Math Chapter Wise

EnglishUP PCS (Pre) 1998 / L.T. 2018

Q241.The distance between the foci of a hyperbola is 16 and its eccentricity is 2. An equation for the hyperbola is:

Ax2 – y2 = 32 Bx2 – y2 = 16 Cy2 – x2 = 8 Dy2 – x2 = 64

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EnglishUP PCS (Pre) 1998

Q242.The two circles x2 + y2 + 2ax + c = 0, x2 + y2 + 2bx + c = 0 will touch if:

A2 2 2 1 1 1 a b c + = B2 2 2 1 1 1 a b c − = C2 2 1 1 1 c a b + = D2 2 1 1 1 c a b − =

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English(GIC) Lecturer Exam, 2015

Q243.If x+y = k is normal to parabola y2 = 12x then value of k is

A3 B9 C–9 D–3

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EnglishUP PCS (Pre) 1994

Q244.The equation r = 9 sin θ, repesents –

Aa straight line Ba pair of straight lines Ca parabola Da circle

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EnglishUP PCS (Pre) 1994

Q245.The curve 2 1 1 cos r 2 4 is–

Aparabola Bhyperbola Cellipse Dstraight line

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EnglishUP PCS (Pre) 1994

Q246.The length of the latus rectum of the conic 7 2 6cos 2r is–

A7/2 B7 C14 D2

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EnglishUP PCS (Pre) 1994

Q247.The equations x =a cos θ and y = b sin θ represent a –

Acircle Bparabola Cellipse Dhyperbola

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EnglishUP PCS (Pre) 1994

Q248.The normal to the hyperbola xy = 4 at (4,1) meets the curve again at the point:

A(2, 2) B(2,2) C1, 16 4 D1,8 2

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EnglishUP PCS (Pre) 1994

Q249.The focus of the parabola 8x2 = y is–

A32,0 B1 0, 2 C1 0, 32 D1,0 8

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EnglishUP PCS (Pre) 1994

Q250.The equation 2 By 2Gx 2Fy C 0 represents –

Aa parabola Ba circle Ca hyperbola Da pair of straight lines

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EnglishUP PCS (Pre) 1994

Q251.The equation of directrix of the parabola 2 y 4x 6y 13 0 is–

Ay = 0 Bx + y = 1 Cx = 0 Dnone of these

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EnglishUP PCS (Pre) 1994

Q252.The equation of the radical axis of the circles 2 2 x y 2x 4 0 and 2 2 x y 2y 4 0 is–

Ay = x By = 4 Cx = 4 Dx + y = 2

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EnglishUP PCS (Pre) 1994

Q253.The eccentricity of the conic 2 2 4x 5y 20 0 is–

A3/2 B3/15 C1/2 D1/5

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EnglishUP PCS (Pre) 1994

Q254.For the curve 3 3 x y 3axy 0 the only real asymptote is–

Ax y a 0 Bx 2y a 0 Cx y a 0 Dx y a 0

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EnglishUP PCS (Pre) 1994

Q255.The asymptotes parallel to the x-axis of the curve y3 + x2 y + 2xy3 – 2xy2 – y + 1=0 is:

Ay = 1 By + 1 = 0 Cy = 0 Dx = 0

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EnglishUP PCS (Pre) 1995

Q256.The number of real asymptotes of the curve 2 y 4a(x a)is

A0 B1 C2 D3

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EnglishUP PCS (Pre) 1995

Q257.The equations x asec,y atan represent–

AA rectangular hyperbola BA non-rectangular hyperbola CA circle DNone of these

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EnglishUP PCS (Pre) 1995

Q258.The equation 1 3 2cos 3 represent–

AA circle BA parabola CAn ellipse DA hyperbola

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EnglishUP PCS (Pre) 1995

Q259.The equation of the diameter of the ellipse 2 2 x 4y 4 which is conjugate to the diameter y = x is–

Ax 4y Bx 4y Cx 2y Dx 2y

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EnglishUP PCS (Pre) 1995

Q260.An asymptote of the curve 2 x 2x 1 y x 1 + − = + is–

Ax = 0 Bx = 1 Cx = –1 Dx = 2

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