Math Chapter Wise

EnglishUKPSC Lecturer (Mains) 2020

Q101.If A and B are square matrices of order n such that AB = A and BA=B, then

AA2 = A, B2 ≠B BA2 ≠A, B2 = B CA2 = A, B2 = B DA2 ≠ A, B2 ≠B

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EnglishUKPSC Lecturer (Mains) 2020

Q102.If A is a square matrix such that A2 = 2A–I, where I is a unit matrix, then for all natural numbers n≥2, An is equal to

AnA–(n–1)I BnA–I C2n–1/A–(n–1)I D2n–1/A–I

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EnglishUKPSC Lecturer (Mains) 2020

Q103.The matrices cosθ –sinθ A = sinθ cosθ and x 0 B = 0 y commute under multiplication, then

Ayor nπ, n = θ = x is a integer Bπ y or n, n 2 = θ = x is an integer Csin ycos θ = θ x Dcos ysin θ = θ x

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EnglishUKPSC Lecturer (Mains) 2020

Q104.The matrix cosθ sinθ A = –sinθ cosθ is:

AInvolutory BOrthogonal CNilpotent DIdempotent

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EnglishUKPSC Lecturer (Mains) 2020

Q105.If x, y, z are respectively, the pth, qth and rth terms of an A.P., then p x 1 q y 1 = r z 1

Axyz B1 C(p – x)(q – y)(r – z) DNone of these

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EnglishUKPSC Lecturer (Mains) 2020

Q106.The inverse of the matrix 3 8 2 1 is:

A1 8 1 2 3 13 − B1 8 1 2 3 13 − C1 8 1 2 3 13 − DNone of these

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EnglishUKPSC Lecturer (Mains) 2020

Q107.If A be a non-singular square matrix of order 3×3 and |A| = 5, then the value of |adj A| is:

A125 B15 C45 D25

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EnglishUKPSC Lecturer (Mains) 2020

Q108.If 1 1 1 A 1 2 3 2 1 3 = − − and A3 – 6A2 + 5A + 11 I = 0, where I is a 3×3 identity matrix, then A-1 is equal to:

A3 4 5 1 9 1 4 11 5 3 1 − − − B3 4 5 1 0 1 4 11 5 3 0 − C3 4 5 1 8 6 2 11 2 0 1 − D3 4 5 1 6 9 4 11 0 8 1 − − − −

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EnglishHaryana PGT 2019

Q109.If 1 sinθ 1 A = –sinθ 1 sinθ –1 –sinθ 1, where 0 ≤ θ ≤ 2π, then:

Adet A = 0 Bdet A ∈ (2, ∞) Cdet A ∈ (2, 4) Ddet A ∈ [2, 4]

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EnglishHaryana PGT 2019

Q110.If 2 3 A = 5 –2 such that A–1 = kA, then k =

A19 B1/19 C–19 D−1/19

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q111.Compute the inverse of the matrix A = 4 2 3 2 2 2 1 0 1

A1 –1 –1 0 1/ 2 –1 –1 1 3 B1 –1 –1 0 1/ 2 –1 –1 1 2 C1 –1 –1 0 1/ 2 –1 1 1 2 D1 –1 1 0 1/ 2 –1 –1 1 2

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EnglishUK SSSC LT 2020

Q112.If determinant 3 x 5 0 x 2 − − =, then x is equal to

A–6, –1 B–1, 6 C3, 2 D–2, 3

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EnglishUK SSSC LT 2020

Q113.If 3 5 2i 3 A 5 2i 7 4i 3 4i 5 + − = − − − −, then iA is a:

AHermitian Matrix BSkew-Hermitian Matrix CSymmetric Matrix DSkew Symmetric Matrix

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EnglishUK SSSC LT 2020

Q114.A square matrix A is said to be orthogonal if:

AAAT = A BAAT = A CAAT = 1 A DAAT = I

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EnglishUK SSSC LT 2020

Q115.If matrix A is both symmetric and skew symmetric then, A will be:

AZero matrix BDiagonal matrix CScalar matrix DUpper triangular matrix

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EnglishUK SSSC LT 2020

Q116.If matrix A is of order of 3×3, then determinant |KA|

A|KA| BK2/|A| CK3/|A| D3K |A|

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EnglishHaryana PGT 2020

Q117.If A = 3 0 0 0 3 0, 0 0 3 then A5 =

A243 A B81 A C27 A D9 A

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EnglishHaryana PGT 2020

Q118.If 1+ x 1 1 1 1+ x 1 1 1 1+ x = 0, then x =

A0, 1, 3 B0, 1, –3 C0, –3 D0, 3

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EnglishHaryana PGT 2018

Q119.Let P be a 4 × 4 matrix whose determinant is 10. The determinant of the matrix –3P is:

A810 B30 C–810 D–108

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EnglishHaryana PGT 2018

Q120.If ω is the cube root of unity, then the inverse of 2 2 1 1 1 A 1 1 = ω is:

A2 1 1 1 1 3 1 ω B2 1 1 1 1 4 1 ω C2 1 1 1 1 2 1 ω D2 1 1 1 1 ω

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