JEE Questions for Maths Matrices And Determinants Quiz 1 - MCQExams.com

Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of A consisting of all determinants with value –1. Then
  • C is empty
  • B has as many elements as C

  • Maths-Matrices and Determinants-38208.png
  • B has twice as many elements as elements as C

Maths-Matrices and Determinants-38210.png
  • ± 1
  • ± 2
  • ± 3
  • ± 5

Maths-Matrices and Determinants-38211.png
  • 0
  • 6
  • – 6
  • –4
  • 4
If n ≥ 2 is an integer
Maths-Matrices and Determinants-38213.png
  • An = I and An-1 ≠ 1
  • Am ≠ I for any positive integer m
  • A is not invertible
  • Am = 0 for a positive integer m
If AB = A and BA = B, then B2 is equal to
  • B
  • A
  • – B
  • B3
Let a, b, c be the real numbers. Then following system of equations in x, y and z
Maths-Matrices and Determinants-38216.png
  • no solution
  • unique solution
  • infinitely many solutions
  • finitely many solutions

Maths-Matrices and Determinants-38218.png
  • A2 + 7A – 5I = 0
  • A2 – 7A + 5I = 0
  • A2 + 5A – 7I = 0
  • A2 – 5A + 7I = 0
If A and B are square matrices of equal degree, then which one is correct among the followings?
  • A + B = B + A
  • A + B = A – B
  • A – B = B – A
  • AB = BA

Maths-Matrices and Determinants-38221.png

  • Maths-Matrices and Determinants-38222.png
  • 0

  • Maths-Matrices and Determinants-38223.png
  • 5I
If P is a 3 × 3 matrix such that PT = 2P + I, where PT is the transpose of P and I is the 3 × 3 identity matrix, then there exists a column matrix,
Maths-Matrices and Determinants-38225.png

  • Maths-Matrices and Determinants-38226.png
  • 2)
    Maths-Matrices and Determinants-38227.png

  • Maths-Matrices and Determinants-38228.png

  • Maths-Matrices and Determinants-38229.png
If ω is a complex cube root of unity with ω ≠ 1 and p = [pij] is a n × n matrix with Pij = ωi + j. Then P2 ≠ 0 when n is equal to
  • 55
  • 58
  • 56
  • All of these
The parameter, on which the value of the determinant
Maths-Matrices and Determinants-38232.png
  • a
  • p
  • d
  • x

Maths-Matrices and Determinants-38234.png
  • (–6, –11)
  • (6, 11)
  • (–6, 11)
  • (6, –11)

Maths-Matrices and Determinants-38236.png
  • 1 , 2
  • - 1 , 2
  • - 1 , - 2
  • 2 , 1
  • - 2 , - 1

Maths-Matrices and Determinants-38238.png
  • 4
  • 3
  • - 4
  • - 3
If the system of equations x – ky – z = 0, kx – y – z = 0, x + y – z = 0 has a non-zero solution, then the possible values of k are
  • –1, 2
  • 1, 2
  • 0, 1
  • –1, 1

Maths-Matrices and Determinants-38240.png
  • 5 , 2 , 2
  • 1 , - 2 , 3
  • 0 , - 3 , 3
  • 11 , 8 , 3
  • 4 , 1 , 3

Maths-Matrices and Determinants-38242.png

  • Maths-Matrices and Determinants-38243.png
  • 2)
    Maths-Matrices and Determinants-38244.png

  • Maths-Matrices and Determinants-38245.png

  • Maths-Matrices and Determinants-38246.png
If AT and BT are transpose matrices of the square matrices A and B respectively then (AB)T is equal to
  • AT BT
  • ABT
  • BAT
  • BT AT

Maths-Matrices and Determinants-38248.png
  • –1
  • 0
  • 1
  • 2

Maths-Matrices and Determinants-38250.png
  • 3ω
  • 3ω(ω-1)
  • 3ω2
  • 3ω(1-ω)
If A is a square matrix, then
  • A + AT is symmetric
  • AAT is skew- symmetric
  • AT + A is skew- symmetric
  • AT is skew-symmetric
If A and B are two symmetric matrices of same order. Then, the matrix AB - BA is equal to
  • a symmetric matrix
  • a skew - symmetric matrix
  • a null matrix
  • the identity matrix
If ω is a complex cube root of unity and
Maths-Matrices and Determinants-38254.png
  • ω2 A
  • ωA
  • A
  • 0

Maths-Matrices and Determinants-38256.png
  • a = 1 = 2b
  • a = b
  • a = b2
  • ab = 1

Maths-Matrices and Determinants-38258.png
  • 2I3
  • 3I3
  • 4I3
  • 5I3
If o(A) = 2 × 3 , o(B) = 3 × 2 and o(C) = 3 × 3 , then which one of the following is not defined?
  • CB + A'
  • BAC
  • C(A + B')'
  • C(A + B' )
IF m [–3 4] + n [4 –3] = [10 – 11] , then 3m + 7n is equal to
  • 3
  • 5
  • 10
  • 1

Maths-Matrices and Determinants-38262.png
  • 1
  • 2
  • 4
  • 8
Find the area of the triangle with vertices (2,3), (0,and (1,2)
  • 1/2 sq unit
  • 0 sq unit
  • 2 sq units
  • 2 (1/sq units
If A and B are square matrices of order 3 such that |A| = –1 , |B| = 3, then |3AB| is equal to
  • – 9
  • –81
  • – 27
  • 81

Maths-Matrices and Determinants-38266.png
  • (p - 1)2
  • 2(p - 1)
  • (p - 1)2/
  • 2p - 1

Maths-Matrices and Determinants-38268.png
  • 1
  • 2
  • 3
  • 4

Maths-Matrices and Determinants-38270.png
  • 1
  • –1
  • 4
  • no real values

Maths-Matrices and Determinants-38272.png
  • 1
  • - 4
  • 4
  • 2
  • - 2

Maths-Matrices and Determinants-38274.png
  • 0
  • 1
  • 4 loge
  • 5 loge

Maths-Matrices and Determinants-38276.png
  • independent of α
  • independent of β
  • independent of α and β
  • None of these

Maths-Matrices and Determinants-38278.png
  • 1
  • 3
  • 4
  • 2

Maths-Matrices and Determinants-38280.png
  • 42 , 3 , - 42 , 3
  • -42 , -3 , 42 , -3
  • 42 , 3 , - 42 , -3
  • 42 , 3 , 42 , 3

Maths-Matrices and Determinants-38282.png
  • 146
  • 21
  • 20
  • 335

Maths-Matrices and Determinants-38284.png
  • - 3
  • 3
  • 0
  • for any value of b

Maths-Matrices and Determinants-38286.png
  • χ = a
  • χ = b
  • χ = c
  • χ has any value

Maths-Matrices and Determinants-38288.png
  • A is singular
  • |A| 0
  • A is symmetric
  • None of these

Maths-Matrices and Determinants-38290.png
  • A
  • |A|
  • |A|.I
  • None of the above

Maths-Matrices and Determinants-38292.png

  • Maths-Matrices and Determinants-38293.png
  • 2)
    Maths-Matrices and Determinants-38294.png

  • Maths-Matrices and Determinants-38295.png

  • Maths-Matrices and Determinants-38296.png
If A is a matrix of order 3 such that A(adj A) = 10I, then |adj A|is equal to
  • 1
  • 10
  • 100
  • 10I

Maths-Matrices and Determinants-38299.png
  • 19
  • 1/19
  • - 19
  • - (1/19)
If A is a square matrix of order n × n, then adj(adj A) is equal to
  • |A|n A
  • |A|n-1 A
  • |A|n-2 A
  • |A|n-3 A

Maths-Matrices and Determinants-38302.png

  • Maths-Matrices and Determinants-38303.png
  • 2)
    Maths-Matrices and Determinants-38304.png

  • Maths-Matrices and Determinants-38305.png

  • Maths-Matrices and Determinants-38306.png

Maths-Matrices and Determinants-38308.png
  • a3n
  • a-3n
  • -a3n
  • 2a3n
0:0:1


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