Math Chapter Wise

EnglishPGT 2009

Q181.Volume of the solid generated by the revolution of the curve y = 3 2 2 a (a x) + about its asymptote is

A2 3 a 3 π B2 4 a 2 π C2 3 a 2 π DNone of these

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EnglishPGT 2009

Q182.If 0 () 2 () a a a f x dx f x dx − = ∫ ∫ ∫ ∫ then

A() f x is an even function B() f x is an odd function C() f x = f(2a – x) DNone of these

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EnglishPGT 2009

Q183.Surface area of a hemisphere of radius a is

A4πa2 B2πa2 Cπa2 Da2

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EnglishPGT 2005

Q184.If [x] stands for greatest integer function, then the value of 2 0 x dx ∫ ∫ is:

A4 B3 C6 DNone of these

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EnglishPGT 2005

Q185.4 sinxcosx dx 1 sin x + ∫ ∫ is:

Alog (1 + sin4/x )+c B2 1 log(1 sin) 2 + + x c C1 2 1 tan (sin) 2 − + x c Dtan –1 (sin2 x) + c

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EnglishPGT 2005

Q186.1 tan xdx − ∫ ∫ is equal to

A() 1 1 tan− + − + x x x c B() 1 1 tan− + + + x x x c C1 tan− + + x x x c D1 tan− − + x x x c

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EnglishPGT 2005

Q187.The area of the region bounded by the graphs of the curves f(x)=x2 and g(x)=x3 is:

A1/2 B1/3 C1/6 D1/12

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EnglishPGT 2005

Q188.The area of the region between the x-axis and the graph of f(x)=x3 –x2 –2x, –1≤ x ≤2 is

A37/12 B27/12 C5/12 D32/12

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EnglishPGT 2005

Q189.1 0 1 x cos 2cot dx 1 x − + ∫ ∫ is equal to

A−1/2 B1/2 C−1/4 D1/4

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EnglishPGT 2004

Q190.Area bounded by the curves y=, 2 3 x x y = + in the first quadrant and x-axis is

A2 3 B18 C9 D34/3

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EnglishPGT 2004

Q191.The area bounded by the curves x = at2, y = 2at x-axis 1≤ t ≤3 is

A26a2 B8a2 C2 26 3 a D2 104 3 a

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EnglishPGT 2004

Q192.The value of 1 3 4 1 1 1 1 4 cos x 2 dx 2sin x 3cos x cos (1 x) − − − − − − − − − − − − − π + + + − + + − + + − + + − ∫ ∫ is equal to

A1/4 B1/8 C1 D1/2

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EnglishPGT 2004

Q193.1 99 0 (1) x x − ∫ ∫ dx is equal to

A1/10100 B11/10100 C11/11100 D1/1010

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EnglishPGT 2004

Q194.() () () b a f x f x f a b x + + − + + − + + − + + − ∫ ∫ dx is equal to

A2 a b + B−2/a b C−2/b a DNone of the above

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EnglishPGT 2004

Q195.The value of the integral 1 1 2 2 2 2 1 2 1 1 2 1 1 − + − − + ∫ x x dx is

A4 log 3 B3 4log 4 C4 4log 3 D3 log 4

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EnglishPGT 2004

Q196.If F[x] stands for the greatest integer function, the value of 2 10 2 2 4 [ ] [ 28 196] [ ] x dx x x x − + + − + + − + + − + + ∫ ∫ is

A0 B1 C3 D4

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EnglishPGT 2003

Q197.∫ π/2 0 2 cosxdx (1 + sinx) (2 + sinx) is equal to

A4 log 3 B3 log 4 C0 DNone of these

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EnglishPGT 2003

Q198.2 0 1 2 cos − + ∫ d a a π θ is equal to (where a<1)

A−1 a/π B1 2 1 a − C2 1 a π − D0

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EnglishPGT 2003

Q199.Find the area of the intersected curve formed by 2 2 1 y x = + = + and 1 0 x y − − = − − = − − = − − =

A4 sq.unit B3 4 Sq.unit C2 4 3 Sq.unit DNone of these

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EnglishPGT 2002

Q200.(()))2 cospx sinqx dx, π −π − ∫ ∫ where p and q are integers, is equal to:

A–π B0 Cπ D2π

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