Math Chapter Wise

EnglishKVS TGT 2017 KVS PGT-2023

Q61.If y y sinx, then dy dx

Acos x/y 1 Bsin y/x 1 Ccos x/2y 1 Dcos y/2x 1

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EnglishKVS TGT 2017

Q62.If 1 3 x sin (3t 4t) and 1 2 y cos 1 t then dy dx is equal to –

A1/2 B2/5 C3/2 D1/3

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EnglishKVS TGT 2017

Q63.2 x x 1 lim 2x 1 is equal to–

A1 B0 C–1 D1/2

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EnglishKVS TGT 2017

Q64.Derivative of 2 1 1 x 1 tan x w.r.t. 1 tan x is–

A1 B2 C1/2 D1/4

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EnglishOPSC PGT 2017

Q65.The number of primes not exceeding x, for indefinitely large x, can be approximated by:

Ax/log x Bexpx/x Ccoxx/x Dcosh x/x

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EnglishOPSC PGT 2017

Q66.The domain of function 1 2 x f(x) sin log 2 is:

A[–1, 4] B[1, –4] C[1, 4] DNone of the above

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EnglishOPSC PGT 2017

Q67.A function, uniformly continuous on an interval [a, b]:

Ais piecewise continuous on real line Bis differentiable on [a, b] Cis Riemann integrable on [a, b] DCan be subjected to mean value theorem

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EnglishOPSC PGT 2017

Q68.2 cosx 1 f(x), cot x 1 for π xxxx ≠≠≠≠ 4444 and f(x), at x. 4 What should be the value of α to make f(x) continuous at x? 4

A1/2 B2 C1/2 D2

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EnglishOPSC PGT 2017

Q69.The function f(x) x 1 x 2 is:

AContinuous at x = 1 only BContinuous at x = 1 and x = 2 CDifferentiable at x = 1 and x = 2 DNot differentiable on (1, 2)

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EnglishUP PGT 2021

Q70.If f(2) = 4 and f' (2) = 1 then () () → x 2 f 2 – 2f lim – 2 x x x is equal to –

A2 B0 C1 D4

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EnglishUP PGT 2021

Q71.If f(x) = bx ax ae be a b +, then f" (0) equals–

A0 Bab Ca + b Dab (a+b)

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EnglishUP PGT 2021

Q72.If f(x) = + 2 + 3 x and y = f –1 (x), then dy dx is equal to–

A() 2 3 + x B() 2 1 –1 x C– 2 – 3 x D() 2 1 + x

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EnglishUP PGT 2021

Q73.If x y = y x, then dy y d x is equal to –

Alog y y y log + x x x Blog y – y ylog – x x x Clog x x x log + y y y Dlog – log – y x x x y y

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EnglishUP PGT 2021

Q74.The function f(x) = ≠ 2 1 – cos x,x 0 x can be made continuous at x = 0 by defining f(0) to be equal to –

A1 B1/2 C0 D2

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EnglishUP PGT 2021

Q75.If y = cos(3 cos–1 x), then 3 d y dx is equal to –

A0 B3 C16 D24

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EnglishUP PGT 2021

Q76.If f(x) = – 1 + x x then f'(1) is equal to –

A0 B1 C–1 Ddoes not exist

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EnglishUP PGT 2021

Q77.For the function f(x) = – 5 x which of the following is not correct?

AThe function f(x) is continuous at x = 5 BThe function f(x) is not continuous at x = –5 CThe function f(x) is differentiable at x = 0 DThe function f(x) is differentiable at x = –5

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EnglishUPPSC GIC 2021

Q78.The value of 1/ x x x x 0 a b lim 2 → + is-

Aab Ba b 2 + Cab Da + b

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EnglishUPPSC GIC 2021

Q79.Which function is not discontinuous at x = 0

Asin (1/x) B1/x2 Ctan-1/(1/x) Dtan x

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q80.x 0 lim → (1 + x)1/x is equal to -

A1/e Be C1 De –1

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