Math Chapter Wise

EnglishPGT 2002

Q201.f: R→ → →R, g:R→ → →R are continuous functions. The value of integral: 2 f(x) f(x) g(x) g(x) dx is: π − + − − − + − − − + − − − + − − − ∫

Aπ B1 C–1 D0

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EnglishPGT 2002

Q202.x 0 f(x) t(t 1)(t 2) = − − = − − = − − = − − ∫ ∫ takes on its minimum value when:

Ax= 1,2 Bx = 0, 1 Cx = 0,2 DNone of these

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EnglishPGT 2002

Q203.Area bounded by the curve y2 (2a–x)=x3 and the line x = 2a is:

A3πa2 B2 a 3 2 π C2 a 3 4 π DNone of these

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EnglishPGT 2002

Q204.Let 2 x: x 0 f(x) x: x 0 < = ≥ Area bounded by the curve y=f(x), y=0 and 2 2 x 9a = is 9a 2, then a=?

A1/2 B–1/2 C0 DNone of these

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EnglishPGT 2000

Q205.2 4 2 x 1 dx x x 1 − + + ∫ ∫ is equal to:

A2 1 x x 1 log 2 x x 1 + − + + B2 1 x x 1 log 2 x x 1 + + − + C2 1 x x 1 log 2 x x 1 − + + + DNone of these

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EnglishPGT 2000

Q206.The value of / 4 0 log(1 tan)d π + θ + θ + θ + θ ∫ ∫ is equal to:

Alog2 2 π − Blog2 8 π − Clog2 2 π Dlog2 8 π

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EnglishPGT 2000

Q207.The value of the integral 1 0 x logsin dx 2 π ∫ ∫ is equal to:

A–log2 Blog2 Clog2 2 π Dlog2 2 π −

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EnglishRajasthan TGT 2016

Q208.2 0 1 x dx − = ∫

A0 B–1 C1 D1/2

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EnglishRajasthan TGT 2016

Q209.The area of the loop of the curve ay2 =x2 (a–x) is equal to

A2 a 5 sq. unit B2 8a 15 sq. unit C2 7a 15 sq. unit D2 6a 15 sq. unit

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EnglishRajasthan TGT 2016

Q210.The area bounded by the curve y=2x4 –x2, the x axis are the two ordinates corresponding to minimum of the function is

A1 24 square unit B1 40 square unit C7 120 square unit DNone of these

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EnglishRajasthan TGT 2016

Q211.The area bounded by the curve xy=1, y= x, x=e and y=0 is divided by the line x=1 in the ratio

A3:1 B1:2 C3:2 D1:4

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EnglishRajasthan TGT 2016

Q212.If ((()) (()) 1 m n m p 0 0 x x 1 x dx dx, 1 x ∞ − = + ∫ ∫ ∫ ∫ then p equal to

Am+n Bm+n–1 Cm+n–2 Dm+n+2

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EnglishRajasthan TGT 2015

Q213.2 dx 1 3sin x + ∫ ∫ is equal to -

A1 tan (tan x) 2 − B−1/2tan (tan x) C1 tan (2tan x) 2 − D1 1 2tan tan x 2 −

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EnglishRajasthan TGT 2015

Q214.If 2 log x 1 x dx gof (x) C 1 x then

A() 2 f(x) log x 1 x = + + and 2 g(x) 1 x = + B2 f(x) log x 1 x = + + and 2 g(x) x = C2 f(x) log x 1 x = + + and 2 x g(x) 2 = D2 x f(x) 2 = and 2 g(x) log x 1 x = + +

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EnglishJharkhand TGT 2017

Q215.The value of (((())))(((()))) 7 6 x sin x cos x dx ∫ ∫ in[ [ [ ] ] 0,π is

A16/π B16 3003 π C3 128 π D3 152 π

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EnglishUP TGT-2016 (08-03-2019) UPPCS Pre- 1998

Q216.The area of the region bounded by to curves y2 = x and x2 = y is

A1/3 B2/3 C1 D2

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EnglishUP TGT-2016 (08-03-2019)

Q217.The value of 3 2 2 4 dx sin xcos x π ∫ ∫ is

A1 B0 C2/3 D1/3

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EnglishUP TGT-2016 (08-03-2019)

Q218.2 1 x x dx − ∫ ∫ is equal to

A0 B2/3 C5/3 D7/3

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EnglishUP TGT-2016 (08-03-2019)

Q219.The area enclosed between the curves y= sinx, y=cosx, 0 x 2 π ≤ is

A2 1 B2 1/+ C−( )/2 2 1 D() 2 2 1 +

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EnglishUP TGT-2016 (08-03-2019)

Q220.Value of the integral 1 2 x log dx 2 x − + ∫ ∫ is

A2 B1 C1/2 D0

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