Math Chapter Wise

EnglishUPPSC GIC 2021

Q61.The area of the circle x2 + y2 = 14x is-

A208 sq. unit B516 sq. unit C108 sq, unit D154 sq, unit

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EnglishUP TGT 2021

Q62.The co-ordinates of a moving point are (2t2 + 4, 4t + 6). Its locus will be

ACircle BStraight line CParabola DNone of the above

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EnglishUP TGT 2021, 2003 / PGT- 2004

Q63.If the foci of the ellipse 2 2 2 x y + = 1 16 b and the hyperbola 2 2 x y 1 – = 144 81 25 coincide, then the value of b2 is

A1 B5 C7 D9

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EnglishUP TGT 2021

Q64.The equation of the directrix of the parabola y2 + 4x + 4y + 2 = 0 is

Ax = –1 Bx = 1 C3 x – 2 = D3 x 2 =

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EnglishUP TGT 2021

Q65.The intercept on the line y = x by the circle x2 + y2 – 2x = 0 is AB. Equation of circle with AB as diameter is

Ax2 + y2 = 1 Bx2 + y2 = 2 Cx2 + y2 – x – y = 0 Dx2 + y2 – 3x – 3y + 4 = 0

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EnglishUP TGT 2021

Q66.The equation 2 2 x y – = 1; r < 1 1 – r 1+ r represents

Aan ellipse Ba hyperbola Ca circle Dnone of the above

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EnglishUP TGT 2021

Q67.Equation of a circle, with center (0, 0) and 2x + 3y = 5 as a tangent, is

Ax2 + y2 = 5 Bx2 + y2 + 2x = 25 Cx2 + y2 + y = 25 D13x2 + 13y2 = 25

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EnglishUP TGT 2021

Q68.The equations of tangents to the ellipse 3x2 + 4y2 = 12 which are parallel to the line y + 2x = 4 are

Ay + 2x = ± 4 By + 2x = ± 7 Cy 2x 15 + = ± Dy 2x 19 + = ±

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EnglishUPPSC Ashram Paddhati 2021

Q69.The length of the latus rectum of the conic 3x2 + 4y2 – 6x + 8y – 5 = 0 is

A3 B3/2 C2/3 Dnone of the above

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EnglishUPPSC Ashram Paddhati 2021

Q70.The distance between the foci of a hyperbola is 8 and its eccentricity is 3. Its equation may be

Ax2 – 3y2 = 32 B6x2 – 3y2 = 16 C6x2 – 3y2 = 32 D3x2 – 3y2 = 16

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EnglishUPPSC Ashram Paddhati 2021

Q71.The area of the ellipse 2 2 x y + = 1 16 9 lying in the first quadrant is

A2π B3π C4π Dnone of these

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EnglishUPPSC Ashram Paddhati 2021

Q72.The equation of a rectangular hyperbola referred to its asymptotes as co-ordinate axes is of the form

A2 2 x y – =1 a b Bx2 – y2 = a2 Cxy = c2 Dx2 – y2 = 2xy

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EnglishUPPSC Ashram Paddhati 2021

Q73.The line y = mx + c touches the ellipse 2 2 x y + = 1 a b, if

Ac2 = a2 m2 + b2 Bc2 = a2 + b2 m2 C2 a c = m D2 m c = a

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EnglishUP TGT 2021

Q74.Two consecutive sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0. If the equation of one diagonal is 11x + 7y = 9, the equation of other diagonal is

Ax + y = 0 B7x – 11y = 0 C7x + 11y = 0 Dx – y = 0

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EnglishUP TGT 2021

Q75.Distance between the straight lines x + 2y = 5 and 2x + 4y = 11 is

A1/5 B1/2 5 C5 D5/2

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EnglishUP TGT 2021 Haryana TGT 2019, 2020

Q76.If points (a, 0), (0, b) and (1, 1) are collinear, then 1 1 + a b is equal to

A1 B2 C–1 D2

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EnglishHaryana PGT 2019

Q77.Let P be the point (1, 0) and Q a point on the parabola y2 = 8x. The locus of midpoint of PQ is

Ax2 – 4y + 2 = 0 Bx2 + 4y + 2 = 0 Cy2 + 4x + 2 = 0 Dy2 – 4x + 2 = 0

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EnglishUKPSC Lecturer (Mains) 2020

Q78.The foci of a hyperbola coincide with the foci of the ellipse 2 2 x y + = 1 25 9. The equation of this hyperbola with eccentricity 2, is:

A2 2 y 1 4 12 − = x B2 2 y 1 9 25 − = x C2 2 y 1 12 9 − = x D2 2 3y 12 − = x

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EnglishUKPSC Lecturer (Mains) 2020

Q79.If x + by + 2 = 0 touches the parabola y2 = 8x, then a value of 'b' and the corresponding point of contact are:

Ab = 1, (2,–4) Bb = –1, (–2,4) Cb = 1, (–2, 4) Db = –1, (2,–4)

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EnglishUKPSC Lecturer (Mains) 2020

Q80.The sum of squares of intercepts made on coordinate axes by the tangent to the curve x2/3 + y2/3 = a2/3 is:

Aa2 B2a2 C3a2 D4a2

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