Math Chapter Wise

English(GIC) Lecturer Exam, 2015

Q341.Eccentricity of the ellipse 25x2 +9y2 = 225 is

A3/5 B3/4 C4/5 D2/5

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English(GIC) Lecturer Exam, 2015

Q342.The tangents from which of the following points to the ellipse 2 2 4x 5y 20 are perpendicular?

A(1,2 2) B(0,1) C(1, 1) D(2 2, 2)

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English(GIC) Lecturer Exam, 2015

Q343.If ax2 – y2 + 4x – y = 0 represents a pair of straight lines the value of a is–

A–16 B16 C4 D–4

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English(GIC) Lecturer Exam, 2015

Q344.The eccentricity of the conic– 2 2 x 4y 6x 8y 3 is–

A3/2 B1/2 C3/4 D3

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English(GIC) Lecture Exam, 2015

Q345.The locus of the mid-points of the chords of the circle 2 2 x y 4 which subtangent right angle at the origin is–

Ax + y = 1 Bx + 2y = 2 Cx2 + y2 = 1 Dx2 + y2 = 2

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English(GIC) Lecturer Exam, 2015

Q346.The conic, whose centre lies at infinity is–

Aan ellipse Ba parabola Ca pair of straight lines Da hyperbola

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English(GIC) Lecturer Exam, 2015

Q347.Equation of a parabola whose vertex is at (–2, 0) and focus is at (0,0) is–

A2/y 8(x 2) B2/y 8(x 2) C2/x 8(y 2) D2/x 8(y 2)

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EnglishTGT 2013

Q348.Equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represent hyperbola if.

Aa = b and h = 0 Bab –h2/< 0 Cab – h2 = 0 Dab – h2/> 0

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EnglishTGT 2013

Q349.Equation of tangent at point φ (asec,btan) of hyperbola 2 2 x y - = 1 a b.

Ax y sec tan 1 a b φ − φ = Bx y sec tan 0 a b φ − φ = Cx y sec tan 0 a b φ + φ = D2 2 x y sec tan 0 a b φ − φ =

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EnglishTGT 2013

Q350.Find the equation of ellipse whose focci (6,7) and directrix x + y + 2 = 0 and eccentricity 1 e 3 =.

A5x2 – 2xy + 5y2 – 76x – 88y + 506 = 0 B5x2 – 7xy + 5y2 – 76x – 88y + 204 = 0 C5x2 – 2xy + 5y2 – 76x + 88y + 204 = 0 D5x2 – 2xy + 5y2 = 0

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EnglishTGT 2013

Q351.Equation of normal of hyperbola 16x2 – 9y2 = 1 at point () 2, 7 is.

A32y 9 7x 7 + = B32y 9 7x 50 7 + = C32y 9 7x 1 + = D32y 9 7x 2 7 + =

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EnglishTGT 2013

Q352.What will be the equation parabola whose focus (–8, –2) and ditrectrix y = 2x–9

Ax2 + 4y2 + 4xy + 111x + 2y + 260 = 0 Bx2 + 4y2 + 4xy +116x + 2y + 260 = 0 Cx2 + 4y2 + 4xy + 116x + 2y + 259 = 0 D4x2 + y2 + 4xy + 116x + 2y + 259 = 0

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EnglishTGT 2013

Q353.Focal length of parabola x = ay2 + by + c is.

Aa Bb Cc D1/a

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EnglishTGT 2013

Q354.The parametric equation of the parabola y2 = 4ax is.

Ax = at, y = 2at Bx = at2, y = 2at Cx = at2, y = at3 Dx = at2, y = 4at

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EnglishTGT 2013

Q355.What will be the number of common tangent of circle x2 + y2 – 6x–14y + 48 = 0 and circle x2 + y2 – 6x = 0.

A0 B1 C2 D4

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EnglishTGT 2013

Q356.ax2 + (2a –3) y2 – 4x–1 = 0 is equation of circle then its center will be.

A(1,1) B(2,0) C2,0 3 D2,0 3 −

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EnglishUP PCS (Pre) 1997

Q357.The locus of the centre of a circle of radius 2, which rolls outward the circle x2 + y2 + 3x – 6y – 9 = 0 is:

A2 2 x y 3x 6y 5 0 + + − + = B2 2 x y 3x 6y 31 0 + + − − = C2 2 29 x y 3x 6y 0 4 + + − + = D2 2 x y 3x 6y 5 0 + + − − =

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EnglishUP PCS (Pre) 1997

Q358.If P(x1, y1) and D(x2, y2) be the extremities of the semi- conjugate diameters CP and CD of the ellipse 2 2 x y 1, a b + = + = then:

A1 2 1 2 2 2 x x y y 1 a b + = B1 2 1 2 2 2 x x y y 2 a b + = C1 2 1 2 x y y x 1 + = ± D1 2 1 2 x y y x ab − = ±

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EnglishUP PCS (Pre) 1997

Q359.The line lx+my=n touches the hyperbola 2 2 x y 1 a b + = + = if:

Aal+bm=n Ba2 l2 +b2 m2 =n2 Cal–bm=n Da2 l2 –b2 m2 =n2

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EnglishUP PCS (Pre) 1997

Q360.The curve having maximum number of asymptotes parallel to co-ordinate axes, is:

A2 x 1 y 3 x = + B() 2 x x 4 y x 2 − = − Cy2 (x2 +x)=x2 +1 Dxy=1

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