Math Chapter Wise

EnglishUP TGT 2016,2021

Q81.→ y a y – a πy lim sin.tan 2 2a is equal to

A0 B1 Ca/π Da – π

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EnglishUP TGT 2021

Q82.The function defined by () ≠ x, x 0 f x = x 0, x = 0 at x = 0 is

Acontinuous Bdiscontinuous at x = 0 and has discontinuity of first kind Cdiscontinuous at x = 0 and has removable discontinuity Ddiscontinuous at x = 0 and has discontinuity of second kind

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EnglishUP TGT 2016, 2021 Rajsthan TGT 2013

Q83.() 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 2021

Q84.If → x a a – x lim = –1, x – a then

Aa = 1 Ba = 0 Ca = e Dnone of these

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EnglishUP TGT 2021

Q85.If x y = x, then dy dx will be

Axx/logx Bxx/(1– logx) Cxx/(1+logx) Dxx/+ logx

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EnglishUP TGT 2021

Q86.Function f(x) = (x + 1)cotx will be continuous at x = 0 if the value of f(0) is

A1/e B0 Ce D1

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EnglishUP TGT 2021

Q87.If 5 x y = log x + log 5, then what will be the value of dy dx at x = 5?

A5 B1/5 C0 D1

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EnglishUP TGT 2021 Haryana PGT 2019

Q88.→∞ x+4 x x + 6 lim x +1 is equal to

A1 Be2 Ce4 De5

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EnglishUPPSC Ashram Paddhati 2021

Q89.Which function is NOT discontinuous at x = 0?

Asin(1/x) B2/x2 Ctan–1/(1/x) D|x|

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EnglishUKPSC Lecturer (Mains) 2020

Q90.If f(x) is a differentiable function, then x αf(x) f(α) lim x α → − x is:

Aαf '(α) f(α) Bαf '(α) f(α)/+ Cαf(α) f '(α) Dαf(α) f '(α)

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EnglishUKPSC Lecturer (Mains) 2020

Q91.If y+...... y+e x = e ∞ then dy dx is equal to:

A1/x B(1) + x C(1) − x x D(1) + x x

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EnglishUP TGT 2002 UKPSC Lecturer (Mains) 2020

Q92.If 2 2 1 – x + 1 – y = a(x – y) then the value of dy dx is:

A2 1 1 y − x B2 1 1 y + − x C2 1 1 y − + x D2 1 1 x − y

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EnglishHaryana PGT 2019

Q93.() { } → x 2 1 – cos 2 x – 2 lim x – 2 is equal to:

A2 B2 C1/2 Ddoes not exist

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EnglishHaryana PGT 2019

Q94.Let y be an implicit function of x defined by x2x – 2xx cot y – 1 = 0, Then y'(1) equals:

A–1 B1 Clog2 D–log2

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q95.Which of these functions is not uniformly continuous on (0,1)?

A1 ÷ x2 Bx2 Csin(x) Dsin(x) ÷x

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EnglishDSSSB TGT 04-09-2021 Shift-I (Male)

Q96.This polynomial x3 + 4x + 8 has

Ano zeros Bthree real zeros Cone positive and two imaginary zeros Done negative and two imaginary zeros

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EnglishHaryana PGT 2018

Q97.If α, β are the roots of the equation 2 2 ax + b + c = 0 then:

A() 2 a 2 α −β B() 2 a 2 α −β C() 2 a 2 − α −β D() 2 a 2 − α −β

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EnglishUKPSC Lecturer (Mains) 2020

Q98.If xy yx = 1, than dy dx is:

Ae y(y + log y) x Be y(+ log) (y + log y) x y x x x Ce –y(+ log) (+ y log y) y x y x x D– – y 1 1 yx x

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EnglishUKPSC Lecturer (Mains) 2020

Q99.→ 3 x 0 tanx -sinx lim = x

A∞ B2 C1 D1/2

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EnglishUKPSC Lecturer (Mains) 2020

Q100.For the function f: [–4,2]→ R defined by f(x)=|x–1|+|x+3|, which of the following is true?

Af is differentiable x = 1 Bf is differentiable at x = –3 CRolle's theorem is applicable for the interval [–3,1] DNone of these

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