Math Chapter Wise

EnglishUKPSC GIC 2018

Q101.The circle ax2 + ay2 + 2gx + 2fy + c = 0 will touch the axis of x, if

Af2 = ac Bg2 = ac Cf2/> ac Dg2/> ac

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EnglishUKPSC GIC 2018

Q102.The line 2x + y = 3 cuts the ellipse 4x2 +y2 = 5 at P and Q. If θ be the angle between normal's at these points, then tan θ is:

A1/2 B3/4 C3/5 D5

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EnglishUKPSC GIC 2018

Q103.Equation of tangent to the hyperbola 2x2 – 3y2 = 6 which is parallel to the line y = 3x +4 is

Ay = 3x 6 ± By = 3x – 6 Cy = 3x ± 5 Dy = 3x + 4

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EnglishUKPSC GIC 2018

Q104.The locus of the middle points of all the chords of the parabola y2 = 64x through the origin

Ax2 + y2 = 64 Bx2 = 32y Cxy = 32 Dy2 = 32x

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EnglishLT 2018

Q105.The locus of the centres of circles, that passes through the origin and cuts off a length 6 from the line y=4, is

A2 x 8y 25 0 − + = B2 x 8y 25 0 − − = C2 x 8y 25 0 + − = DNone of the above

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EnglishLT 2018

Q106.For what values of k, the line y=kx+2 will be tangent to the conic 2 2 4x 9y 36 − = − =?

A2 3 ± B2 2 3 ± C8 9 ± D4 2 3 ±

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EnglishLT 2018

Q107.Let y=mx+c be the equations of normal to the parabola 2 y 4ax = at 2 (am, 2am) − −. Then c is equal to

Aam3 B–2am+am3 C2am+am3 D–2am–am3

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EnglishDSSSB TGT (SECTION-B) 28 DEC 2014

Q108.The equation 2 2 x y 0 represents–

AA circle BAn ellipse CPair of straight lines DA hyperbola

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EnglishDSSSB TGT (SECTION-B) 28 DEC 2014

Q109.If ax by c is tangent to the circle 2 2 x y 16then–

A2 2 2/16(a b ) c B2 2 2/16(a b ) c C2 2 2/16(a b ) c D2 2 2/16(a b ) c

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EnglishUKPSC GIC- 2018 SECTION B PGT TIER-I 31.11.2014

Q110.The area of the circle centered at (1, 2) and passing through (4, 6) is–

A5π B10π C25π DNone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015/ PGT 2011/ Jharkhand TGT 2017/ Rajasthan 2013

Q111.If e and e′ ′ ′ are the eccentricities of a hyperbola and its conjugate, then 2 2 1 1 e (e) + ′ is equal to–

A2 B3 C4 D1

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q112.If the circles 2 2 x y 2x y 2 0 + + − − = + + − − = + + − − = + + − − = and 2 2 x y x 4y k 0 + − + + = + − + + = + − + + = + − + + = cut orthogonally then k is equal to –

A1 B2 C–1 D5

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EnglishTGT 2003

Q113.The angle between the curve y2 = x and x2 = y at (1,1) is

Atan–1 4/3 Btan–1 3 4 C90° D45°

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EnglishTGT 2003

Q114.The equation x2 –3xy +λy2 +3x – 5y +2 =0, when λ is a real number, represents a pair of straight lines. If θ is the angle between the lines, then cosec2 θ equal to

A3 B9 C10 D100

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EnglishTGT 2003

Q115.Circles are drawn through the point (2,0) to cut intercept of length 5 units on the x-axis. If their centres lie in the first quadrant then their equation is

Ax2 + y2 – 9x + 2ky + 14 = 0 B3x2 + 3y2 +27x – 2ky +42=0 Cx2 + y2 – 9x –2ky + 14=0 Dx2 + y2 –2kx – 9y + 14 =0

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EnglishTGT 2003

Q116.The locus of the centre of a circle which touches externally the circle x2 + y2 – 6x – 6y + 14 =0 and also touches the y- axis is given by the equation.

Ax2 – 6x – 10y + 14 = 0 Bx2 – 10x – 6y + 14 = 0 Cy2 –6x – 10y + 14 = 0 Dy2 – 10x – 6y + 14 = 0

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EnglishTGT 2003

Q117.If OA and OB are the tengents from origin to the circle x2 + y2 +2gx + 2fy+c =0(c <0)and C is the centre of the circle, the area of the quadrilaterals OACB is

A() 2 2 1 c g f c 2 + − B2 2 (g) + − c f c C2 2 (g) + − c f c DNone of the above

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EnglishTGT 2003

Q118.Equation of circle which touches the line x=0, y=0 and x=4 is:

A2 2 x y 4x 4y 16 0 + − − + = B2 2 x y 8x 8y 16 0 + − − + = C2 2 x y 4x 4y 4 0 + + + + = D2 2 x y 4x 4y 4 0 + − − + =

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EnglishTGT 2003

Q119.The equation of the tangent to the parabola y2 = 4x at the point (2, 1) is

A2x – y + 2 = 0 B2x + y + 2 = 0 Cx – y +1 = 0 DNone of these

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EnglishTGT 2003

Q120.The equation (((()))) 2 2 2 a 1 2a x,y 1 1 − θ = + θ + θ + θ + θ + θ + θ + θ + θ, where a is a constant, is the parametric equation of the curve

Ax2 – y2 = a2 Bx2 + y2 = a2 Cx2 + 4y2 = 4a2 Dx = 2y

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