Math Chapter Wise

EnglishJSSC PGT 2018

Q41.Find the focus of the below conic. x2 + 19 – 8x – y = 0

A(4, 3.25) B(2.75, 4) C(3.25, 4) D(4, 2.75)

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EnglishJSSC PGT 2018

Q42.Consider an ellipse represented with following equation: 2 2 x y + = 1 16 49 The length of the latus rectum of this ellipse is:

A32/7 B49/4 C49 D49/16

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EnglishJSSC PGT 2018

Q43.For the conic r = 1 + sinθ, the slope of tangent to the conic at θ = π/3 is:

A–1/2 B1/2 C–1 D1

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EnglishJSSC PGT 2018

Q44.The equation x2 – 6x + 6y + y2 +2=0 represents:

AAn ellipse with latus rectum 4 and focus at (– 3, 3) BA circle with radius 4 and centre at (–3, 3) CA circle with radius 4 and centre at (3, –3) DAn ellipse with latus rectum 4 and focus at (3, –3)

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EnglishJSSC PGT 2018

Q45.For what value of c is the line y = 0.5x + c tangent to the parabola represented by Y2 = 4ax?

Aa/2 Ba/4 C2a Da

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EnglishJSSC PGT 2018

Q46.Which conic does the below equation represent? () 5 R = 4 -11Cos(θ)

AHyperbola BParabola CEllipse DCircle

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EnglishKVS TGT 2017

Q47.The length of latus rectum of the ellipse 5x2 +9y2 = 45 is–

A10/3 B5/3 C5 5/3 D10 5/3

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EnglishKVS TGT 2017

Q48.The two tangents, perpendicular to each other, to the parabola y2 = 4ax intersect on the line–

Ax = a Bx + a = 0 Cx + 2a = 0 Dx – 2a = 0

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EnglishKVS TGT 2017

Q49.What angle the tangent to the parabola x2 = 2y at the point 1 1, 2 makes with x – axis?

A00 B450 C300 D600

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EnglishUP TGT 2021

Q50.If the equation x2 + y2 +(c–2)xy – 4x–4y + c2 = 0 represents a circle, then its radius is

A1 B2 C3 D5

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EnglishUPPSC GIC 2021 UPPCS (Pre) 1994

Q51.The equation xy = 1 represents-

Aa pair of straight lines Ba parabola Can ellipse Da hyperbola

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EnglishUPPSC GIC 2021

Q52.The equation of the circle described on the line joining the points (-1, -2) and (1, 3) as diameter is-

Ax2 + y2 – y – 7 = 0 Bx2 + y2 = 7 Cx2 + y2 – y – 6 = 0 Dx2 + y2 – x – 7 = 0

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EnglishUPPSC GIC 2021 UPPSC Ashram Paddhati 2021

Q53.How many normals can be drawn from a given point to a given parabola?

A2 B3 C4 D6

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EnglishUPPSC GIC 2021

Q54.What is the equation of the chord of the circle x2 + y2 = 49, whose mid – point is (-4, 5)?

A4x – 5y – 41 = 0 B4x +5y + 41 = 0 C4x – 5y + 41 = 0 D5x – 4y + 41 = 0

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EnglishUP PGT 2021

Q55.If the straight line y = mx lies outside the circle x 2 + y 2 – 20y + 90 = 0, then the value of m will satisfy–

Am 3/< Bm < 3 Cm > 3 Dm 3/>

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EnglishUP PGT 2021

Q56.If the line ax + by + c = 0 touches the parabola y2 = x, then which of the following is correct?

Aabc = 1 Bb2 = 4ac Ca2 = 4bc Dc2 = 4ab

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EnglishUP PGT 2021

Q57.The equation of the tangents drawn from the point (–2, –1) to the hyperbola 2x2 – 3y2 = 6 are

A3x + y + 5 = 0, x – y + 1 = 0 B3x + y + 5 = 0, x + y + 1 = 0 C3x – y + 5 = 0, x + y + 1 = 0 D3x – y + 5 = 0, x – y + 1 = 0

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EnglishUP PGT 2021

Q58.The straight lines 3x – 4 y + 4 = 0 and 6x – 8y + 13 = 0 are tangents to the same circle. The radius of the circle is

A1/2 B1/4 C3/2 D2

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EnglishUP PGT 2021

Q59.The distance between the foci of a hyperbola is 16 and its eccentricity is 2 the equation of hyperbola is –

Ax2 – y2 = 32 B2x2 – y2 = 16 Cx2 – 2y2 = 32 Dx2 – y2 = 8

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EnglishUP PGT 2021

Q60.The circles (x–1)2 + (y–3)2 = r2 and x2 + y2 – 8x + 2y + 8 = 0 intersect at two distinct points. Which of the following is correct?

Ar = 1 B1 < r < 1 Cr = 2 D2 < r < 8

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