Math Chapter Wise

EnglishKVS PGT 2023

Q01.If ƒ ƒ ƒ(x) = 3x and g(x) = 2 x 4 2 +, then which of the following can be a discontinuous function?

Aƒ(x) + g(x) Bƒ(x) - g(x) Cƒ(x). g(x) Dg(x)/f (x)

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EnglishKVS PGT 2023

Q02.() 2 x 1 (x 1) 2x 3 lim 2x x 3 → − − + − is equal to:

A−1/10 B1/10 C1 D–1

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EnglishKVS PGT 2023

Q03.For the function f(x) = 1 x +, x∈[1, 3], the value of c for mean value theorem is:

A3 B3 C3/2 D1/3

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EnglishNVS PGT 2022 JDD-75-PGT TIERII-X -15 28.06.2015

Q04.If f(x) = x3 and g(x) = x3 − 4x in −2 ≤ x ≤ 2, then consider the statements

Aand BOnly statements Care correct. DStatements

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EnglishKVS PGT 2022

Q05.If function f(x)=x3 +x2 −6x satisfies Lagrange’s mean value theorem in [−1, 4], then the value of c is:

A1 B2 C–2 D–1

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EnglishDSSSB PGT 2021

Q06.If f(x) satisfies the requirements of Rolle's theorem in [1, 2] and f'(x) is continuous in [1, 2], then the value of () ∫ 2 1 f' x dx is

A0 B1 C–1 D2

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EnglishJSSC PGT 2018

Q07.Let () 2 1 f x = – 5 x be a function defined on interval [1, 4]. Which of the points holds true?

AThere exists a point x in [1, 4] such that f is not differentiable at x BThe function has a tangent line between [1, 4] with slope –1/64 CThe function has a tangent line between [1,4] with slope 3/2 DThe function has a tangent line between [1, 4] with slope –5/16

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EnglishUPPSC GIC 2021

Q08.Writing Lagrange's mean value theorem as f

A1/4 B1/3 C1/5 D1/6

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EnglishUPPSC Ashram Paddhati 2021

Q09.Applying Lagrange's mean value theorem to the function f(x) = (x – 1)(x – 2) in the interval [0, 1], the value of 'c' is obtained as

A1/2 B1/3 C1/4 D1/5

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EnglishUKPSC Lecturer (Mains) 2020 UP PCS (Pre) 1999, 2006 RPSC PGT- 2022

Q10.The value of 'C' from Lagrange's mean value theorem for the function f(x) = x(x – 1) (x – 2) in the interval 1 0, 2 is equal to:

A1 (6 2 3) 6 + B1 (6 21) 6 − C1 (6 21) 6 + D1 (6 2 3) 6 −

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EnglishUKPSC Lecturer (Mains) 2020

Q11.Let f''(x) be continuous on [a, b] and f(x) has three zeros is (a, b), then the minimum number of zeros of f"(x) is:

A2 B3 C4 DNone of these

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EnglishUKPSC Lecturer (Mains) 2020

Q12.Let the function f be differentiable for all x. If f(1) = –2 and f'(x) ≥ 2 for all x ∈ [1,6], then

Af(6)≥6 Bf(6)< 6 Cf(6)≥8 Df(6)< 8

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EnglishUKPSC Lecturer (Mains) 2020

Q13.The function, in which Rolle's theorem is applicable, is

Af(x) = log 2 ab (a b) + x in the interval [a, b], 0 < a < b Bf(x) = (x– 1) (2x – 3) in [1, 3] Cf(x)=2+(x–1)2/3 in [0,2] Df(x)=cos 1 x in [–1,1]

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EnglishUP PGT 2009 UP PCS (Pre) 2000 UKPSC Lecturer (Mains) 2020

Q14.If a curve is continuous between two points A and B on the curve and possesses a unique tangent at each of its point, then there exists at least one point on the curve lying between A and B, where the tangent is parallel to the chord AB. This result is known as:

ARolle's theorem BLagrange's mean value theorem CCauchy's mean value theorem DMaclaurin's theorem

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EnglishUKPSC GIC 2018

Q15.If f(x) = x sinx e, then the value of x in (0, π) for which Rolle's theorem is verified, is

Aπ B4/π C2/π D3 4 π

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EnglishUKPSC GIC 2018

Q16.For the function f(x)= 1 x + 1, defined on the interval[0, 2], the point at which the derivative satisfies mean value theorem is

A3 B2 1 C3 1 D1

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EnglishGIC Lecturer Exam-2015

Q17.In the Lagrange's Mean value theorem f(b)-f(a) = f'

A1/7 B2/7 C3/7 D4/7

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EnglishGIC Lecturer Exam-2015

Q18.The value of C in Rolle’s theorem, where C 2 2 and f(x) cosx, is equal

Aπ/4 Bπ/3 Cπ D0

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EnglishGIC Lecturer Exam-2015

Q19.Given f (2) 6 and f (1) 4 then 2 h 0 f(2h 2 h) f(2) lim f(h h 1) f(1) is equal to–

A3/2 B5/2 C–3 D3

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EnglishLT 2018

Q20.The function ((())) ((())) ((()) m n x x a x b φ = − − φ = − − φ = − − φ = − − satisfies the conditions of Rolle's theorem, when

Am, n are positive integers Bm, n are positive integers and a< b Ca < b Dm > n

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