Math Chapter Wise

EnglishUP PCS (Pre) 2003

Q301.The equation r cos sin 1 2 2 represents–

Aan ellipse Ba hyperbola Ca parabola Da circle

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EnglishUP PCS (Pre) 2003

Q302.If PSP’ is a focal chord of the conic 4 cos 2cos r then 1 1 SP SP' + + is equal to –

A1 B2 C4 D8

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EnglishUP PCS (Pre) 2003

Q303.The polar equation of the straight line joining two points 4, 2 and 3, 2 is–

A6 r (2 3 3)cos 2sin 0 B6 r (2 3 3)cos 2sin 0 C6 r (2 3 3)cos 2sin 0 Dnone of the above

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EnglishUP PCS (Pre) 2003

Q304.The polar equation of the tangent to the conic 1 ecos r = + θ = + θ = + θ = + θ l at the point " " is–

Acos ecos r l Becos cos() r l Ccos ecos() r l Desin sin() r l

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EnglishUP PCS (Pre) 2003

Q305.The straight line 2x+11y=5 is a bisector between the lines 24x+7y=20 and 4x–3y=λ, then λ is equal to–

A4 B3 C2 D1

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EnglishUP PCS (Pre) 2003

Q306.If the co-ordinate axes on a plane are rotated by an angle of 600 in anti-clockwise direction, the new co-ordinates of the point (1,2) are:

A1 2 3 2 2 3,, 2 2 B1 2 3 2 3,, 2 2 + − C1 2 3 2 2 3,, 2 2 D1 2 3 2 2 3,, 2 2

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EnglishUP PCS (Pre) 2003

Q307.The asymptotes of the curve 4 2 2 2 2 2 x x y a (a y) 0parallel to y-axis are–

Ax 0,x 1 By 0,x 1 C2 2/a y 0 D2 2/a x 0

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EnglishUP PCS (Pre) 2004

Q308.The locus of the point of intersection of perpendicular tangents to a parabola is a–

Ahyperbola Bparabola Ccircle Dstraight line

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EnglishUP PCS (Pre) 2004

Q309.The sum of the focal radii of any point of an ellipse is equal to–

Athe length of the major axis Bthe length of the minor axis Cthe length of the latusrectum Dnone of the above

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EnglishUP PCS (Pre) 2004

Q310.The following equation represents: 2 2 3x 12xy 12y 435x 9y 72 0 + + + − + = + + + − + = + + + − + = + + + − + = 2 2 3x 12xy 12y 435x 9y 72 0 + + + − + = + + + − + = + + + − + = + + + − + =

Acircle Bellipse Chyperbola Dparabola

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EnglishUP PCS (Pre) 2004

Q311.The centre of the conic 2 2 14x 4xy 11y 44x 58y 71 0 is–

A(3,2) B(2,3) C(3,3) D(2,2)

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EnglishUP PCS (Pre) 2004

Q312.The number of tangents that can be drawn from the point (8,6) to the circle 2 2 x y 100is–

A0 B1 C2 DNone of the above

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EnglishUP PCS (Pre) 2004

Q313.The equation of the tangent to the curve x = at2, y = 2at at point ‘t’ is:

A2/x ty at 0 B2/x ty at 0 C2/x ty at 0 D2/x ty at 0

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EnglishUP PCS (Pre) 2005

Q314.If e > 1 then the equation = 1+ e cos θ r ℓ represents:

Aa circle Ba parabola Can ellipse Da hyperbola

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EnglishUP PCS (Pre) 2005

Q315.Which of the following points lies outside the ellipse 2 2 x y + = 1: a b

A(a, 0) B(0, b) C(– a, 0) D(a, b)

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EnglishUP PCS (Pre) 2005

Q316.The locus of the middle points of the focal chords of a hyperbola is:

Aa parabola Ba circle Can ellipse Da hyperbola

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EnglishUP PCS (Pre) 2006

Q317.The angle between the pair of tangents drawn from the point (1,2) to the ellipse 3x2 +2y2 =5, is

A1 12 5 tan 5 − B1 6 5 tan 5 − C1 3 5 tan 5 − DNone of the above

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EnglishUP PCS (Pre) 2006

Q318.The equation x2 + k1y2 + k2y = a2 represents a pair of perpendicular straight lines if:

A1 2 k 1,k a = − = ± B1 2 k 1,k 2a = − = ± C1 2 k 1,k a = − = D1 2 k 1,k 2a = − =

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EnglishUP PCS (Pre) 2006

Q319.The asymptotes of the curve y4 + x2 y2 + 2xy – 4x2 – y + 1 = 0 which are parallel to the X-axis are

Ay=±1 By=±2 Cx=±1 Dx=±2

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EnglishUP PCS (Pre) 2006

Q320.For the curve y2 =x3 +x2, the origin is a:

Anode Bcusp Cpoint of inflexion Dnone of the above

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