Math Chapter Wise

EnglishUP PCS (Pre) 2001

Q281.The value of [ ] f(x) -f(-x) dx ∫ a -a is equal to:

A2∫ a 0 f(x) dx B4∫ a 0 f(x) dx C2∫ a 0 [f(x)- f(-x)dx Dzero

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EnglishUP PCS (Pre) 2001

Q282.The value of the integral ∫ 1 -1 -1 -1 2 -1 2sin x + 3tan x + 4cos x dx 1 - x is:

A0 Bπ Cπ2 D4π2

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EnglishUP PCS (Pre) 2002

Q283.The surface of the solid formed by the revolution of the curve 3 2 t x = t,y = t - 3 about axis is:

Aπ B2π C3π D4π

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EnglishUP PCS (Pre) 2002

Q284.The whole area of the curve r = a cos 2θ is:

Aπa2 B2πa2 C2 a 4 π D2 a 2 π

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EnglishUP PCS (Pre) 2002

Q285.The length of the normal at the point (x,y) to the curve x -x a a 1 y = a e +e 2 is:

A2 x a cos a B2 x a sin a C2 x a sin h a D2 x a cos h a

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EnglishUP PCS (Pre) 2002

Q286.The function x x x f(x) = + +1 is: 2 e -1

Aan odd function Ban even function Cneither an odd nor an even function Da periodic function

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EnglishUP PCS (Pre) 2002

Q287.The area bounded by the curves y = x2 and y = 2 x is

A4/3 B2/3 C8/3 D1/3

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EnglishUP PCS (Pre) 2002

Q288.0 π ∫ 2 xsinx dx is equal to: 1+ cos x

A4/π B2/π C2 4 π Dnone of the above

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EnglishUP PCS (Pre) 2003

Q289.The volume generated by the revaluation of the ellipse 2 2 x y 1 a b about its major axis:

A2 1 ab 3 B2/ab C2/4 ab D2 4 ab 3

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EnglishUP PCS (Pre) 2003

Q290.n 1 2 2 n r 1 1 lim n r

AImage/formula option A (see source) Bπ/2 Cπ/3 Dπ/4

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EnglishUP PCS (Pre) 2004

Q291.The value of the integral / 2 0 (x)dx (x) x 2 is

AImage/formula option A (see source) Bπ/2 Cπ/3 Dπ/4

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EnglishUP PCS (Pre) 2004

Q292.The value of the integral a 3 0 0 r d dr is–

A4 3 a 10 B4 a 5 C4 5 a 20 D5 5 a 25

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EnglishUP PCS (Pre) 2004

Q293.5n n r 1 1 lim n r →∞ →∞ = + + ∑ ∑ is equal to-

A5 0 1 dx 1 x B1 0 1 dx 1 x C5 1 dx 1 x D1 dx 1 x

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EnglishUP PCS (Pre) 2004

Q294.Length of curve 2/ 3 2/ 3 2/ 3 x y a in the first quadrant is–

Aa B2a Ca/2 D3a/2

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EnglishUP PCS (Pre) 2004

Q295.The area of the region bounded by y x 1 and y 1 is–

A0 unit B1 unit C1 2 unit Dunit

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EnglishUP PCS (Pre) 2005

Q296.The value of the integral 1 0 ∫∫ 2 0 (4- x - y)dx dy is:

A2 B4 C5 D– 4

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EnglishUP PCS (Pre) 2005

Q297.The area enclosed by the curve y = 2 cos x and the x-axis, from x = 0 to x = 2π, is:

A0 B2 C4 D8

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EnglishUP PCS (Pre) 2005

Q298.The volume of a sphere, whose surface area is (100π), is:

A500π B250 3 π C500 3 π D600π

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EnglishUP PCS (Pre) 2006

Q299.() () = − ∫ b a f(x)dx b a f r, where r is some number such that:

Aa<r<b Ba≤r≤b Cb<r<a Db≤r≤a

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EnglishUP PCS (Pre) 2006

Q300.The value of 0 sinx cosx dx π + ∫ ∫ is:

A2 B2 2 C3 2 D4 2

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