Math Chapter Wise

EnglishDSE TGT 2022

Q41.() → x 2 log x –1 Lt x – 2 =

A0 B1 C–1 D2

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EnglishDSE TGT 2019

Q42.If y = log(sin (log x), then dy/dx =

A(1/x) cos (log x) B(1/x) cot (log x) Clog (cot x) Dlog (sin x)

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EnglishOAVS TGT 2021

Q43.If y = 5 log xx, they dy/dx is:

A5 (1 + log x) B5 (1 – log x) C5 (1 – 2log x) D5 (1 + 2log x)

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EnglishOAVS TGT 2021

Q44.If 2x y e 1, then find 2 d y dx at x 0.

A4 B5 C3 D1

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EnglishOAVS TGT 2019

Q45.The value of the limit (()) x 1 2 x 0 2 – 1 limit 1+ x – 1 → is equal to:

A–2 log 2 B0 C1 D2 log 2

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EnglishOAVS TGT 2019

Q46.If () 3 x f = 3e x then () () () () – 2 1 –3 + 0 0 3 f' x x f x f f' is equal to:

A0 B1 C2 –x e D2 x e

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EnglishOAVS TGT 2019

Q47.If () –1 f x = xtan x then () f' 1 is:

A2 4 + π B1 C0 D8/π

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EnglishOAVS TGT 2019

Q48.If () 1 f x = 1+, x then the value of 1 f f x is:

A–x/x –1 Bx 2 x 1 + Cx x 1 + Dx

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EnglishOAVS TGT 2019

Q49.The domain of () () () 2 x –x f x = 2sin 1 – x – e + 2 is:

AR BR – {0} Cx > 1 D–1 ≤ x ≤ 1

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EnglishDSE TGT 2019

Q50.If z = (y/x) f(x+y), then (y/x)(x+y) f '(x+y) =

Ayzx + xzy Bzx + zy Cxyz(xy) Dxzx + yzy

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EnglishDSE TGT 2019

Q51.If y = log(sec x + tan x), then dy/dx =

Atan x Bsec x Clog|sec x| Dsec x + tan x

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EnglishDSE TGT 2019

Q52.If Z = eax sin by, where 'a' and 'b' are real constants, then Zxy =

Aabeax/cos by Bbeax/cos by Cabeax/sin by Daeax/sin by

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EnglishDSE TGT 2019

Q53.Let E ⊆ ⊆ ⊆ℝ ℝ ℝ, f: E → ℝ ℝ ℝ and a ∈E. Suppose there exists a positive real number 'r' such that (a - r, a+r) ∩ E = {a}, then f is

Acontinuous at r Bdiscontinuous at a Ccontinuous at a Ddiscontinuous at r

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EnglishOAVS TGT 2018

Q54.Find the derivative of cos–1 (cot x).

Acot x B2 cot x 1 csc x C2 cosec x 1 cot x − D2/csc x

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EnglishOAVS TGT 2018

Q55.If a function on R is defined by f(x) = 1 when x is rational and f(x) = –1 when x is irrational, then f(x) is discontinuous at:

A1 B2 CR D0

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EnglishOAVS TGT 2018

Q56.If Signum function () x f x | x | = when x 0 and f(x)=0 when x = 0, then it is discontinuous at:

A2 B1 CR D0

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EnglishJSSC PGT 2018

Q57.Let f & g be the two real-valued functions defined on [a, b] and h (x) = max {f (x), g (x)} for x ∈ [a, b]. Which of the below is true?

AIf f & g are differentiable, then so is h, as well as if f & g are convex, then h is also convex BIf f & g are convex, then h is also convex CIf f & g are differentiable, then so is h DIf f & g are linear then h is also linear

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EnglishJSSC PGT 2018

Q58.Calculate lim (x2 – 4)/(x2 + 5x – 14) as x ≥ 2.

AUndefined B2/7 C4/5 D4/9

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EnglishJSSC PGT 2018

Q59.Function () () f x = x + sin x is:

AConvex BContinuous and differentiable at x = 0 CContinuous but not differentiable at x = 0 DConcave

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EnglishOAVS TGT 2017

Q60.Derivative of tan (2x + 3) is:

A2sec2/(2x+3) B2sec2/(3) C3sec2/(2x+3) D2sec2/(2x)

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