Math Chapter Wise

EnglishUKPSC Lecturer (Mains) 2020

Q81.The equations of the normals at the ends of the latus rectum of the parabola y2 = 4ax are:

Ax2 – y2 – 6ax+ 9a2 = 0 Bx2 – y2 – 6ax– 6ay + 9a2 = 0 Cx2 – y2 – 6ay + 9a2 = 0 Dy2 = x2 + ax

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EnglishUKPSC Lecturer (Mains) 2020

Q82.Intercept on the line y = x by the circle x2 + y2 – 2x = 0 is AB. Equation of the circle whose diameter is AB, is:

Ax2 + y2 + x – y = 0 Bx2 + y2 – x – y = 0 Cx2 + y2 + x – y = 0 Dx2 + y2 + x – y = 0

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EnglishUKPSC Lecturer (Mains) 2020

Q83.The point on the parabola y2 = 12x at which the normal makes an angle 300 with its axis is:

A() 1, 2 3 B() 1, 2 3 C(3,6) D(3, 6)

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EnglishUKPSC Lecturer (Mains) 2020

Q84.The circle x2 + y2 – 8x+ 4y + 4 = 0 touches:

Ax- axis only By-axis only Cboth x and y axes DNone of these

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EnglishUKPSC Lecturer (Mains) 2020

Q85.The line y = mx+ c cuts the circle x2 + y2 = a2 in two real points only if

Ac2 < a2 (1+m2) Bc2 > a2 (1+m2) Cc < a (1+m2/) Dc < a (1+m2/)

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EnglishHaryana PGT 2019

Q86.The locus of the foot of perpendicular drawn from the center of the ellipse x2 + 3y2 = 6 on any tangent to it, is:

A(x2 – y2)2 = 6x2 + 2y2 B(x2 – y2)2 = 6x2 – 2y2 C(x2 + y2)2 = 6x2 + 2y2 D(x2 + y2)2 = 6x2 – 2y2

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EnglishHaryana PGT 2019

Q87.The equation of a tangent to be parabola y2 = 8x is y = x + 2. The point on this line from which the other tangent to this parabola is perpendicular to the given tangent is:

A(–1, 1) B(0, 2) C(2, 4) D(–2, 0)

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EnglishHaryana PGT 2019

Q88.If 3x + y = 0 is a tangent to the circle with center (2, –1), then the equation of another tangent to the same circle from origin is:

Ax + 3y = 0 B3x –y = 0 Cx – 3y = 0 Dx + y = 0

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EnglishHaryana PGT 2019

Q89.If the line 3x – 4y = m intersects the circle x2 + y2 = 4x + 8y + 5 in two distinct points, then:

A–85< m < –35 B–35< m < 15 C15< m < 65 D35< m < 85

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EnglishHaryana PGT 2019

Q90.Foci of the hyperbola are (–2, 0) and (2,0). If its eccentricity is 2, then its equation will be:

A–3x2 + y2 = 3 Bx2 –3y2 = 3 C3x2 – y2 = 3 D–x2 + 3y2 = 3

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EnglishHaryana PGT 2019

Q91.In the ellipse, the distance between its foci is 6 and minor axis is 8. Then its eccentricity is:

A1/2 B4/5 C1/5 D3/5

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EnglishHaryana PGT 2019

Q92.The slope of the line touching both the parabola y2 = 4x and x2 = –32y is:

A1/2 B3/2 C1/8 D2/3

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EnglishHaryana PGT 2020

Q93.Directrix of the parabola y2 + 4x +4y – 3 = 0 is:

A4x = 11y B11x = 4y C4x = 11 D4y = 11

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EnglishHaryana PGT 2020

Q94.Two tangents are drawn from the origin to the circle x2 + y2 – 14x + 2y + 25 = 0. Angle between these two tangents will be:

A0º B30º C45º D90º

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EnglishHaryana PGT 2020

Q95.If line lx + my + n = 0 touches the ellipse ax2 + by2 = 1, then:

An2 = a2 l2 + b2 m2 Bn2 = 2 2 m a b + l Cn2 = 2 2 m a b + l Dn2 = al + bm

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EnglishHaryana PGT 2020

Q96.Let A(a, 0) and B(–a, 0) be two fixed points. The locus of variable point P which moves in such a way that (PA)2 – (PB)2 = 4a2 is:

AStraight line BCircle CParabola DEllipse

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EnglishHaryana PGT 2018

Q97.Let () φ P asecθ,b tanθ and Q(asec,b tan), where φ π θ + =, 2 be two points on the hyperbola − 2 2 x y = 1 a b.If (h, k) is the point of intersection of the normal's of P and Q, then k =

A2 2 a b a + B2 2 a b b + C2 2 a b a + − D2 2 a b b + −

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EnglishHaryana PGT 2018 UKPSC GIC 2018

Q98.The line ℓ = Acosθ + Bsinθ r will touch the conic ℓ = 1+ ecosθ, r if:

A() 2 2 A e B 1 + + = B() 2 2 A e B 1 − + = CA e B 0 + + = DA e B 0 − − =

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EnglishHaryana PGT 2018

Q99.Three normals to the parabola 2 y = x are drawn through a point (c, 0), then:

A1 c 8 < B1 c 4 < C1 c 2 < D1 c 2 >

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EnglishUKPSC GIC 2018

Q100.The equation of an ellipse whose foci are at () 3,0 ± and which passes through (4,1) will be

A2 2 x y 1 18 12 + = B2 2 x y 1 18 9 + = C2 2 x y 1 9 18 + = D2 2 x y 1 12 18 + =

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