Math Chapter Wise

EnglishRajasthan TGT 2016

Q241.If the function f(x) = min {x, x2 }, then f(x) is

Acontinuous and differentiable ∀x∈R Bcontinuous ∀x∈R Cdiscontinuous at x=1 only Ddiscontinuous at x=0 and x=1

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EnglishRajasthan TGT 2016

Q242.If f∈IR [a, b], consider the following statements:

Anor BImage/formula option B (see source) Cboth Dneither

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EnglishRajasthan TGT 2015

Q243.2x x lim 1 x →∞ + is equal to

Ae B2e C1/e D2 1 e

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EnglishRajasthan TGT 2015

Q244.The function f is defined as At x 1 = 2 ax b, x 1 f(x) 1 x 1 x − < = − − ≥ is differentiable then the value of a and b are-

Aa 1,b 1 = − Ba = b = 1/2 Ca = 1/2, b = 3/2 Da = 1/2, b = –1

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EnglishUP TGT-2016 (08-03-2019) Rajasthan TGT 2013

Q245.(((()))) (((()))) 2 1 d tan cos x dx − is equal to

A3 -2 x B3 2 x C2 1- x x D2 x 1- x −

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EnglishUP TGT-2016 (08-03-2019)

Q246.y a y a y lim sin tan 2 2a → − π is equal to

A0 B1 Ca/π Da − π

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EnglishUP TGT-2016 (08-03-2019)

Q247.1 x 1 1 x lim cos x − → − is equal to

A0 B1/2 C1/4 D1

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EnglishUP TGT-2016 (08-03-2019)

Q248.n 1 n 1 lim 1 2n + →∞ − is equal to

Ae B1/ e Ce D1/e

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EnglishUP TGT-2016 (08-03-2019)

Q249.The derivative of the function y =3|x|+1 at the point x=0 is

A3 B–3 C0 Dnot existing

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EnglishUP TGT-2016 (08-03-2019)

Q250.If 2 x 3x 2 f(x),x 2 x 2x − + = ≠ − is defined and function f(x) be continuous at x=2, then the value of f(2) is

A0 B1/2 C1 D3/4

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EnglishNVS PGT 10-06-2019

Q251.Let f(x) be a continuous function defined for all x>0 that satisfy f(x/y)= f(x)–f(y) for all x, y and f(e)=1. Then:

Axf(x)→1as x →0 B1 f 0 x → as x →0 Cf(x) = log x Df(x) is bounded

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EnglishNVS PGT 10-06-2019

Q252.(((()))) 2 x 0 sin cos x lim x → π equals:

Aπ B1 Cπ/2 D–π

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EnglishKVS PGT 23-12-2018

Q253.Let f:[1, [ [2, [ ∞ → ∞ ∞ → ∞ ∞ → ∞ ∞ → ∞ be a differentiable function such that f '(2) 4 =. If x 3 1 6 f(t)dt 3xf(x) x 5, x 1 = − − ∀ ≥ = − − ∀ ≥ = − − ∀ ≥ = − − ∀ ≥ ∫ ∫ then the value f(2) of is:

A6 B4 C1/4 D1/6

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EnglishKVS PGT 23-12-2018

Q254.If y y log x, = then dy dx is equal to:

A1 x log y + B() 1 log x 1 y + C() 1 x 1 log y + D1 y log x +

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EnglishUP PGT-2016 (02-02-2019)

Q255.(()) (()) 5 7 x 0 x 1 1 lim x 1 1 → + − is equal to

A7/5 B5/7 C2/7 D2/5

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EnglishUP PGT-2016 (02-02-2019)

Q256.Number of points, where the function 2 f(x) | x 3 | | x 4 | = + + − = + + − = + + − = + + − is not differentiable, is

A0 B1 C2 D3

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EnglishUP PGT-2016 (02-02-2019)

Q257.If ((())) 2 f x 4 x, = − = − then x 1 f(1) f(x) lim x 1 → − is equal to

A1/3 B3 C0 D2/3

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EnglishUP PGT-2016 (02-02-2019)

Q258.If 1 1 x 1 x 1 y sec sin, x 1 x 1 − − + − = + − + then value of dy dx at x=2 is

A1 B2 C0 D3

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EnglishUP PGT-2016 (02-02-2019)

Q259.If xy = 1, then 4 4 dy dy 1 y 1 x + + + is equal to

A0 B1 Cy Dnot defined

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EnglishUP PGT-2016 (02-02-2019) Rajasthan TGT 2015

Q260.If (((()))) 2 3 1 2 2 3a x x y tan, a a 3x − − − − = − then dy dx is equal to

A2 2 3x x a + B2 2 3a x a + C2 2 3 x a + D2 2 a x a +

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