Math Chapter Wise

EnglishPGT 2011

Q181.If y = a sin (log x) then x2 y2 + xy1 + y is equal to:

A2 B3 C0 D–1

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EnglishPGT 2011

Q182.If x sin, y 1 cos = θ − θ = − θ = θ − θ = − θ = θ − θ = − θ = θ − θ = − θ then the value of 2 d y dx at the point ((()),2 π is:

A−1/4 B−1/2 C1/2 D1/4

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EnglishPGT 2013

Q183.1 2 2 1 lim − →∞ = − − ∑ n x r n r find the value?

Aπ B2/π C3/π D4/π

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EnglishPGT 2013

Q184.Find the differential equation of this value 1 − ∫ ∫ x dx:

A0 B1/2 C1 D2

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EnglishPGT 2013

Q185.If the function f (x) (()) 3 1 11 1 5 2 1 + > = − < ax b if x f x if x ax b if x is continuous then find the value of a and b

Aa = 2, b = 3 Ba = 1, b = 4 Ca = 3, b = 2 Da = 4,b = 1

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EnglishPGT 2013

Q186.1 2 2 2 2 2 2 2 1 2 3 lim 1 1 1...... 1 →∞ + + + + + + + + + + + + + + + + n n n n n Find the value of this equation

A() 4 − e π B() 4 3 − e π C4 2 − e π D4 2 − e π

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EnglishPGT 2010

Q187.The function f(x) = |x|+3 is

Acontinuous as well as differentiable on R Bcontinuous on R but not differentiable anywhere on R Ccontinuous on R but not differentiable somewhere on R Dnot continuous on R

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EnglishPGT 2010

Q188.The value of 2 2 2 2 2 x n n n lim..... n 1 n 2 2n →∞ + + + + + + + + + + + + + + is

A4/π B8/π C2 8 π D2 4 π

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EnglishPGT 2010

Q189.Differentiation of sin–1 x with respect to 1 2 cos 1 x − − is

A2 1 1 x − Bsin–1/x Ccos–1/x D1

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EnglishPGT 2010

Q190.The value of C for which the function (())) 3 9x 3sin3x C x 0 f x 5x x 0 − = ≠ = is continuous at x = 0, is

A0 B4 C27 DNone of these

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EnglishPGT 2010

Q191.Function ((()) 1 f x sin x a = − at point x = a

Ais continuous Bis discontinuous and has discontinuity of first kind Cis discontinuous and has discontinuity of second kind Dis discontinuous and has infinite discontinuity

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EnglishPGT 2010

Q192.At the point x=1, the given function (()) 3 x 1, 1 x f x x 1, x 1 − < < ∞ − < < ∞ − < < ∞ − < < ∞ = − −∞ < ≤ − −∞ < ≤ − −∞ < ≤ − −∞ < ≤ is

Acontinuous and differentiable Bcontinuous and not differentiable Cdiscontinuous and differentiable Ddiscontinuous and not differentiable

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EnglishPGT 2009

Q193.The value of 1 x 0 (1 x) (1 x) lim sin x − → + − − + − − + − − + − − is

A1 B–1 C–2 D2

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EnglishPGT 2009

Q194.If In= n d (x logx), dx then

An n 1 I nI (n 1)! − = + − Bn n 1 I (n 1)I n! − = + + C1 (1)! − = + + n n I nI n Dn n 1 n 1 I I (n 1)I − + = + −

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EnglishPGT 2009

Q195.lim x→∞ →∞ →∞ 3 sin x x x − is

A0 B1 C1/6 D6

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EnglishPGT 2009

Q196.If 5 x, when x 2 2 f(x) 1, when x 2 3 x, when x 2 2 < = − > then the

Afunction is continuous at x = 2 Bfunction is discontinuous at x = 2 Clim 2 x → () 2 f x = DNone of these

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EnglishPGT 2009

Q197.2 2 1 2 2 (1) (1) tan (1) (1) x x d dx x x − + + − + + − + + − + + − + − − + − − + − − + − − find the value of?

A4 (1) − x B4 1 2 (1) − x C4 1 2 (1) − − x D4 (1) − x

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EnglishPGT 2009

Q198.2 1 x f x + can be expanded in the form of series

A2 1 () '() ''().... 1 2!(1) + + + + + x x f x f x f x x x B2 1 () '() ''().... 1 2! (1) − + + + + x x f x f x f x x x C2 4 2 1 () '() ''().... 1 2! (1) + + + + + x x f x f x f x x x D2 4 2 1 () '() ''().... 1 2!(1) − + + + + x x f x f x f x x x

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EnglishPGT 2009

Q199.The value of 2 0 log(1) lim x xe x x → − + is

A1/3 B2/3 C3/2 D3/4

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EnglishPGT 2009

Q200.If x 1, when x 2 f(x) 2x 1, when x 2 + < = − ≥ then f' (2) equals

A0 B1 C2 Ddoes not exist

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