Math Chapter Wise

EnglishDSE TGT 2019

Q41.The equation x2 + y2 = 4 is solved for all integral values of x and y. These solutions are plotted on coordinate axes. What will be the area of the figure formed by joining these points?

A8sq.units B4 sq.units C4 2sq.units D8 2sq.units

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EnglishJSSC PGT 2018

Q42.The density of a r.v. X is given by: () [ ] 2 x a + bx for x 0,1 f x = 0 otherwise ∈. Find (a, b) if E (X) is 3/5.

A(3/5, – 3/5) B(3, –3) C(1, 2) D(3/5, 6/5)

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EnglishJSSC PGT 2018

Q43.Evaluate ∫ D xy∂ ∂ ∂ A where D is the region bounded by the line y = x – 1 and the curve y2 = 2x + 6.

A100 B36 C10 D6

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EnglishOAVS TGT 2017

Q44.∫ 1 0 1 dx =? 1+ x

A1 log2 2 Blog 3 Clog 2 D1

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EnglishOPSC PGT 2017

Q45.The value of integral 0 2 sin xdx is:

A0 BFormula option B (see source) C2 D2

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EnglishOPSC PGT 2017

Q46.The value of / 2 0 sin xlog(sinx)dx is:

Alog(/ 2) Blog(e / 2) Clog(2/) Dlog(2/ e)

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EnglishOPSC PGT 2017

Q47.The value of integral 1 x x dx is:

A–1 B2 C1 D0

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q48.Value of 3 0 xdx ∫ is equal to

A162 3 7 B27 3 7 C162 3 DNone of the above

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EnglishUP PGT 2021

Q49.The value of 7 16 1 0 d 1+ ∫ x is equal to –

A4/π B0 C32/π D1

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EnglishUP PGT 2021

Q50.() ∫ π/4 3 2 0 cos2θ cosθ dθ is equal to -

A2/π B4 2/π C3 16 2 π D3 8 π

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EnglishUP PGT 2021

Q51.If f(a – x) = f(x) then () ∫ a 0 xf x dx is equal to –

A() a 0 a f x dx 2 ∫ B() a 0 a f x dx ∫ C0 D() a 0 2 f x dx ∫

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EnglishUP PGT 2021

Q52.∞ ∫ 2 –x 0 e dx is equal to

A1 2 π B2/π C2/π Dπ

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EnglishUP PGT 2021

Q53.The area of the region bounded by the curve y = x3, x axis and the ordinates x = –2 and x = 1 is

A1 square unit B1 4 square unit C3 4 square unit D17 4 square unit

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EnglishUP PGT 2021

Q54.The area inside the cardioid r = a (1+cosθ) and outside the circle r = a is –

Aa2/(π + 2) Ba2 π 2 4 + Ca2/(π – 2) DNone of these

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q55.A function f(x) is defined in [0, 2] as follows- f(x) = 2 x;if xisrational x;if xisirrational The value of the upper Riemann integral of f(x) over [0, 2] is-

A14/3 B4 C8/3 D17/6

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EnglishUPPSC GIC 2021

Q56.The value of the integral () () () / 2 0 sin x dx sin x cosx π + ∫ is

Aπ B3 4 π C2/π D4/π

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q57.The value of the integral 2 2 d v d u u v dx dx dx − ∫ is-

A−dv du/dx dx Bdv du u v dx dx + Cdv du u v dx dx − Ddv du dx dx +

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EnglishUPPSC GIC 2021 UP PGT 2004

Q58.The value of the integral () 1 3/ 4 1 1 1 1/ 4 sin x 2 dx 2cos x 3sin x sin 1 x − − − − π + + + − ∫ is-

A1/4 B1/8 C3/4 D1

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EnglishUPPSC GIC 2021

Q59.An appropriate substitution for the integral 1/ 2 1/3 1 x dx 1 x + ∫ is-

Ax = t2 Bx = t3 Cx = t6 Dx = t12

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EnglishUPPSC GIC 2021

Q60.The value of the integral () 10 7 10 4 x dx x 11 x + − ∫ is-

A3 B310 C710/– 410 D3/2

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