CUET Mathematics MCQs Determinants

Question. If A is a square matrix of order 3 and |A| = 5 then |3A| = ?
a) 15
b) 135
c) 32
d) 45

Answer : A

Question. Find the area of the triangle whose vertices are (-2, 6), (3, -6) and (1, 5).
a) 40 sq. units
b) 35 sq. units
c) 30 sq. units
d) 15.5 sq. units

Answer : D

Question. If A is a square matrix of order 3 and |A| = 5, then the value of |2A′| is
a) -10
b) 10
c) 40
d) -40

Answer : B

Question. For a given system of equations if |A|=0 and (adj a) B≠O(zero matrix), then which of the following is correct regarding the solutions of the given equations?
a) there will be exactly one solution
b) there are one or more solutions
c) the solution does not exist
d) there will be exactly two solutions

Answer : C

Question. If A is a square matrix of order 3 and |A| = 7 then |AT| =
a) 7
b) 1/7
c) 21
d) 3

Answer : A

Question. If A and B are invertible matrices, then which of the following is not correct
(a) adj A = 
(b) det (i)^-1 = [det (i)]^-1
(c) (AB)^-1 = B^-1A^-1
(d) (A + B)^-1 = B^-1 + A^-1
a) d
b) b
c) a
d) c

Answer : D

Question. 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) 24
b) 9
c) 16
d) 1

Answer : A

Question. 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 = 3
c) a – b – 8 = 0
d) a + b + 1 = 0

Answer : A

Question. 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) 0
b) 2
c) 1
d) -1

Answer : C

Question. The system of linear equations:
x + λy - z = 0
λr - y - z = 0
x + y - λz = 0
a) Exactly three values of λ
b) Exactly one value of λ
c) Exactly two values of λ
d) Exactly four values of λ

Answer : A

Question. If fot the non-singular matrix A, A² then find A^-1
a) I
b) A
c) O
d) None of these

Answer : B

Question. If the area of the triangle is 35 sq. units with vertices (2, -6), (5, 4) and (k, 4). Then k is
a) 12, -2
b) 12
c) -12, -2
d) -2

Answer : A

Question. If S is the set of distinct value of 'h' for which the following system of linear equations:
a) an infinite set
b) a finite set containing two or more elements
c) a singleton
d) an empty set

Answer : C

Question. If 4x + 3y + 6z = 25, x + 5y + 7z = 13, 2x + 9y + z = 1, then z = …………….
a) 1
b) -2
c) 3
d) 2

Answer : D

Question. The minor Mij of an element aij of a determinant is defined as the value of the determinant obtained after deleting the
a) ith row of the determinant
b) ith column and jth row of the determinant
c) ith row and jth column of the determinant
d) jth row of the determinant

Answer : C

Question. We can add two matrices having real numbers A and B if their
a) order is same
b) rows are same
c) elements are same
d) columns are same

Answer : A

Question. 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) 9
c) 0
d) 3

Answer : D

Question. Find the area of the triangle with vertices P(4, 5), Q(4, -2) and R(-6, 2).
a) 21 sq. units
b) 30 sq. units
c) 35 sq. units
d) 40 sq. units

Answer : C

Question. If A is a symmetric matrix, then At =
a) Diagonal matrix
b) A
c) |A|
d) 12:00 AM

Answer : B

Question. If A is any square matrix of order 3 x 3 such that |a| = 3, then the value of |adj. A| is?
a) 9
b) 13
c) 27
d) 3

Answer : A

Question. Using determinants, find the equation of the line joining the points (1, 2) and (3, 6).
a) 4x – y = 5
b) y = x
c) x = 3y
d) y = 2x

Answer : D

Question. Given that A is a square matrix of order 3 and |A| = -4, then |adj A| is equal to
a) -4
b) 16
c) 4
d) -16

Answer : B

Question. A system of linear equations AX = B is said to be inconsistent, if the system of equations has
a) No Solution
b) Unique Solutions
c) Infinite Solutions
d) Trivial Solution

Answer : A

Question. 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) 6
c) 3
d) 9

Answer : C

Question. Inverse of a matrix A exists, if
a) Matrix A is singular
b) AT = A
c) Matrix A is non-singular
d) | A | = 0

Answer : A

Question. Let A be a squre matrix of order 3 x 3. Then │KA│ is equal to
(a) K│A│
(b) K²│A│
(c) K³│A│
(d) 3K│A│
a) b
b) d
c) c
d) a

Answer : C

Question. Which of the following is correct?
a) Determinant is a number associated to a matrix
b) Determinant is a number associated to a square matrix
c) Determinant is a square matrix
d) None of these

Answer : B

Question. If the system of equations 2x - 3y - 5 = 0, kx - 12y - 14 = 0 has non-trivial solution then the value of k is
a) a
b) b
c) c
d) d

Answer : C

Question. System of equations AX = B is inconsistent if
a) │A│ ≠ 0
b) │B│ = 0
c) (adj a) B ≠ 0
d) (adj a) B = 0

Answer : C

Question. 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) 9
c) 3
d) 6

Answer : C

Question. 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

Question. If the points (2, -3), (k, -1) and (0, 4) are collinear, then find the value of 4k.
a) 7/140
b) 40/7
c) 4
d) 47

Answer : B

Question. Which of the following conditions holds true for a system of equations to be consistent?
a) It should have exactly two solutions
b) It should have exactly one solution
c) It should have one or more solutions
d) It should have no solutions

Answer : C

Question. 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

Question. If A and B be two square matrices such that AB = O, then
(A) det A = 0 or det B = 0
(B) det B = 0
(C) B = A^-1
(D) det A = 0
a) a
b) c
c) d
d) b

Answer : B

Question. If the points (2, -3), (k, -1) and (0, 4) are collinear, then find the value of 4k.
a) 4/7
b) 40/7
c) 7/140
d) 4

Answer : B

Question. 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 = 3, y = 6, z = 9
c) x = -1, y = -3, z = 2
d) x = 2, y = 4, z = 6

Answer : C

Question. If A is an invertible matrix of order 2, then det (A–1) is equal to
a) 1/det (a)
b) 1
c) 0
d) det (a)

Answer : A

Question. The number of values of 'K' for which the linear equations:
4x + ky + 2z = 0
kx + 4y + z = 0
2x + 2y + z = 0
a) 3
b) Zero
c) 2
d) 1

Answer : C