a) a finite set containing two or more elements
(b) a singleton
(c) an empty set
(d) an infinite set

Answer: (b) a singleton

Question 29: System of equations AX = B is inconsistent if

(a) │B│ = 0

(b) (adj A) B = 0

(d) │A│ ≠ 0

Answer: (c) (adj A) B ≠ 0

Question 30: Points (a,a,c),(1,0,1) and (c,c,b) are collinear if

(a) a,b,c in GP

(b) a,b,c in AP

(d) C = ab

Answer: (c) C² = ab

Question 31: Find the minor of 6 and cofactor of 4 respectively in the determinant

$math semester 1 determine isc img 3$

(a) 6, 6
(b) 6, -6
(c) -6, -6
(d) -6, 6

Answer: (d) -6, 6

Question 32: The value of the determinant

$math semester 1 determine isc img 4$

(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: (b) (α – β)(β – γ)(γ – α)(α + β + γ)

Question 33: Find the minor of the element of second row and third column in the following determinant

$math semester 1 determine isc img 5$

(a) 13
(b) 4
(c) 5
(d) 0

Answer: (a) 13

Question 34: In a third order determinant, each element of the first column consists of sum of two terms, each element of the second column consists of sum of three terms and each element of the third column consists of sum of four terms. Then it can be decomposed into n determinants, where n has value

(a) 1

(b) 9

(d) 16

Answer: (c) 24

Question 35: The system of equations kx + 2y – z = 1,

(k – 1)y – 2z = 2

(k + 2)z = 3 has a unique solution, if k is

(a) – 1

(b) – 2

(d) 0

Answer: (a) – 1

Question 36: If A’ is the transpose of a square matrix A , then

(a) |A| ≠ |A′|

(b) |A|+|A′| = 0

(d) None of these

Answer: (c) |A| = |A′|

Question 37: If A B be two square matrices such that AB = O, then

(a) Det. B = 0

(b) BA

(d) Det. = A = 0

Answer: (c) Det. A = 0 or Det. B = 0

Question 38: 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, 12/5
(b) -1, 1/5
(c) -6, 17/5
(d) 6, −12/5

Answer: (c) -6, 17/5

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ISC Class-12 Maths Determinants MCQ Type Questions

Determinants MCQ Type Questions for ISC Class-12 Maths

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