Math Chapter Wise

EnglishUP PCS (Pre) 2006

Q301.The volume of the solid generated by revolution about the initial line of the area bounded by the curve r = f(θ) and the radii vectors θ=α and θ=β is given by

A3 3 2 r sin d β α π θ ∫ B3 2 2 r sin d 3 β α π θ ∫ C3 2 r sin d 3 β α π θ ∫ D2 rsin d 3 β α π θ ∫

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EnglishUP PCS (Pre) 2006

Q302.The whole area enclosed by the curve r = acos2θ is equal to:

Aπa2 B2 1 a 2 π C2 1 a 4 π D2 1 a 8 π

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EnglishUP PCS (Pre) 2006

Q303.The perimeter of loop of curve x=t2, 3 1 y t t 3 = − = − is:

A3 B2 3 C4 3 D6 3

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EnglishUP PCS (Pre) 2006

Q304.The value of the integral: 2 1 1 x 2 2 0 0 dxdy 1 x y + + + ∫ ∫ ∫ ∫ is equal to

A() e log 2 1 4 π + B() e log 2 1 2 π + C2 8 π D2 16 π

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EnglishUP PCS (Pre) 2007

Q305.x / 2 1 sinx e 1 cosx is equal to–

Ax / 2 x e sec C 2 Bx / 2 x e sec C 2 Cx / 2 x e tan C 2 Dx / 2 x e tan C 2

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EnglishUP PCS (Pre) 2007

Q306.The value e 0 log (1 cosx)dx of is–

Alog2 B1 log 2 Clog 2 Dlog 2

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EnglishUP PCS (Pre) 2007

Q307.The value of 7 1/ 4 1/ 4 1/ 4 2 x dx x (9 x) is–

A5/2 B7/2 C9/2 Dnone of the above

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EnglishUP PCS (Pre) 2008

Q308.The value of C yds ∫ ∫ along the curve C given by y 2 x = from x = 3 to x = 24, is

A28 B56 C98 D156

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EnglishUP PCS (Pre) 2008

Q309./ 2 0 π ∫ e sin2x log tan x dx is equal to

A0 Be log 2 8 π Ce log 2 4 π De log 2 6 π

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EnglishUP PCS (Pre) 2008

Q310.The value of / 2 0 2 2 3 3 sin x -cos x dx is sin x + cos x π ∫

A0 B1 C1/2 D1/3

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EnglishUP PCS (Pre) 2008

Q311.The radius of curvature is

Athe curvature Bthe square of the curvature Cthe reciprocal of the curvature Dthe double of the curvature

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English(GIC) Lecturer Exam, 2015

Q312.The area enclosed by the ellipse x=a cos t, y = sin t, t∈[0, 2π] is

A2πa B2 a 2 π Cπa D2 a 4 π

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English(GIC) Lecturer Exam, 2015

Q313.The value of − ∫ 100π 0 1 cos2x dx is

A100 B100 2 C200 2 D400 2

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English(GIC) Lecturer Exam, 2015

Q314.The area of the triangle formed by the lines x-y = 0 and x+y = 0 any tangent to hyperbola x2 –y2 =a2 is

A2 1 a 2 Ba2 C2a2 D4a2

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English(GIC) Lecturer Exam, 2015

Q315.If ∫ 2 1 2 1 dx I = 1+ x and ∫ 2 1 dx I = x then

Al1>l2 Bl2>l1 Cl1=l2 Dl1>2l2

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English(GIC) Lecturer Exam, 2015

Q316.The value of − ∫ 2 x 2 1 e (x 1) dx x is equal to

Ae e 1 2 − Be(e–1) C0 D1

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English(GIC) Lecturer Exam, 2015

Q317.The area of the region bounded by the parabolas x = –2y2 and x = 1 –3y2 is

A5/3 B4/3 C7/3 D3

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English(GIC) Lecturer Exam, 2015

Q318.The value of ∫ 1 -1 1- x dx is equal to

A–2 B0 C2 D4

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English(GIC) Lecturer Exam, 2015

Q319.If f(x) is an odd function, then which one of the following is correct for the function ∫ x 0 f(t) dt?

Aodd Beven Cneither even nor odd Dperiodic

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English(GIC) Lecturer Exam, 2015

Q320.If f is an odd function, then () ∫ 2 -2 x + x f(x) dx is equal to

A0 B2 C4 D–4

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