Math Chapter Wise

EnglishUP PGT-2016 (02-02-2019)

Q261.What is 3 x 0 sinx x lim 2x → − equal to?

A–1/2 B–1/4 C–1/12 Ddoes not exist

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EnglishRajasthan TGT 2015

Q262.If f

A0 Bf C′ + Df

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EnglishRajasthan TGT 2015

Q263.If p q p q x y (x y), + = + dy dx then is equal to

Ay/x Bx/y C(x y) x + D(x y) y +

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EnglishRajasthan TGT 2015

Q264.If 2 2 1 x y t; t + = − + = − + = − + = − 4 4 2 2 1 x y t t + = + + = + + = + + = + then dy dx is equal to

A3 1 x y B3 1 xy C3 1 x y − D3 1 xy −

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EnglishRajasthan TGT 2015

Q265.If 1 2 sin x y 1 x − = − then 2 dy (1 x) dx − − is equql to

Ax y/+ Bxy 1/+ C1 xy Dxy 2

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EnglishRajasthan TGT 2015

Q266.The function f(x) g(x) x =,x 0 ≠ has an extreme value when

Af (x) f(x) ′ = Bg (x) f(x) ′ = Cf(x) 0 = Dg(x) f (x) ′ =

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EnglishRajasthan TGT 2013

Q267.If () → = 1 x 3 x 0 x lim 1+ x + e x f, then f(x) =

A2x B–4x C2x2 D–4x2

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EnglishRajasthan TGT 2013

Q268.If f(x) = ≥ 2 ax -bx + 2,if x< 3 bx - 3, if x 3 is differentiable everywhere, then (a, b) =

A25 30, 117 117 − B30 25, 117 117 − C25 30, 117 117 − D30 25, 117 117 −

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EnglishRajasthan TGT 2013

Q269.If f(x) = 5 sin3x+ Asin2x + Bsinx x, x ≠ 0 is continuous at x = 0, then the values of A, B and f(0) are respectively-

A4, –5 and –1 B2, –3 and –1 C3, –2 and 1 D–4, 5 and 1

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EnglishRajasthan TGT 2013

Q270.The function f(x) = a0 + a1 |x| + a2 |x|2 + a3 |x|3 is differentiable at x = 0

Aif both a1 = 0 and a3 = 0 Bif a1 = 0 Cfor any values of a0, a1, a2, a3 Dfor no value of a0, a1, a2, a3

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EnglishRajasthan TGT 2013

Q271.If xy + yx = ab, then dy dx =

A() () y x x y e e yx y log y / xy x log x + + B() () y 1 x x 1 y e e yx y log y / xy x log x − − + + C– () () y x x y e e yx y log y / xy x log x + + D– () () y 1 x x 1 y e e yx y log y / xy x log x − − + +

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EnglishRajasthan TGT 2011

Q272.x 2 lim x 2 → − is equal to

A1 B-1 C0 DDoes not exist

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EnglishRajasthan TGT 2011

Q273.If x, when x is rational 1-x, when x is irrational f(x) {, = then f is continuous at

AAll rational numbers BZero only C½ only DNo where

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EnglishRajasthan TGT 2011

Q274.n 1 1 1 1 lim..... 1.3 3.5 5.7 (2n 1)(2n 1) →∞ + + + + + + + + + + + + + + + + − + is equal to

A1/2 B1/3 C1/4 D0

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EnglishRajasthan TGT 2011

Q275.The set of points where f(x) x x x R = ∀ ∈ = ∀ ∈ = ∀ ∈ = ∀ ∈ is twice differentiable, will be -

A(,) −∞ ∞ B[0,) ∞ C[,0] −∞ D(,0) (0,) −∞ ∪ ∞

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EnglishRajasthan TGT 2011

Q276.Function f(x) x 1 x R = − ∀ ∈ = − ∀ ∈ = − ∀ ∈ = − ∀ ∈ is not differentiable at

A1 B1/± C0, 1 ± D-1

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EnglishRajasthan TGT 2011

Q277.The function 2 f(z) z =

AEverywhere analytic BNowhere analytic CAnalytic only at z=0 DAnalytic only at z= +i

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EnglishRajasthan TGT 2011

Q278.For which one of the following conditions the function 2 z 1 f(z) z 3z 2 + = − + is continuous for all z?

AInside the circle |z| = 2 BInside the circle |z–1| = 2 COutside the circle |z| = 2 DOutside the circle|z| = 1

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EnglishJharkhand TGT 2017

Q279.If y=log (sec x + tan x) then dy dx =

Asec x+ tan x Bsec x Ctan x Dlog |sec x|

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EnglishJharkhand TGT 2017

Q280.If for 'A' and 'B' are two parameters y = A cos3x + B sin 3x, then

A2 d y 9y 0 dx + = B() 2 2 dy x y dx − –xy=0 Cdy x y 0 dx + = D2 d y x y 0 dx + =

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