Math Chapter Wise

EnglishPGT 2011

Q141.The eccentricity of ellipse 2 2 x y 1 a b + = + = whose latus rectum is half of its minor axis is:

A1/2 B2/3 C3/2 DNone of these

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EnglishPGT 2011

Q142.The line xcosα+ysinα=p is tangent to the ellipse 2 2 x y 1 a b + = + = is:

Aa2 cos2 α–b2 sin2 α= p2 Ba2 sin2 α+b2 cos2 α= p2 Ca2 cos2 α+b2 sin2 α= p2 Da2 cos2 α–b2 sin2 α= p

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EnglishPGT 2011

Q143.The equation of the ellipse passing through (2,1) having eccentricity 1 e 2 = is

A3x2 +4y2 =16 B3x2 +5y2 =17 C5x2 +3y2 =23 DNone of these

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EnglishPGT 2011

Q144.The vertices of the hyperbola 9x2 –16y2 –36x+96y–252=0 is

A(6, 3) and (–6, 3) B(6,3) and (–2,3) C(–6,3) and (–6,–3) DNone of these

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EnglishPGT 2011

Q145.If y=mx+6 is a tangent to the hyperbola 2 2 x y – 1 100 49 = then the value of m is:

A17/20 B20/17 C3/20 D20/3

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EnglishPGT 2011

Q146.If e1 and e2 are the eccentricities of the hyperbola xy=c2 and x2 –y2 =c2 then 2 2 1 2 e e + =

A1 B4 C6 D8

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EnglishPGT 2013

Q147.What will be the vertex of the parabola y2 – 8x – 4y – 4 = 0.

A(1, 2) B(–1, 2) C(1, –2) D(–1, –2)

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EnglishPGT 2013

Q148.The asymptote of the curve x2 –y2 =a2.

Ax=0, y=a Bx=a, y=0 Cx2 –y2 =0 Dx2 +y2 =0

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EnglishPGT 2013

Q149.The coordinate of the center of the conic x2 – xy–y2 –6x+3y+5=0.

A(3, 3) B12,1 5 C(3, 0) D12,1 5

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EnglishPGT 2013

Q150.The eccentricity of the hyperbola 2 2 x 2x 4y 0 − − = − − = − − = − − = is.

A5/2 B3/2 C1/4 D2

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EnglishPGT 2010

Q151.A circle of radius a is drawn with centre O. From the point P a tangent is drawn on the circle which touches the circle at the point Q. QT is perpendicular drawn from Q on OP. If OP = l then QT is equal to

A2 2 -a a ℓ B2 2 a -a ℓ C2 2 + a a ℓ D2 2 a + a ℓ

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EnglishPGT 2010

Q152.Which of the following constructions is being represented by the equation? x2 – 2y2 + xy + 6y – 4 = 0

ACircle BParabola CEllipse DNone of these

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EnglishPGT 2010

Q153.The volume of the sphere passing through the circle x2 +y2 =4, z= 0 and the point (1,2,–1) is

A40 3 π B17 17 6 π C20 5 3 π DNone of these

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EnglishPGT 2010

Q154.If the circles x2 +y2 =a2 and x2 +y2 –2gx+g2 –b2 = 0 touch each other externally, then

Ag= ab Bg2 =a2 +b2 Cg2 = ab Dg = a+b

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EnglishPGT 2009

Q155.Common chord of circles x2 + y2 + 4x + 1 = 0 and x2 + y2 + 6x + 2y + 3 = 0 is

A5x + y + 2 = 0 B3x + y + 3 = 0 Cx + y + 1 = 0 D2x + 2y + 5 = 0

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EnglishPGT 2009, 2010

Q156.If the eccentricities of two ellipses 2 2 1 25 169 x y + = + = and 2 2 1 a x y b + = + = are equal, then value of a b is

A5/13 B13/5 C6/13 D13/6

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EnglishPGT 2009

Q157.The point of intersection of latus rectum and axis of the parabola y2 + 4x + 2y – 8 = 0 is

A5, 1 4 − B4, 1 9 − C7 5, 5 2 D5 7, 2 5

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EnglishPGT 2009

Q158.The asymptotes of the curve 2 2 a b 1 x y + = + = are

Ax =, ± = ± a y b B, = − = − x a y b Cx = a, y = b D, = ± = ± x b y a

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EnglishPGT 2009

Q159.The product of perpendiculars drawn from any point on a hyperbola to its asymptotes is

A2 2 a b + B2 2 a b + Cab a b + D2 2 ab a b +

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EnglishPGT 2009

Q160.From an external point normal's are drawn to the parabola y2 = 4ax. Two of then are mutually perpendicular. Then locus of the point is

Ay2 = ax By2 = a(x – 3a) Cy = ax Dx = 3a

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