Math Chapter Wise

EnglishUP PCS (Pre) 1998

Q161.The Cartesian sub tangent at any point of the parabola y2 = 4ax:

Avaries as the abscissa of the point Bis of constant length Cvaries as the ordinate of the point Ddoes not satisfy any of (a), (b), (c)

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EnglishUP PCS (Pre) 1998

Q162.The abscissae of points on the curve x3 – 6x2 + 8x – y = 0 at which the normals to the curve are parallel to the axis of y, are:

A2 3 ± B4 2 3 ± C1 2 3 ± D() 1 2 3 3 ±

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EnglishUP PCS (Pre) 1994

Q163.The angle of intersection of the curves 2 xy a and 2 2 2 x y 2a is–

Aπ/4 Bπ/2 C0 Dπ

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EnglishUP PCS (Pre) 1994

Q164.The orthogonal trajectory of family of curve y = ax2 is–

A2 2 2/x 2y a B2 2 2/x y a C2 2 x y 1 a a D2 2 2/2x y a

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EnglishUP PCS (Pre) 1994

Q165.The point at which the tangent to the curve y = x3 is parallel to the chord through points A (–1, –1) and B (2,8) is–

A(1,1) B(1,2) C(–1, 1) D(1, –1)

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EnglishUP PCS (Pre) 1995

Q166.A particle moves in a straight line and describe a distances s in time t given by 3 2 s t 6t 2t 1 Its acceleration becomes zero after–

A2 seconds B4 seconds C6 seconds D8 seconds

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EnglishUP PCS (Pre) 1995

Q167.On the curve 2 2 3 y ax ax (a 0) the origin is–

Aa node Ba cusp Ca conjugate point Dan isolated point

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EnglishUP PCS (Pre) 1995

Q168.The maximum rectangle, inscribed in a circle of radius 1, is of area:

A1 B2 C4 D8

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EnglishUP PCS (Pre) 1995

Q169.For the curve 2 y (x a)(x b)(x c) where a 0,b 0,c 0 the incorrect statement is–

Athe curve is not passing through origin Bthe curve cuts the axis of x in points (a,0) (b,0) (c,0) Cthe curve cuts the y–axis Dthe curve is symmetric about x-axis

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EnglishUP PCS (Pre) 1996

Q170.The equation of the tangent at the point (2,2) to the curve 2 2 x 2xy y 2x y 6 0 − + + + − = − + + + − = − + + + − = − + + + − = is–

A2x y 6 Bx 2y 6 Cx y 3 Dx 2y 3

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EnglishUP TGT-2016 (08-03-2019)

Q171.The equation of the normal at the point (1, 1) on the curve 2y + x2 = 3 is

Ax+y = 0 Bx+y+1 = 0 Cx–y=0 Dx–y = 1

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EnglishUP PCS (Pre) 1996

Q172.If the tangent of the curve 1/ 2 1/ 2 1/ 2 x y c at any point on it cuts the axes OX, OY at P, Q respectively. Then OP+OQ is equal to:

A1/ 2/c Bc C3/ 2/c D2/c

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EnglishUP PCS (Pre) 1999

Q173.The maximum slope attained by the curve y = –x3 +18x+7 is

A–1 B–3 C18 D20

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EnglishUP PCS (Pre) 1999

Q174.For the curve rθ = a, the polar subtangent at (r, θ) equals:

Ar Bθ C–a D2a

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EnglishUP PCS (Pre) 2000

Q175.The least value of f (x) = x3 –x2 +x+1 on [0, 1] is:

A0 B1/2 C1 D2

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EnglishUP PCS (Pre) 2002

Q176.If xy = c2, the maximum value of ax +by is:

A-2c ab B2abc C-2c abc D2c ab

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EnglishUP PCS (Pre) 2008

Q177.The necessary condition for a maximum or a minimum of a function f(x) is

Adf 0 dx ≠ B2 d f ve dx = + C2 d f ve dx = − Ddf 0 dx =

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EnglishUP PCS (Pre) 2009

Q178.Maximum value of 2x 1 f(x) = x is

Ae Be C1/e DNone of the above

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EnglishUP PCS (Pre) 2009

Q179.The point on the curve y2 = 4x, which is nearest to the point (2, 1) is

A(1, 2) B(1, –2) C(0, 0) DNone of the above

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EnglishGIC Lecturer Exam-2015

Q180.The minimum value of 27cos2x. 81sin2x is

A1/3 B1/9 C1/27 D1/243

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