Math Chapter Wise

EnglishUP PCS (Pre) 2000

Q281.The number of asymptotes parallel to the y- axis of the curve x2 y2 = a2 (x2 + y2) is:

A1 B2 C3 D4

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EnglishUP PCS (Pre) 2000

Q282.The conic 22x2 – 12xy + 17y2 – 112x + 92y + 178 = 0 represent a:

Aparabola Bellipse Chyperbola Dcircle

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EnglishUP PCS (Pre) 2000, 2002

Q283.The eccentricity of the ellipse 4x2 + 9y2 – 8x – 36y + 4 = 0 is:

A5/3 B4/3 C8/3 D4

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EnglishUP PCS (Pre) 2001

Q284.The curve xy–2y–x=0 has:

Ax =2 as the only asymptote By =1 as the only asymptote Cx =2 and y=1 as asymptotes Dno asymptote

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EnglishUP PCS (Pre) 2001

Q285.The direction of the asymptote of the hyperbola 1 = 1+ e cosθ (e > 1) r is given by:

A1 1 cos e − B1 1 cos e − C1 1 cos e − D1 1 cos e −

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EnglishUP PCS (Pre) 2001

Q286.The straight line x cos α+y sinα =p touches the circle x2 +y2 = 9 if:

Ap=± 3 cos α Bp=± 3 Cp=± 3 cot Dp=± 3 cosec α

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EnglishUP PCS (Pre) 2001

Q287.If the focal distance of a point on the parabola y2 = 8x is 4 then the coordinates of that point are:

A() 2, 2 B(2, 4) C(8, 8) D(18, 12)

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EnglishUP PCS (Pre) 2001

Q288.The centre of the sphere passing through the points (1, 0, 0), (0, 2, 0), (0, 0, 1) is:

A1 2 1,, 3 3 3 B4 2 4,, 9 9 9 C2 10 2,, 9 9 9 D5 8 5,, 18 9 18

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EnglishUP PCS (Pre) 2001

Q289.The eccentricity of the conic 9x2 +5y2 –30y = 0 is:

A1/3 B2/3 C3/4 D3/2

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EnglishUP PCS (Pre) 2001

Q290.If circles x2 +y2 +2px+r = 0 and x2 +y2 +2qy+r = 0 touch each other then:

A1 1 1 p q r − = B2 2 2 1 1 1 p q r + = C2 2 2 p q r + = D2 2 1 1 1 r p q + =

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EnglishUP PCS (Pre) 2002

Q291.The angle between the tangents drawn from the origin to the parabola y2 = 4a(x–a) is:

A90° B45° C30° D1 1 tan 2 −

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EnglishUP PCS (Pre) 2002

Q292.The length of the focal chord of the conic y2 =9x making angle π 3 with the axis of the conic is:

A36 B18 C12 D9

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EnglishUP PCS (Pre) 2002

Q293.The straight line y = 3x–1 touches the curve x4 -2x2 +3x at:

Aone point Btwo points Cthree points Dfour points

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EnglishUP PCS (Pre) 2002

Q294.The equation 2 = 5 + 3 cos θ + 4 sin θ r represents:

Aa circle Ba parabola Can ellipse Da hyperbola

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EnglishUP PCS (Pre) 2002

Q295.The minimum radius vector of the curve 2 2 a b + = 1 x y is of length:

Aa Bb Ca–b Da+b

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EnglishUP PCS (Pre) 2002

Q296.All points of the curve y2 = 4a {x+a sin (x/a)} at which the tangent is parallel to the axis of X lie on a:

ACircle Bparabola Chyperbola Dnone of the above

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EnglishUP PCS (Pre) 2002

Q297.The angle of intersection of the curves y =4 – x2 and y = x2 is:

A1 4 tan 7 − B1 2 2 tan 7 − C1 4 2 tan 7 − D1 8 2 tan 7 −

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EnglishUP PCS (Pre) 2002

Q298.The number of asymptotes of the curve y2 = x is:

A0 B1 C2 D3

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EnglishUP PCS (Pre) 2003

Q299.The line x my n 0 l is a tangent to the parabola 2 y 4ax if:

A2 m an l B2 n am l C2/mn al Dm n al

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EnglishUP PCS (Pre) 2003

Q300.The slope of the line joining the point (1, 2) with the point of intersection of the pair of lines 2 x 2xy 4x 0 is–

A4 B6 C8 Dnone of the above

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