Math Chapter Wise

EnglishPGT 2000

Q181.The polar equation r= a sec θ represents a:

AParabola BStraight line CCircle DEllipse

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EnglishRajasthan TGT 2016

Q182.If co-ordinates of foci are (± ± ±5, 0) and vertices are (± ± ±13, 0), then equation of ellipse is

A2 2 x y 1 169 144 − = B2 2 x y 1 144 169 + = C2 2 x y 1 144 169 − = D2 2 x y 1 169 144 + =

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EnglishRajasthan TGT 2016

Q183.The co-ordinates of the centre of the hyperbola 2x2 +y2 –3xy–5x+4y+6=0 is

A(1,2) B(2,1) C(1,1) D(2,2)

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EnglishRajasthan TGT 2016

Q184.Number of distinct chords of the circle 2 2 1 x y 2x y 0, 2 + − − = + − − = + − − = + − − = passes through the point 1 2, 2 and bisected by x-axis, is

Azero Bone Ctwo Dinfinite

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EnglishRajasthan TGT 2016

Q185.The radius of circle, which touches the circles given by (x ± ± ±1)2 +(y± ± ±1)2 =1 is

A() 2 1 − unit B2 unit C2 2 unit DNone of these

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EnglishRajasthan TGT 2016

Q186.The point (a cosθ + b sinθ, a sinθ – b cosθ) lies on

Aellipse Bparabola Chyperbola Dcircle

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EnglishRajasthan TGT 2016

Q187.The maximum number of normals which can be drawn common to y2 =4ax and x2 =4by is

A2 B3 C4 D5

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EnglishRajasthan TGT 2016

Q188.One of the asymptote of curve x3 +3x2 y–4y3 –x+y+3=0 is

Ay+x=1 By–x=0 C2y+x=0 D2y–x=0

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EnglishRajasthan TGT 2015

Q189.The equation of circles which touches x 0, = y 0, = and x c, = is

A2 2 2 1 x y cx cy c 0 4 + − ± + = B2 2 2 1 x y cx cy c 0 4 + ± − + = C2 2 2 c x y cx cy 0 4 + − − ± = D2 2 2 c x y cx cy 0 4 ± + + − =

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EnglishRajasthan TGT 2015

Q190.If PQ is a focal chord of the parabola 2 y 4ax = with focus at S, then 2.SP.SQ SP SQ + is equal to

Aa B2a C4a D2/a

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EnglishRajasthan TGT 2015

Q191.The product of slopes of the conjugate diameters of the ellipse 2 2 x y 1 a b + = + = is

A2 a b B2 4a b − C2 b 4a D2 b a −

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EnglishRajasthan TGT 2015

Q192.If 3 3 x 2y xy(2x y) y(x y) 1 0 − + − + − + = − + − + − + = − + − + − + = − + − + − + = are the asymptotes of the curve x y 0, − = − = x y 1 0, + + = + + = + + = + + = x 2y 1 0, + + = + + = + + = + + = cut the curve again in three points, then these points lie on the straight line

Ax y 1 0 − − = Bx y 2 0 + + = Cx y 1 0 − + = Dx y 2 0 − + + =

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EnglishRajasthan TGT 2013

Q193.If the co-ordinates of two points A and B are respectively (c, 0) (–c, 0), then the locus of a point P which moves such than PA2 + PB2 = AB2, is-

Aa parabola Ba circle Can ellipse Da hyperbola

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EnglishRajasthan TGT 2013

Q194.A line passing through the point (2, 2) encloses an area λ with the axes. The intercepts on the axes made by the line are given by the two roots of equation-

Ax2 – |λ|x + 2|λ| = 0 Bx2 + |λ|x + 2|λ| = 0 Cx2 – 2|λ|x + |λ| = 0 Dx2 + 2|λ|x + |λ| = 0

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EnglishRajasthan TGT 2013

Q195.The circles x2 + y2 + 2gx + 2fy = 0 and x2 + y2 + 2g'x + 2f 'y = 0 touches internally if-

Aff' = gg' Bf + f' = g + g' Cf' g = g' f D|f – f'| = |g – g'|

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EnglishRajasthan TGT 2013

Q196.If any tangent to the ellipse 2 2 x y + =1 a b intercepts equal lengths 'l' on the axes, then l =

A() 2 2 a b + B2 () 2 2 a b + C2 2 a b + D2 2 2 a b +

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EnglishRajasthan TGT 2013

Q197.In general the number of points of intersection of nth degree curve with its ‘n’ asymptotes will be-

An(n–1) Bn(n+1) Cn(n–2) Dn(n+2)

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EnglishRajasthan TGT 2011

Q198.If one end of diameter of the circle 2 2 x y 4x 6y 11 0 + − − + = + − − + = + − − + = + − − + = is (3,4) then its other end is

A(0,0) B(1,1) C(1,2) D(2,1)

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EnglishRajasthan TGT 2011

Q199.The focus of the parabola 2 y 4y 4x = − = − is

A(1,2) B(2,1) C(0,2) D(2,0)

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EnglishRajasthan TGT 2011

Q200.The locus of the point of intersection of perpendicular tangents of the ellipse 2 2 16x 9y 144 + = + = is

A2 2 x y 16 + = B2 2 x y 9 + = C2 2 x y 25 + = D2 2 x y 7 + =

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