Math Chapter Wise

EnglishUP PCS (Pre) 1997

Q321.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

Q322.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

Q323.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

Q324.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

Q325.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

Q326.2 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

Q327.The value of 3 0 sin θdθ π ∫ ∫ is

A0 B3/8 C4/3 Dπ

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EnglishTGT 2010

Q328.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

Q329.The integration of loge x is

A1/x B0 Cx loge x–1 DNone of these

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EnglishTGT 2009

Q330.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

Q331.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

Q332.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

Q333.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

Q334.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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EnglishTGT 2005

Q335.The area bounded by y tanx,y cot x =, x-axis in interval 0, 2 π

Alog2 Blog2 2 π C1 log2 4 π DNone of these

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EnglishTGT 2005

Q336.The area under the curve y 3 sinx sin2x + = + = between the co-ordinate x = 0 and x 6 π = is

A() 1 7 4 4 − B() 1 7 4 3 4 − C() 1 7 3 4 − DNone of these

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EnglishTGT 2005

Q337.What will be the curve y x 1.y 0 = − = − = − = − = and x 2 = the area of region bounded by-

A5 B4 C9/5 DNone of these

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EnglishTGT 2005

Q338.Which of the following function in an even function -

A() 1 x a f x x a + = − B() 1 x a f x x x a − = + C() x x a a f x x x a a − = − + D() sin f x x =

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EnglishTGT 2004

Q339.The value of [ [ [ ] ] 4 e 1 log x ∫ ∫ dx is: ([x] is the greatest integer less than or equal to x)

A4 loge 2 Bloge 4 Cloge 6 D–loge 6

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EnglishTGT 2004

Q340.If a, b, c are non -zero real number, such that (((()))) (((()))) 3 3 2 2 0 1 3ax 2bx + c dx 3ax 2bx + c dx + = + + = + + = + + = + ∫ ∫ ∫ ∫ then the relation between a, b, c is

Aa + b + c = 3 Ba + b + c = 1 Ca + b + c = 0 Da + b + c = –2

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