Math Chapter Wise

EnglishUP PCS (Pre) 2000

Q321.The value of n 1 2 2 r 1 1 n r − = − − ∑ ∑ is:

A0 B2/π Cπ D2π

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EnglishUP PCS (Pre) 2000

Q322.The value of { {{ { } }} } 2 x 0 1 1 x lim x → − − is equal to

A1 B1/2 C1/4 D1/8

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EnglishUP PCS (Pre) 2000

Q323.The value of the limit 2 x 0 tan x x lim x tan x → − is equal to:

A0 B–1 C−1/2 D1/3

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EnglishUP PCS (Pre) 2000

Q324.The value of the 4 2 3 x 1 x sin x x lim 1 | x| →−∞ + is equal to:

A–1 B0 C1 Dnone of these

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EnglishUP PCS (Pre) 2000

Q325.The function ((()) (()) (()) p 1 x sin x 0 x f x 0 x 0 = ≠ = is both continuous and differentiable at x = 0 if:

A–1 < p < 0 B0 ≤ p ≤ 1 C1 < p Dnone of these

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EnglishUP PCS (Pre) 2001

Q326.The value of the n lim →∞ ∑ n-1 2 2 r=0 n n + r is:

Aπ/8 Bπ/4 Cπ/2 Dπ

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EnglishUP PCS (Pre) 2001

Q327.Let ≠ x f(x) =, for x 0 x f(0) = 5k then:

Af is continuous at all the points except x=0 Bf is not continuous at any point Cf is continuous at all the points if k =0 Df is continuous at all the points if k =1/5

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EnglishUP PCS (Pre) 2001

Q328.If 2 f(x) = log(x +1) then x 2 lim → f(x)-f(2) x - 2 is equal to:

A0 B4/5 C1/2 D5/4

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EnglishUP PCS (Pre) 2001

Q329.x 0 log cos ax lim log cos bx → is equal to:

Aa/b B2 a b Cb/a D2 b a

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EnglishUP PCS (Pre) 2001

Q330.A function f(x) is defined for all x>0 and satisfies f(x)2 =x3 for all x>0. The value of f'(4) is:

A3 B4 C5 D64

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EnglishUP PCS (Pre) 2001

Q331.The value of x 0 lim → x e - 1 x is equal to:

A–1 B0 C1 D2

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EnglishUP PCS (Pre) 2001

Q332.The value of the 0 → 2 x log(1- x) lim log cos x is:

A0 B1 C–2 D2

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EnglishUP PCS (Pre) 2001

Q333.A particle moves in a straight line according to the equation x=4t3 +2t+5 where x is in meters and t in seconds. The average acceleration of the 4th second is:

A84 meter/sec2 B96 meter/sec2 C194 meter/sec2 D110 meter/sec2

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EnglishUP PCS (Pre) 2002

Q334.2 1/x x 0 tanx lim x → is equal to:

A1 Be1/2 Ce1/3 D0

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EnglishUP PCS (Pre) 2003

Q335.x sin x lim x

A1 B0 Cneither 1 nor 0 D∞

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EnglishUP PCS (Pre) 2004

Q336.At x = 0, the fuction 1 xcos, x 0 (x) x 0, x 0 f is

Aundefined Bdiscontinuous Ccontinuous but not differentiable Ddifferentiable

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EnglishUP PCS (Pre) 2005

Q337.If ∫ x c A(x) = (f(t) + 2)dt. then A' (x) is:

Af(x) Bf(x)+2 Cf(c) Df(c)+2

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EnglishUP PCS (Pre) 2005

Q338.If 2 f(x) = 1- x and g(x) = 1- x, where –1≤ x≤ 1, then Rolle's theorem is:

Aapplicable to both f(x) and g(x) Bapplicable to f(x), but not to g(x) Capplicable to g(x), but not to f(x) Dapplicable neither to f(x) nor to g(x)

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EnglishUP PCS (Pre) 2005

Q339.x 1 lim 1+ x →∞ is equal to:

A1 B0 Ce D1/e

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EnglishUP PCS (Pre) 2006

Q340.x 1 1 1 lim....... n 1 n 2 2n →∞ + + + + + + + + + + + + + + is equal to:

Aloge2 B–loge2 C0 D∞

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