Math Chapter Wise

EnglishPGT 2003

Q121.In case of Rolle’s Theorem which of the following statement is false?

A= f BImage/formula option B (see source) Cf DNone of these

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EnglishPGT 2002

Q122.If (((()))) 1 2 2 3 f(x) 3 x x = − = − then the maximum and minimum values of f(x) are respectively:

A+1and –1 B1 and 1 2 C2 and 0 D0 and –2

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EnglishPGT 2002

Q123.Greatest Value of (1/x)x is:

Ae B() 1 e Ce 1 e DNone of these

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EnglishPGT 2002

Q124.Two positive numbers whose sum is 16 and sum of whose cubes in maximum are given by:

A8, 8 Bno such numbers exist C0, 16 DNone of these

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EnglishPGT 2002

Q125.The minimum value of (((()))) 2 2 2x 2x 1 sin x e − + is:

Ae B1/e C1 D0

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EnglishPGT 2002

Q126.The length of the sub-normal to the curve y2 =x3 at the point (4, 8) is:

A24 B8/3 C3/8 DNone of these

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EnglishPGT 2002

Q127.The greatest value of ((()) 1 3 y x 1 (x 1) = + − − = + − − = + − − = + − − on [0,1] is:

A1 B0 C1 3 2 DNone of these

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EnglishPGT 2002

Q128.The straight line x+y=a will be tangent to the ellipse 2 2 x y 1 9 16 + = + = if a=

A8 B±5 C±10 D±6

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EnglishPGT 2000

Q129.The function f(x) = 2+(x–1) satisfies condition of Rolle's Theorem on the interval:

A[0, 2] B[0,4] C3 3, 2 2 − D1 1, 2 2 −

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EnglishPGT 2000

Q130.The function sinx(1+cos x) is maximum in the interval (0,π). Then:

Ax /3 = π B2 x 3 π = Cx / 2 = π Dx / 4 = π

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EnglishPGT 2000

Q131.A particle moves along a straight lines so that the distance covered it in t second is given by- S=(t–1)2 (t–2) where S is in meters. It's velocity after 3 second is:

A8m/sec B16m/sec C4m/sec DNone of these

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EnglishPGT 2000, 2011

Q132.The slope of the tangent to the curve x=t2 +3t–8, y = 2t2 –2t–5 at point (2,–1) is:

A22/7 B–6 C6/7 DNone of these

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EnglishRajasthan TGT 2016

Q133.If f(x) = 3x4 –4x2 +5, then the interval for which f(x) satisfy all the conditions of Rolle's theorem, is

A[0, 2] B[–1, 1] C[–1, 0] D[1, 2]

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EnglishRajasthan TGT 2016

Q134.For all real values of x, the minimum value of 2 1 x x 1 x x − + + + is equal to

A0 B1 C3 D1/3

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EnglishRajasthan TGT 2016

Q135.From a point P, normal is drawn to the curve 3x2 +6y2 =18, which is perpendicular to the line x+y=8. Co-ordinates of P are:

A(1,1) B(2,1) C(8,1) D(9,1)

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EnglishRajasthan TGT 2015

Q136.Function 4 x f(x) x 4 = − = − is increasing in the interval

A1 x 1/− < < B1 x 1/− ≤ Cx 1/≤ Dx 1/≥

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EnglishRajasthan TGT 2015

Q137.1/ x f(x) x = is a decreasing function if

Ax e/> Bx e/< Cx e = Dx>1/e

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EnglishRajasthan TGT 2015

Q138.The length of the normal to the curve x a(sin), = θ + θ = θ + θ = θ + θ = θ + θ y a(1 cos) = − θ = − θ = − θ = − θ at 2 π θ = θ = is

A2a Ba/2 C2a Da/ 2

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EnglishRajasthan TGT 2013

Q139.If f(x) = x – loge|2x +1|, − − − 1 1 x 100, 2 2 ∈, then the function f(x) is monotonically decreasing in the interval...........

A1 1, 2 2 − B1 100, 2 − − C1,100 2 D1,1 2

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EnglishRajasthan TGT 2013

Q140.If the line ax + by + c = 0 is normal to the curve xy = 1, then-

Aab = 0 Bab < 0 Ca > 0, b > 0 Da < 0, b < 0

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