Math Chapter Wise

EnglishRajasthan TGT 2013

Q141.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

Q142.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

Q143.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

Q144.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

Q145.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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EnglishRajasthan TGT 2011

Q146.Function f(x)=(1-x)2 ex is minimum at

Ax 1 = − Bx 1 = Cx 0 = Dx 2 =

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EnglishRajasthan TGT 2011

Q147.if a 0,b 0 > > > > then maximum value of acosθ+bsinθ is

Aa+b Ba-b Ca or b D2 2 a b +

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EnglishRajasthan TGT 2011

Q148.Minimum value of function 1 1 f(x,y) xy x y = + + = + + = + + = + + is

A3 B2 C1 D0

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EnglishKVS TGT DEC 2017

Q149.The maximum value of sin θ.cos θ is–

A1 B1/2 C1/2 D2

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EnglishKVS TGT DEC 2017

Q150.If 1 f(x) log(1 x), x 1 x 0 then f is–

Aan increasing function Ba decreasing function Cboth increasing and decreasing function Dneither increasing nor decreasing function

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EnglishKVS TGT DEC 2017

Q151.The maximum value of 2 x f(x) 4 x x on 1,1 is–

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

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EnglishKVS TGT DEC 2017

Q152.What angle the tangent to the parabola x2 = 2y at the point 1 1, 2 makes with x – axis?

A00 B450 C300 D600

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EnglishTGT 2011

Q153.The normal to the given curve is parallel to x- axis if

Ady 0 dx = Bdy 1 dx = Cdx 0 dy = Ddx 1 dy =

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EnglishTGT 2011

Q154.The greatest slope of the curve y = –x3 +3x2 +9x– 27 is -

A0 B12 C16 D32

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EnglishTGT 2011

Q155.If the value of function 1 x f(x) x,x 0 = > = > is maximum at x = e

Ae eπ > π Be eπ < π Ce eπ = π De eπ ≤ π

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EnglishUP PCS (Pre) 1998

Q156.The angle of intersection of the curves y = 4 – x2 and y = x2 is:

A-1 4 tan 7 B-1/tan 2 2 C() -1 tan 2 3 − D-1 4 tan 2 7

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EnglishUP PCS (Pre) 1998

Q157.The orthogonal trajectories of the hyperbolas xy = c2 are:

Ax2 + y2 = c2 Bx2 – y2 = k2 C2 2 x y 1 a b + = Dxy = k2

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EnglishUP PCS (Pre) 1998

Q158.The angle between the straight lines x y 3 4 0 + − = + − = + − = + − = and x 3 y 5 0 − − = − − = − − = − − = is:

Aπ/6 Bπ/3 Cπ/4 Dπ/2

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EnglishUP PCS (Pre) 1998

Q159.The maximum value of ((()) 1 sinx cosx 2 − − for x in R is:

A2 B3 C2 D1

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EnglishUP PCS (Pre) 1998

Q160.The area of the greatest rectangle, which can be inscribed in the circle x2 + y2 – 2ax + 2by + b2 = 0 is:

Aab 2 π B2ab C2a2 D2 a 2 π

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