Math Chapter Wise

EnglishRPSC PGT 2022

Q21.The evaluate of the parabola y2 = 4 ax is -

A27 ay2 = 4 (x +3a)2 B27 ay2 = 4 (x –3a)2 C27 ay2 = 4 (x +2a)3 D27 ay2 = 4 (x –2a)3

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EnglishRPSC PGT 2022

Q22.If (0, 4) and (0, 1) are vertex and focus respectively of a parabola, then its equation will be -

Ax2 + 12y = 0 Bx2 + 12y = 48 Cx2 – 12y = 48 Dy2 + 12y = 48

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EnglishRPSC PGT 2022

Q23.If latus rectum of an ellipse is one third of its minor axis, then the eccentricity of the ellipse is

A2/3 B2 2/3 C2/3 D35/6

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EnglishRPSC PGT 2022

Q24.The locus of the points from which three mutually perpendicular planes can be drawn to touch the ellipse 2 2 x y + = 1;z = 0 a b, is-

Ax2 – y2 – z2 = a2 – b2 Bx2 – y2 + z2 = a2 – b2 Cx2 + y2 + z2 = a2 + b2 Dx2 + y2 – z2 = a2 + b2

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EnglishRPSC PGT 2022

Q25.The coordinate of the point at which the line 2x – y = 12 is normal to the parabola y2 = 4x, is -

A(9, 6) B(9, –6) C(4, 4) D(4, –4)

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EnglishDSE TGT 2022

Q26.Eccentricity of Hyperbola x2 – y2 = a2

A3/2 B1 C2 D1

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EnglishDSE TGT 2022

Q27.Eccentricity of ellipse is always

AZero Bgreater than 2 Cless than 1 Dless than 2 but greater than 1

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EnglishDSSSB PGT 2021

Q28.The hyperbolas x2 –y2 = a2 and xy = c2

AIntersect orthogonally BIntersect but not orthogonally CDo not intersect DMeet at imaginary points

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EnglishDSSSB PGT 2021

Q29.The locus of the middle points of the parallel chords of a parabola is-

AA straight line passing through its vertex BA straight parallel to the axis of the parabola CA directrix DA straight perpendicular to the axis of the parabola

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EnglishDSSSB PGT 2021

Q30.If the straight lines y = mx and y = m'x be a pair of conjugate diameters of an ellipse 2 2 x y + = 1 a b, then -

Amm' = 2 a b Bmm' = 2 b a Cmm' = 2 a – b Dmm' = 2 b – a

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EnglishDSSSB PGT 2021

Q31.The eccenricity and semi-latus rectum of the curve 1 = 8 + 5cosθ r are respectively-

A1,8 8 B5 1, 8 8 C1 5, 8 8 D5,8 8

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EnglishDSSSB PGT 2021

Q32.The diameter of the parabola x2 = 4ay is parallel to-

Ay'-axis Bx'-axis CA line equally inclined to co-ordinate axis DThe straight line y + 3x = 0

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EnglishDSSSB PGT 2021

Q33.The equation of the diameter of the ellipse 3x2 +4y2 = 5 conjugate to the diameter y + 3x = 0 is -

A3y – x = 0 By – 4x = 0 Cx – 4y = 0 Dy – 3x = 0

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EnglishDSSSB PGT 2021

Q34.Which of the following is the eccentricity of parabola x2 = 4ay?

A2/7 B1/2 C5/2 D1

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EnglishDSE TGT 2019 Jharkhand TGT-2017

Q35.From the focus of the parabola y2 = 32x, a line of slope 1 is drawn. The equation of the line is

Ay = x-4 By = x-8 Cy = x Dy = x+8

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EnglishDSE TGT 2019

Q36.The distance between the centers of two circles of radii r1 and r2 is d. They will touch each other internally if

Ad = r1 / r2 Bd = r1 r2 Cd = r1 + r2 Dd = r1 – r2

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EnglishDSE TGT 2019

Q37.If θ1, θ2 are the eccentric angles of the extremities of a focal chord of the ellipse x2 /a2 + y2 /b2 = 1, a > b, then for 'e' is the eccentricity of the ellipse, (e+1)/(e-1) =

A1 2/tan( / 2)tan( / 2) B1 2/sin( )/ 2 C1 2/cos( )/ 2 D1 2/cot( / 2)cot( / 2)

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EnglishOAVS TGT 2018

Q38.The point (–4, –2) lies on a circle. What is the length of the radius of the circle if the centre is located at (–8, –10)?

A4 5 B2 5 C5 D3 5

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EnglishOAVS TGT 2018

Q39.The equation of the family of the circles that touch both the coordinate axes can be put in the form of:

Ax2 – y2 + 2hx + 2hy + h2 = 0 Bx2 + y2 + 2hx + 2hy – h2 = 0 Cx2 + y2 – 2hx – 2hy + h2 = 0 Dx2 + y2 – hx – hy + h2 = 0

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EnglishJSSC PGT 2018

Q40.For what value of m is the line y = mx + 5 tangent to the ellipse represented by 2 2 4x y + = 1 9 16

A2 B± 2 C+3 D3

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