Math Chapter Wise

EnglishUPPSC GIC 2021

Q61.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

Q62.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

Q63.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

Q64.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

Q65.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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EnglishUP TGT 2021

Q66.The area of cut off the parabola 4y = 3x2 by the straight line 2y = 3x + 12 is

A15 sq. units B18 sq. units C24 sq. units D27 sq. units

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EnglishUP TGT 2016, 2021 UP PCS (Pre) 1998

Q67.The area of the region bounded by the curves y2 = x and x2 = y is

A1 B2 C1/3 D2/3

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EnglishUP TGT 2021

Q68.() ∫ x 3 e x – 1 x +1 dx equal to

A() x 2 e C x 1 + Bx e C x 1 + C() x 2 –e C x 1 + D() x 2 e C x –1 +

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EnglishUP TGT 2021

Q69.Integral of ∫ cotx dx log sinx is

Alog(sinx) + C Blog(cosx) + C Clog(log tanx) + C Dlog(log sinx) + C

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EnglishUP TGT 2021

Q70.() ∫ 3 logx 1 e +1 dx is equal to

A2 B6 C0 D–2

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EnglishUP TGT 2021

Q71.() ∫ 1 –1 2 0 tan x dx 1+ x is equal to

A1 B2 8 π C2 32 π D2 3 π

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EnglishUP TGT 2021

Q72.∫ π 3 2 2 π 4 dx sin xcos x is equal to -

A1 B0 C2/3 D1/3

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EnglishUP TGT 2021

Q73.∫ π/2 2 0 sinx cosx dx cos x + 3cosx + 2 is equal to

A3 log 2 B9 log 8 Clog 2 D1

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EnglishUPPSC Ashram Paddhati 2021

Q74.The value of the integral ∫ π 2 0 log cosx dx is

Aπ – log 2 2 Bπ log 2 2 C– log 2/π Dlog 2/π

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EnglishUKPSC Lecturer (Mains) 2020

Q75.If [x] is the greatest integer function, then 2 0 d ∫ 2 x x is:

A2 2 B2 2/+ C2 1 D2 1/+

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EnglishUKPSC Lecturer (Mains) 2020

Q76.∫ 1 a- n 1 n x dx = a - x + x

Aa 1 2 n + B−a 1/2 n C2 a n + D−a 2/2 n

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EnglishUKPSC Lecturer (Mains) 2020

Q77.Let 2 0 1 2 () a a a, φ = + + x x x then 1 0 ()d φ = ∫ x x

A1 (0) 4 (1) 2 φ + φ +φ B1 1 (0) 4 (1) 2 2 φ + φ +φ C1 1 (0) 4 (1) 3 2 φ + φ +φ D1 1 (0) 4 (1) 6 2 φ + φ +φ

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EnglishUKPSC Lecturer (Mains) 2020

Q78.If π / 2 sin d sin 2, θ = θ ∫ x x then the value of θ satisfying 0 π < θ < is:

A2π/3 Bπ/6 C5π/6 Dπ/2

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EnglishUKPSC Lecturer (Mains) 2020

Q79.2 1 d (1)2(2) + + + ∫ x x x is equal to:

A() 1 e e 3log | 1| 1 3log 2 c − + + + − + + x x x B() 1 e e 3log | 1| 1 3log 2 c − + − + − + + x x x C() 1 e e log | 1| 1 log 2 c − + − + − + + x x x D() 1 e e 3log | 1| 2 1 3log 2 c − + + + − + + x x x Where c is an arbitrary constant.

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EnglishUP TGT 2016 UKPSC Lecturer (Mains) 2020

Q80.The value of 1 2 log d 2 − + ∫ x is:

A2 B1 C–1 D0

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