Math Chapter Wise

EnglishUP PGT-2016 (02-02-2019)

Q241.The sum of two distinct root of the equation 6 x 3 3 3 6 x 3 0 3 3 6 x − − = − is

A3 B12 C15 D9

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EnglishUP PGT-2016 (02-02-2019)

Q242.If Q is non-singular matrix and P ia a square matrix such that det(Q–1 P2 Q)=4 then det P is equal to

A0 B1 C2 D4

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EnglishUP PGT-2016 (02-02-2019)

Q243.If 1 1 2 A, 3 4 − = then 2A is equal to

A−4 2/3 1 B4 2 3 1 − − − C−4 2/3 1 D4 2 3 1 − −

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EnglishPGT 2005

Q244.A, B are two square matrices of same order 3 and det A=2, det B= 3, then det (2AB) is equal to

A96 B48 C24 D12

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EnglishPGT 2005

Q245.The system of equations 2x+2y–3z –1=0, 4x+4y+z–2=0, 6x+6y–z–3=0 has

Aunique solution Bno solution Cinfinite solution Dzero solution

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EnglishPGT 2005

Q246.If the roots of the equation 1 1 1 2 2 2 3 3 3 − a x b c a b x c a b c x are 1, 2, 3 then the value of the determinants 1 1 1 2 2 2 3 3 3 a b c a b c a b c is

A11 B6 C–6 D0

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EnglishPGT 2005

Q247.If 1 0 1 0 1 1, 1 1 0 = A then

AA3 –2A2 –A+2I= 0 BA3 –2A2 –A+2= 0 CA3 +2A2 –A+2I= 0 DA3 +2A2 –A+2= 0

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EnglishPGT 2005

Q248.If x x x D x x x, x x x + λ = + λ = + λ = + λ = + λ + λ then D is equal to

Ax3/(x+λ) Bx2/(x+3λ) Cλ2/(3x+λ) Dλ2/(x+3λ)

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EnglishPGT 2005

Q249.If 3 1 2 6 2 4, 3 1 2 A − = − − = − − = − − = − − − − then what is the rank of A?

A0 B1 C2 D3

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EnglishPGT 2004

Q250.If 0 0 0 a h g A b c c = then the characteristic value of adj A is

Aab, bc, ca B1 1 1,, a b c C1 1 1,, ab bc ca DNone of the these

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EnglishPGT 2004

Q251.The system of equations x + y - 2z = a, x - 2y + z = b, -2x + y + z = c is consistent, if

Aa + b – c = 0 Ba – b + c = 0 Ca + b + c = 0 DNone of the above

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EnglishPGT 2004

Q252.Let A and B have 4 and 8 elements respectively. Then what can be maximum and minimum number of elements in A × × × B?

A16 B32 C35 D64

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EnglishPGT 2004

Q253.If α, β, γ are the roots of the equation x3 + ax2 + b = 0, then the value of α β γ α β γ α β γ α β γ β γ α β γ α β γ α β γ α γ α β γ α β γ α β γ α β will be

Aa3/– 3b B–a3 Ca3 DNone of the above

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EnglishPGT 2004

Q254.If 1 1 1 1 1 1 0, 1 1 1 + + = + a b c then 1 1 1 a b c − − − − − − − − − − − − + + + + is equal to

A1 B-1 Cabc DNone of the above

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EnglishPGT 2000 & 2004

Q255.If a b c m n p = k x y z, then the value of 6a 2b 2c 3m n p 3x y z will be

A6/k B2k C3k D6k

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EnglishPGT 2004

Q256.If 2 2, ij A a × = where ij 2 i j, i j a i 2j, i j + ≠ = − = then A-1 is equal to

A4 1 1 1 2 9 − B0 3 1 3 1 9 − − − C0 3 1 3 1 9 DNone of the above

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EnglishPGT 2003

Q257.If A = 2 1 3 5 then A–1 is equal to

A−5 1/3 2 B5 1 3 2 1 7 − C5 1 3 2 − − − D−2 1/3 5

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EnglishPGT 2003

Q258.Determine K so that the set S is linearly dependent in ((())) ((())) ((()) { { } } 3, 1,2,1,,3,1, 2,,0 IR S K K =

A2,–1 B2,1 C–2,–1 D–2,1

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EnglishPGT 2003

Q259.What is the value of the determinant? 2a a+b a+c a+d b+a 2b b+c b+d? c+a c+b 2c c+d d+a d+b d+c 2d =

A1 B–1 C(a–b)(b–c)(c–d)(d–a) DNone of these

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EnglishPGT 2003

Q260.What is the value of the determinant? 2 3 1 m m m 3 2 m 1 m m 2 3 m m 1 m 2 3 m m m 1

A(1–m4/)3 B(1–m4/) C(1–m4/)2 DNone of these

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