Math Chapter Wise

EnglishPGT 2009

Q201.If y = 1 1 2 sin x sin 1 x − − + − + − then dy dx =?

A0 B1 Csin x DNone of these

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EnglishPGT 2009

Q202.Points of discontinuity of function tan x + cot x is

A3/π B6/π C2 ± nπ DNone of these

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EnglishPGT 2009

Q203.1 1 1 lim.... 1 2 6 n n n n →∞ + + + + + + + + + + + + + + is:

A1/6 Blog 6/e Clog 2/e D0

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EnglishPGT 2005

Q204.1 1 1 tan 1 1 − − + − − + − − + − − + − − + + − + + − + + − + + − d x x dx x x is equal to:

A2 1 1− x B2 1 2 1− x C2 1 2 1 − − x D2 1 − − x

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EnglishPGT 2005

Q205.If f(x) is defined as f(x) = x2 1 sin, x x ≠ 0 f(0)= 0 then

A0 lim () → x f x does not exist B0 lim () → x f x exists but f '(0) does not exist C0 lim () → x f x and f '(0) both exist Df '(x) is continuous at x = 0

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EnglishPGT 2005

Q206.(())) ((()) 1 1 0 lim 2 tan 2 tan − − → + + − + + − + + − + + − x x x x x is-

A0 Bπ C∞ Ddoes not exist

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EnglishPGT 2005

Q207.The non-zero value for the constant k so that the function f(x) defined by 2 tankx,x 0 x f(x) 3x 2k, 0 < = + ≥ will be continuous at x=0, is:

A1 B2 C44 DNone of these

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EnglishPGT 2005

Q208.(()) 2 h 0 f(x 2h) 2f x h f(x) lim h → + − + + + − + + + − + + + − + + is equal to

A() " f x h B() " f x C() 2 " f x Ddoes not exist

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EnglishPGT 2005

Q209.If f(x)=xn, then the value of (())) ((())) ((())) ((()) n f ' 1 f " 1 f '" 1 f 1 f(1)...... 1! 2! 3! n! + + + + + + + + + + + + + + + + + + + + is

Aπ B2n+1 C2n–1 D2n

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EnglishPGT 2005

Q210.x 1 lim n →∞ [n+1)(n+2)(n+3).......(n + n)]1/n is equal to

Ae B1/e C2/e D4/e

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EnglishPGT 2005

Q211.2 2 2 3 x 1 lim 1 2... n n →∞ + + + + + + + + + + + + is equal to

A1/2 B1/3 C1/4 D1

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EnglishPGT 2005

Q212.The value of 1/ 2 1 d 1 cosx tan dx 1 cosx − + is:

A() 2 sin x 2 1 cos x − B() 2 cosx 2 1 cos x − C() 2 sin x 2 1 cos x + D() 2 cosx 2 1 cos x +

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EnglishPGT 2004

Q213.If x = secθ - cosθ and y = secn θ - cosn θ, then the value of 2 2 dy (x 4) dx + is

A2 2 (4) + n y B2 2 (4) + x y C2 (4) + y DNone of the above

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EnglishPGT 2004

Q214.The value of 0 1 (1 cos2) 2 lim x → −

Ais 1 Bis –1 Cdoes not exist DNone of the above

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EnglishPGT 2004

Q215.If f(x) 3 2 sin cos tan 2 1 1 x x x x x x x = (x) then 2 0 () lim x f x x → is equal to

A3 B–1 C0 D1

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EnglishPGT 2004

Q216.If 2 3 1... 1! 2! 3! x x x y = + + + + = + + + + = + + + + = + + + + then 2 d y dx is

Ax Bx2 Cy Dy2

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EnglishPGT 2004

Q217.If 2x + 2y = 2x + y, then dy dx is equal to

A2 2 x y + − B2 2 1 2 x y + C2 1 2 1 2 y x y x − D2 2 2 x y x y + −

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EnglishPGT 2004

Q218.If y= () + + 2 2 1 x x, then 2 (1) d y dy x x dx + + then is equal to

A22/y B-x2/y C-y D2x2/y

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EnglishPGT 2004

Q219.p p p p p 1 x 0 1 2 3..... n lim n + + → + + + + + + + + + + + + + + + + is equal to

A−1/1 p B1/p + C1 1 1 p p − D1 2 p +

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EnglishPGT 2004

Q220.If 2 1 lim 0 1 x ax b x →∞ + − − = − − = − − = − − = +, then the value of a and b are?

Aa = 1, b = -1 Ba = 1, b = 1 Ca = -1, b = 1 Da = -1, b = -1

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