Math Chapter Wise

EnglishUP PGT 2021

Q81.The value of the determinant 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 3 4 2 3 4 5 3 4 5 6 4 5 6 7

A60 B96 C120 DNone of the above

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EnglishUPPSC GIC 2021

Q82.The value of the determinant 3 3 3 1 1 1 x y z x y z is

A(x – y) (y – z) (z – x) (x + y + z) B(x – y) (y – z) (z – x) (x + y – z) Cxyz (x + y + z) D(xy + yz + zx) (x2 + y2 + z2)

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EnglishUPPSC GIC 2021 UPPCS (Pre) 2002

Q83.The value of the determinant x y z 1 y z x 1 z x y 1 + is-

A(x + y) (y + z) (z + x) Bxyz C1 D0

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q84.If A is a square matrix of order n, then value of adj (adj A) is-

A|A|n/A B|A|n-1/A C|A|n-2/A DNone of these

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EnglishUPPSC GIC 2021

Q85.If 3A-2B = 6 9 6 3 − and 2A -B = 8 10 8 2 − then A is-

A−10 11/10 1 B−10 11/10 1 C−10 11/10 1 DNone of these

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EnglishUPPSC GIC 2021

Q86.If a matrix 5 8 6 3 2 4 1 7 9 is expressed as A+B, where A is symmetric and B is skew - symmetric, then B is equal to -

A5 11/ 2 7 / 2 11/ 2 2 11/ 2 7 / 2 11/ 2 9 B0 5/ 2 5/ 2 5/ 2 0 3/ 2 5/ 2 3/ 2 0 − − − C0 5/ 2 5/ 2 5/ 2 0 3/ 2 5/ 2 3/ 2 0 − − − D5 11/ 2 7 / 2 11/ 2 2 11 7 / 2 11 9

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EnglishUP TGT 2021

Q87.If A and B are two matrices such that AB = B and BA = A, then A2 + B2 is equal to

A2AB B2BA CA + B DAB

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EnglishUP TGT 2021

Q88.The system of equations x + z = 3 ax + y = 2 3x + y + bz = 7 has a unique solution if (a, b) is equal to

A(1, 2) B(2, 1) C(1, 1) D(–1, 4)

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EnglishUP TGT 2021

Q89.If x1 and x2 are the roots of the equation 2 1 4 20 1 –2 5 = 0 1 2x 5x, then the value of 2 2 1 2 x + x is

A1 B3 C5 D0

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EnglishUP TGT 2021

Q90.If 1 –2 A = –1 2 and 2 6 B = 1 3 then AB is equal to

A0 0 B1 0/0 1 C1 1 DNone of the above

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EnglishUP TGT 2021

Q91.If ω is an imaginary cube root of unity, then value of 6 8 6 3 7 8 7 1 ω 1 is

A0 B3 C4 D1

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EnglishUP Higher Asst. Prof. 2021

Q92.The matrix () a ic b id b id a ic − − − + + will be unitary if and only if

Aa2 – b2 + c2 – d2 = 1 B–a2 + b2 – c2 + d2 = 1 Ca2 + b2 + c2 + d2 = 1 Da2 + b2 + c2 + d2 ≠ 1

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EnglishUPPSC Ashram Paddhati 2021

Q93.The inverse of the matrix 1 2 2 –1 is

A1 2 5 5 2 –1 5 5 B1 2 5 5 2 1 5 5 C1 –2 5 5 2 –1 5 5 D1 2 5 5 –2 –1 5 5

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EnglishUPPSC Ashram Paddhati 2021

Q94.If A and B are symmetric matrices, which of the following is a skew-symmetric matrix?

A5(A + B) B3(A – B) CAB + BA DAB – BA

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EnglishUPPSC Ashram Paddhati 2021

Q95.If the matrix A is invertible, then the value of |A–1 | is

A|A| B1/| A | C1 Dnone of the above

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EnglishUPPSC Ashram Paddhati 2021 KVS TGT Dec 2017

Q96.The value of the determinant b +c a a b c + a b c c a +b is

A2abc Babc C4abc D8abc

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EnglishUKPSC Lecturer (Mains) 2020

Q97.If A = 1 a 0 1, then An (where n∈N) is equal to:

A1 na/0 1 B2 1 an 0 1 C1 an/0 0 Dn na/0 n

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EnglishUKPSC Lecturer (Mains) 2020

Q98.If p(x), q(x) and r(x) be polynomials of degree one, a1, a2, a3 be three numbers, then the value of the determinant 1 2 3 1 2 3 1 2 3 p(a) p(a) p(a) q(a) q(a) q(a) r(a) r(a) r(a) is

A0 B–2 C1 D3

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EnglishUKPSC Lecturer (Mains) 2020

Q99.The value of the determinant (a b) (b c) (c a) (b c) (c a) (a b) (c a) (a b) (b c) − − − − − − − − − is:

A(a–b) (b–c) (c–a) B3 abc C1 DNone of these

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EnglishUKPSC Lecturer (Mains) 2020

Q100.If A be a matrix of order 3 such that |A| = 4 and B = adj

A8 B6 C4 D1

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