Math Chapter Wise

EnglishPGT 2013

Q21.If ((())) ((()) 2 3 1 1 = − − = − − = − − = − − f x x then rolle's theorem

ASatisfy in [ ] 0,1 BSatisfy in [ ] 0,2 CSatisfy in [ ] 1, 1 DNot satisfy any of the interval given above

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EnglishPGT 2013

Q22.Function ((())) = f x x Lagrange's means - value theorem is not to in the interval

A[ ] 1,0 B1 0, 2 C[ ] 0,1 D[ ] 1,1

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EnglishPGT 2010

Q23.Let f be a function defined as [a,a +h];h > 0 so that (i) f is continuous of [a,a+h] (ii) f is derivable on (a,a +h) then there exist θ, 0 <θ<1 so that f(a+h) = f(a)+hf' (a+θh) is known as

ARolle's Theorem BTaylor's Theorem CNewton's Theorem DLagrange's theorem

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EnglishPGT 2010

Q24.If two functions f and g (i) are continuous in [a,b] (ii) are derivable in ]a, b[ (iii) f' (x) = g' (x) ∀ ∀ ∀ x∈ ]a,b[ then which is correct?

Af and g differ by a constant Bf and g are always equal Cf and g can never equal DNone of these

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EnglishPGT 2009

Q25.Rolle's theorem is true for the function 2 f(x) x 4 = − = − in the interval

A[ 2, 0] B[ 2, 2] C1 0, 2 D[0,2]

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EnglishPGT 2009

Q26.If f(x) is continuous in closed interval [a, b] and differentiable in open interval (a, b), then there must be a value of x between a and b such that () () () '() − = − − = − − = − − = − f b f a b a f x. This statement is known as

ARolle's theorem BMean value theorem CCauchy's theorem DNone of these

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EnglishPGT 2009

Q27.Expansion Maclaurin's theorem of tan–1 x will be

A3 5... 3 5 + + + x x x B3 5... 3 5 − − − − x x x C3 5... 3 5 − + − + x x x D3 5... 3 5 − + − x x x

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EnglishPGT 2004

Q28.The value of C (0) C π < < < < in Rolle's theorem for the function f(x) = sinx is

Aπ/4 Bπ/3 C0 Dπ/2

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EnglishRajasthan TGT 2015

Q29.Using Rolle's theorem the equation n n 1 0 1 n a x a x... a 0 has atleast one root between 0 and 1, if

A0 1 n 1 a a... a 0 n n 1 − + + + = − B0 1 n 2 a a... a 0 n 1 n 2 − + + + = − − C0 1 n 1 na (n 1)a... a 0 − + − + + = D0 1 n a a... a 0 n 1 n + + + = +

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EnglishRajasthan TGT 2011

Q30.If 3 2 f(x) 3x 5x 2x, = − + = − + = − + = − + then the interval for which ƒ satisfied all the conditions of Roll’s theorem is

A[0,1] B[-1,1] C[-1,0] D[1,2]

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EnglishRajasthan TGT 2011

Q31.If f(x) x x R, = ∀ ∈ = ∀ ∈ = ∀ ∈ = ∀ ∈ then the interval for which ƒ satisfied all the conditions of Lagrange’s mean value theorem is

A[-1,1] B[-2,1] C[-1,2] D[1,2]

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EnglishUP PCS (Pre) 1998

Q32.A convergent series is:

A() n 1 n 1 n n 1 ∞ = + + ∑ Bn 1 n 1 n n ∞ = + − ∑ Cn 2 1 n logn ∞ = ∑ Dn n 1 1 n ∞ = + ∑

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EnglishUP PCS (Pre) 1998

Q33.The Lagrange's mean value theorem is applicable to ((()) 1 f x sin x = in the interval:

A[–3, 3] B[–2, 5] C[2, 3] D[–1, 4]

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EnglishUP PCS (Pre) 1994

Q34.If f(x) = 4x2, then the value of c in the interval [–1, 3] for which f(3) f(1) f

A0 B1 C2 D3

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EnglishUP PCS (Pre) 1994

Q35.Function f(x) 2 x 1 satisfies conditions of Rolle's theorem on the interval:

A1 1, 2 2 B3 3, 2 2 C0,2 D0,4

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EnglishUP PCS (Pre) 1995

Q36.If f (x) = x3 + 3x, then f(4) f(?) f(c) 4 0 the value of c ∈ (0,4) such that–

A19/3 B4/3 C4/3 DNone of these

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EnglishUP PCS (Pre) 1999

Q37.Let f be a continuous function on the closed interval [a, b], a<b, such that f is differentiable in the open interval (a, b) and f(a) =f(b).Then:

A, B, Cis true Dnone of

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EnglishUP PCS (Pre) 1999

Q38.Amongst the following the correct statement is:

AEvery bounded function on a closed interval [a, b] is continuous BEvery bounded function on a open interval [a, b] is continuous CEvery continuous function on a closed interval [a, b] is bounded DEvery continuous function on a open interval [a, b] is bounded

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EnglishUP PCS (Pre) 2000

Q39.If f (x) = (x – 1)2/3 – 1, then Rolle's theorem is:

AApplicable in [0, 1] BApplicable in [0, 2] CApplicable in [–1, 1] DNot applicable in any interval

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EnglishUP PCS (Pre) 2000

Q40.If f (x), defined on [a, b], is continuous on [a, b] and differentiable on ] a, b [ then there exists at least one point c ∈ ] a, b, [ such that:

A() () () f b f a f c b a − = − B() () () f b f a f ' c b a − = − C= 0 Df'

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