Math Chapter Wise

EnglishKVS PGT 2022

Q21.The area of the region (in sq. units) bounded by the lines y=x+1, x=2 and x=3 is:

A9/2 B11/2 C7/2 D13/2

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EnglishKVS PGT 2022

Q22.2a 0 f(x) ∫ dx is equal to:

A2a 0 2 f(x)dx ∫ B0 C2a 2a 0 0 2 f(x)dx f (2a x)dx + − ∫ ∫ DFormula option D (see source)

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EnglishKVS PGT 2022

Q23.∫ x 2 x + 2 e dx (x + 3) is equal to;

Ax e c x 3 − + − B2x 1 e. c x 3 + Cx e c x 3 + − Dx e c x 3 +

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EnglishKVS PGT 2022

Q24.2 dx 5 4x 2x − − ∫ is equal to:

A1 1 2(x 1) sin c 2 7 − + B1 2 sin (x 1) c 7 − + + C1 1 2(x 1) sin c 2 7 − + D1 log | x x 1 | c 2 + + +

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EnglishRPSC PGT 2022

Q25.∫ 2 1 e x dx is equal to

Ae B(2 1) C(2 1)e D−2 1/e

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EnglishRPSC PGT 2022

Q26.Value of the integral ∫ 1 0 log(1+ x) dxis x

A2 12 π B2 6 π Cx 2 1 2 2 x 1 + > + D∇

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EnglishRPSC PGT 2022

Q27.Area bounded by the curves y = 3 – x2 and y = 2x, is -

A16 sq. units 3 B27 sq. units 6 C12sq. units D32 sq. units 3

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EnglishRPSC PGT 2022

Q28.The integral I = ∫ tanx dx sinx cosx is equal to -

Alog (tan x 2) + c Blog (sinx) + c C2 tan x c/+ D–tan–1 (cosx) +c (Where c in constant of integration)

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EnglishDSSSB PGT 2021

Q29.The improper integral () ∫ 1 0 3 dx 2x 2x – 1 has

APoint of infinite discontinuity of 1, 1 2 BPoint of infinite discontibuity at 0, 1 2 CPoint of infinite discontinuity at 0, 1 DPoint of infinite discontinuity at 0

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EnglishDSSSB PGT 2021

Q30.The integral ∞ ∫ 0 sinx dx x

Ais convergent but not absolutely Bis not convergent Cis absolutely convergent Dis absolutely divergent

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EnglishDSSSB PGT 2021

Q31.The integral ∞ ∫ 0 sinxdx -

AExists and is equal to 1 BExists and is equal to 0 CExists and is equal to –1 DDoes not exist

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EnglishDSSSB PGT 2021

Q32.The integral P 1 sin x dx x ∞ ∫ converges -

AAbsolutely for P > -1 BAbsolutely for P > 0 CAbsolutely for P > 1 DAbsolutely for P = 1

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EnglishDSSSB PGT 2021

Q33.∞ ∫ 2 2 –a t 0 e dt is equal to:

A3a/π B2/π Ca π D2a/π

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EnglishDSSSB PGT 2021

Q34.If f is Riemann integrable with respect to α on [a, b], then:

Af is bounded and α is increasing function Bf and α are both bounded Cf is increasing and α is bounded function Df and α are increasing

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EnglishDSSSB PGT 2021

Q35.Which one of the following is not correct on an interval [a, b]?

AEvery integrable function is bounded BEvery discontinuous function is integrable CEvery continuous function is integrable DEvery continuous function has a primitive

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EnglishDSSSB PGT 2021

Q36.The value of definite integral ∫ a –a x dx is equal to:

A2a Ba2 C0 Da

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EnglishOAVS TGT 2021

Q37.The integral 2 6sin xdx is:

A2 (2x sin 2x) 3 B3 (2x sin 2x) 2 C3 (2x sin 2x) 2 D2 (2x sin 2x) 3

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EnglishOAVS TGT 2019

Q38.The value of ∫ π/2 0 x dx=? sinx + cosx

Aπ log 2 + 2 2 2 Bπ log 2 –1 2 2 C0 Dπ log 2 +1 2 2

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EnglishOAVS TGT 2019

Q39.The value of ∫ π 7 0 sin xdx =?

A32 35 π B38 35 π C32/35 D0

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EnglishOAVS TGT 2019

Q40.The value of () ∫ 2 –2 f x dx,where f(x) = 1 + 2x, x ≤ 0; f(x) = 1 – 2x,x ≥ 0 is:

A4 B– 4 C– 2 D0

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