Math Chapter Wise

EnglishUP TGT 2021

Q61.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

Q62.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

Q63.() ∫ 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

Q64.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

Q65.() ∫ 3 logx 1 e +1 dx is equal to

A2 B6 C0 D–2

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EnglishUP TGT 2021

Q66.() ∫ 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

Q67.∫ 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

Q68.∫ 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

Q69.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

Q70.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

Q71.∫ 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

Q72.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

Q73.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

Q74.2 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

Q75.The value of 1 2 log d 2 − + ∫ x is:

A2 B1 C–1 D0

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EnglishUKPSC Lecturer (Mains) 2020

Q76.The value of the integral 3/2 1 sin π d − ∫ x x x is:

A2 1 π B2 (3π 1) π + C2 (3π 1) π − D3/π

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EnglishUKPSC Lecturer (Mains) 2020

Q77.Solution of 4 1 d 1 − ∫ x x is:

A1 e 1 1 1 log tan c 4 1 2 − − + + x /j B1 e 1 1 1 log tan c 4 1 2 − + − + − x /j C1 e 1 1 1 log tan c 4 1 2 − + + + x /j DNone of these where c is an arbitrary constant.

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EnglishUP PCS (Pre) 2000 UKPSC Lecturer (Mains) 2020

Q78.If I(n) π/4 n 0 tan d = ∫ x x. Then I(n) + I(n - 2) =

A−1/n 1 B1/n C1 n 1 + Dn 1

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EnglishUKPSC Lecturer (Mains) 2020

Q79.1 0 sin 2π d ∫ x x is equal to:

A0 B−1/π C1/π D2/π

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EnglishUKPSC Lecturer (Mains) 2020

Q80.The area bounded by the curves y = 2x2 and y= x4 –2x2 is:

A16/15 B32/15 C64/15 D128/15

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