Math Chapter Wise

English(GIC) Lecturer Exam, 2015

Q321.The value of − ∫ 3 cos x cos x dx π/2 -π/2 is equal to

A1 B1/3 C4/3 D2/3

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English(GIC) Lecturer Exam, 2015

Q322.The area of the region bounded by the curve 1 y sin (sin x), 0 x and x-axis is–

A2 B2 C2/4 D2/8

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English(GIC) Lecturer Exam, 2015

Q323.The value of / 4 0 sin(x [x])dx is equal to: ([x] denotes the greatest integer ≤ x)

A1/2 B1 C1/2 D1/2

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English(GIC) Lecturer Exam, 2015

Q324.The value of cos x 0 1 dx 1 e is equal to–

Aπ/4 Bπ/2 Cπ D2π

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English(GIC) Lecturer Exam, 2015

Q325.1 2 0 2x 1 tan dx 1 x x is equal to–

A0 B1 C–1 D2

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EnglishTGT 2013

Q326.The value of 3 /4 /4 dx 1 cosx π + + ∫

A1 B–1 C0 D2

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EnglishUP PCS (Pre) 1997

Q327.The orthogonal trajectories of the family of curves xy=c2 are:

A2 2 2 2x 3y a − = B2 2 2 2x 3y a + = C2 2 2 x y a + = D2 2 2 x y a − = Where a is a constant

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EnglishUP PCS (Pre) 1997

Q328.Let / 6 2 2 0 I sin ucos udu, π = ∫ ∫ ∫ then:

AI 48 π = BI 48 π < CI 48 π > DNone of these

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EnglishUP PCS (Pre) 1997

Q329.The value of (((()))) 2 2 x y 0 0 e dxdy ∞ ∞ − + ∫∫ ∫∫ is

Aπ/2 Bπ/4 Cπ/3 DNone of these

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EnglishUP PCS (Pre) 1997

Q330.The solution of x y 2 y dy e x e dx − − = + = + is:

Ay x 3 1 e e x c 3 − = + + By x 3 1 e e x c 3 − = + + Cy x 3 1 e e x c 3 = + + DNone of these where c is an arbitrary constant

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EnglishTGT 2010

Q331.n dx x(x 1) + ∫ ∫ is equal to

A1 log 1 n x n x + Blog 1 n x x + C1 n x x + D1 n x x +

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EnglishTGT 2010

Q332.2 2 dx (x 1)(x 4) + + ∫

A1 1 tan tan / 2 3 3 x x c − − − + B1 1 tan tan / 2 3 3 x x c − − + + C1 1 tan tan / 2 3 6 x x c − − − + D1 1 tan 2tan / 2 x x c − − − +

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EnglishTGT 2010

Q333.The value of 3 0 sin θdθ π ∫ ∫ is

A0 B3/8 C4/3 Dπ

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EnglishTGT 2010

Q334.dx cos(x a)cos(x b) − − ∫

Asin() cosec()log sin() x a a b c x b − − + − Bcos() cosec()log cos() x a a b c x b − − + − Csin() cosec()log sin() x b a b c x a − − + − Dcos() cosec()log cos() x b a b c x a − − + −

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EnglishTGT 2010

Q335.The integration of loge x is

A1/x B0 Cx loge x–1 DNone of these

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EnglishTGT 2009

Q336.The value of (()))((()) cosx dx 1 sinx 2 sinx + + ∫ ∫ –

A1 sin x log 2 sin x + B2 sin x log 1 sin x + C1 sin x 2 sin x + DNone of these

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EnglishTGT 2009

Q337.What is the area of the region bounded by the parabola y = 2x and coordinates x = 1, x = 4?

A4 2 3 Square unit B28 2 3 Square unit C56 3 Square unit DNone of these

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EnglishTGT 2005

Q338.The value of cos x dx ∫ ∫ is equal to-

A2 sin cos x x x c + + B2 sin cos x x x c − + C2 2 sin cos x x x c − + DNone of these

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EnglishTGT 2005

Q339.If 'a' such that a 0 xdx a 4 ≤ + ∫ ∫ then:

A0 4 a ≤ B2 0 a − ≤ C2 4 a or a ≤ − ≥ D2 4 a − ≤

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EnglishTGT 2005

Q340.The value of 2 6 sin xcos x dx − ∫ ∫ is

A1 1 3 5 tan x tan x tan x c 3 5 + + + B1 1 3 5 tan x tan x c 3 5 + + C1 1 3 5 tan x tan x c 3 5 − − + DNone of these

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