Math Chapter Wise

EnglishPGT 2005

Q221.If 2 3 1 7 1 5 1 9 8 = A is equal to B+C, where B is symmetric and C is skew symmetric, then B is equal to

A2 5 1 5 1 7 1 7 8 B2 3 1 3 1 5 1 5 8 C0 2 0 2 0 2 0 2 0 − D0 5 1 5 7 1 1 1 8

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EnglishPGT 2005

Q222.Which of the following determinants is equal to a h g h b f g f c?

Ag f c a h g a g h Bh g a b f h f c g Ca g h h f b g c f Da h g g f c h b f

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EnglishUP TGT-2016 (08-03-2019)

Q223.The value of the determinant 2 a ab ac ab b bc ac bc c − is

A0 B- (a2 + b2 + c2) C4 a2 b2 c2 D2 (ab + bc + ca)

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EnglishUP TGT-2016 (08-03-2019)

Q224.If x 2 2 2 2 x 2 2 0, 2 2 x 2 + + = + then values of x satisfying this equation are

A0, –2, –6 B0, –1, –2 C0, 0, –2 D0, 0, –6

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EnglishUP TGT-2016 (08-03-2019)

Q225.If coshx sinhx A sinhx coshx = −, then trace (A2) is equal to

A2 B–2 Ccosh2x Dsinh2x

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EnglishUP TGT-2016 (08-03-2019)

Q226.If 1 3 x 2 A 1 x 2 y 1 2 5 y 3 + = − + = − + = − + = − + − is a symmetric matrix, then 3x+y is equal to

A–1 B0 C1 DNone of the above

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EnglishUP TGT-2016 (08-03-2019)

Q227.If 1 1 A 1 1 − = − and 1 1 B 1 1 = then the value of AB is

A1 1 B0 1/1 0 C−1 0/0 1 D0 0

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EnglishNVS PGT 10-06-2019

Q228.If 0 i A i 0 − = and 1 0 B 0 1 = − are matrices, then AB + BA is:

Aan invertible matrix Ba unit matrix Ca null matrix Da diagonal matrix

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EnglishNVS PGT 10-06-2019

Q229.If 1 0 2 A 5 1 x 1 1 1 = is a singular matrix, then the value of x is equal to:

A–11 B11 C9 D–9

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EnglishNVS PGT 10-06-2019

Q230.Let 2 0 0 A 0 2 0 0 0 2 = and 1 2 3 B 0 1 3 0 0 2 = be matrices. Then the determinant of AB equals:

A32 B16 C8 D4

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EnglishKVS PGT 23-12-2018

Q231.Let 1 1 1 A 2 1 3 1 1 1 − = − = − and 4 2 2 1 B 5 0 10 1 2 3 = − α = − α = − α = − α −. If B is the inverse of A, then α is:

A–2 B–1 C2 D5

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EnglishKVS PGT 23-12-2018

Q232.If α, β ≠ 0 and ((())) n n f n = α + β = α + β = α + β = α + β, and 3 1 f(1) 1 f(2) 1 f(1) 1 f(2) 1 f(3) 1 f(2) 1 f(3) 1 f(4) + + + + + + + + + + + + + + + + + + + + + + + + + + (())) ((())) ((()) 2 2 2 K 1 1 = − α − β α − β = − α − β α − β = − α − β α − β = − α − β α − β then K is equal to:

Aαβ B1/αβ C1 D–1

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EnglishKVS PGT 23-12-2018

Q233.If ((()))((()))2 x 4 2x 2x 2x x 4 2x A Bx x A 2x 2x x 4 − − = + − − = + − − = + − − = + − −, then the ordered pair (A, B) is equal to:

A(4,5) B(–4, –5) C(–4, 3) D(–4,5)

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EnglishKVS PGT 23-12-2018

Q234.If a, b, c are positive and unequal, then the value of a b c b c a c a b ∆ = ∆ = is:

A0 B<0 C1 D>1

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EnglishUP PGT-2016 (02-02-2019)

Q235.The inverse of a skew-symmetric of order 3

Ais a skew- symmetric matrix Bis a symmetric matrix Cis a diagonal matrix Ddoes not exist

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EnglishUP PGT-2016 (02-02-2019)

Q236.The system of linear equations 1 2 3 x 2x x 3 + + = + + = + + = + + = 1 2 3 2x 3x x 3 + + = + + = + + = + + = 1 2 3 3x 5x 2x 1 + + = + + = + + = + + = has

Ainfinitely many solutions Bexactly 3 solutions Cunique solution Dno solution

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EnglishUP PGT-2016 (02-02-2019)

Q237.If 5th term of a harmonic progression is 7 and 7th term is 5, then 35th term is

A0 B1 C7/12 D1/35

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EnglishUP PGT-2016 (02-02-2019)

Q238.If log3, log(3x –2) and log(3x +4) are in arithmetical progression, then x is equal to

Alog34 Blog23 Clog38 Dlog83

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EnglishUP PGT-2016 (02-02-2019)

Q239.If A and B are symmetric matrices, then AB is symmetric matrix if and only if

AAB = BA BAB = –BA CAB–1 =B–1 A DNone of the above

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EnglishUP PGT-2016 (02-02-2019)

Q240.The matrix sin cos A cos sin θ = − θ − θ − θ − θ is

ASymmetric BSkew-symmetric COrthogonal DSingular

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