Math Chapter Wise

EnglishPGT 2002

Q121.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

Q122.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

Q123.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

Q124.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

Q125.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

Q126.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

Q127.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

Q128.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

Q129.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

Q130.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

Q131.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

Q132.1/ 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

Q133.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

Q134.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

Q135.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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EnglishRajasthan TGT 2013

Q136.If the tangent to the curve f(x) = x2 at any point (c, f(c)) is parallel to the line joining the points (a, f(a)) and (b, f(b)) on the curve, then a, c, b are in-

AA.P. BG.P. CH.P. DNone of these

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EnglishRajasthan TGT 2013

Q137.If y =, − 2 2 a b + x a x then y is maximum at x =

A−a/a b Ba a b + C2 a a b + D2 a a b −

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EnglishRajasthan TGT 2013

Q138.The maximum value of the function sin x.sin y. sin(x+y) is-

A3 3/8 B1/8 C3/8 D3 3/4

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EnglishRajasthan TGT 2011

Q139.Function f(x)=x3 –3x2 –24x+5 is increasing in the interval

A(, 2) (4,) −∞ − ∪ ∞ B(2,) − ∞ C(2,4) D(,4) −∞

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EnglishRajasthan TGT 2011

Q140.Function f(x)=x2 e-x is monotonic increasing when

Ax R [0,2] ∈ − B0 x 2/< < C2 x/< < ∞ Dx 0/<

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