Math Chapter Wise

EnglishUP PGT-2016 (02-02-2019)

Q221.The focus of parabola 4y2 –6x–4y = 5 is

A5 1, 8 2 − B3 1, 8 2 − C7 1, 8 2 − D5 1, 8 2 −

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EnglishUP PGT-2016 (02-02-2019)

Q222.If the line y = x + 3 meets the circle x2 + y2 =9 at A and B, then the equation of the circle whose diameter is AB, is

A2 2 x y 3x 3y 0 + + − = B2 2 x y 3x 3y 0 + − + = C2 2 x y 3x 3y 0 + + + = D2 2 x y 3x 3y 0 + − − =

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EnglishUP PGT-2016 (02-02-2019)

Q223.Circles 2 2 x y 2x 4y 0 + − − = + − − = + − − = + − − = and 2 2 x y 8y 4 0 + − − = + − − = + − − = + − − =

Atouch externally Btouch internally Cdo not touch Dnone of the above

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EnglishUP PGT-2016 (02-02-2019) UPPCS (Pre.) 2001

Q224.If e and e' be the eccentricities of the hyperbola 2 2 x y 1 a b − = − = and its conjugate hyperbola, then

A2 2 e e' 1 + = Be = e' C2 2 1 1 1 e e' + = D2 2 1 1 1 e e' − =

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EnglishUP PGT-2016 (02-02-2019)

Q225.The vertices of a hyperbola are (1, 0) and (–1, 0) and the foci are (2, 0) and (–2, 0). The equation of the hyperbola is

A2 2 3x y 3 − = B2 2 2x 3y 3 − = C2 2 x 3y 2 − = D2 2 3x 2y 6 − =

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EnglishUP PGT-2016 (02-02-2019)

Q226.Number of asymptotes of the curve 2 2 x y 3x 5xy 6y 2 0 − − + + = − − + + = − − + + = − − + + = is

A0 B1 C2 D3

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EnglishUP PGT-2016 (02-02-2019)

Q227.Let S and S' be the foci and BB' be the minor axis of an ellipse. If ∠ ∠ ∠BSS'=θ, then eccentricity of the ellipse is

Acosθ Bsinθ Ctanθ Dcotθ

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EnglishTGT 2013

Q228.If y + b = m1(x + a) and y + b = m2 (x + a) are two tangents of parabola y2 = 4ax, then-

Am1m2 = 1 Bm1m2 = –1 Cm1 + m2 = 0 Dm1 + m2 = –1

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EnglishUP. PCS. (Pre) 2006 TGT 2011

Q229.Which of the following pairs will be represent conics.

A1 ecos, 1 ecos r r = + θ = − θ l l B1 ecos, 1 ecos r r = + θ = − + θ l l C1 ecos, 1 ecos r r = − θ = − − θ l l DNone of these

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EnglishTGT 2011

Q230.The length of tangent from the point (2, –3) to the circle 2x2 + 2y2 = 1 is-

A5 B–5 C5/2 D−5/2

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EnglishTGT 2011

Q231.Two circles x2 +y2 =r2 and x2 +y2 –10x+16=0 will intersects each other at real and distinct point if the value of r.

A2< r<8 Br<2 or r<8 Cr=2 or r= 8 DNone of these

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EnglishTGT 2011

Q232.If the directrix of parabola y2 –kx+8 = 0 is x– 1=0 then the value of k is.

A1/6 B8 C4 D1/4

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EnglishTGT 2011

Q233.What will be the locus of the midpoints of all the chords of the parabola y2 =4x. If the chords are drawn from the top?

Ay2 =8x By2 =2x Cx2 +4y2 =16 Dx2 =2y

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EnglishTGT 2011

Q234.Equation 2 2 x y + +1 = 0 2-r r - 6 represent the ellipse, if.

Ar > 2 Br > 6 C2< r < 6 DNone of these

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EnglishTGT 2011

Q235.The line lx + my + n = 0 is perpendicular to the ellipse 2 2 x y + = 1 a b, if-

A() 2 2 2 2 2 2 a b m n − + = l B() 2 2 2 2 2 2 a b m n − + = l C() 2 2 2 2 2 2 a b m n − − = l DNone of these

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EnglishTGT 2011

Q236.If the eccentricities of two conics S1 and S2 are e1 and e2 and 2 2 1 2 e +e = 3. then both S1 and S2 will be.

AEllipse BParabola CHyperbola DCircle

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EnglishTGT 2011

Q237.At which point of the hyperbola x2 – y2 = 3 the tangent line will be parallel to the given line 2x + y + 8 = 0.

A(2,1) or (1,2) B(2,–1) or (–2,1) C(–1,–2) D(–2,–1)

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EnglishTGT 2011

Q238.If 2x + y + 8 = 0 and 2 2 x - 2qxy - y = 0 are bisected angle to each other, then.

Ap + q = 1 Bpq = 1 Cpq + 1 = 0 Dp2 + pq + q2 = 0

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EnglishTGT 2011

Q239.If the vertices of a triangle are (0, 3), (–3, 0) and (3, 0), then the coordinates of the perpendicular center are.

A(0,–2) B(0, 2) C(0, 3) D(0,–3)

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EnglishTGT 2011

Q240.The coordinates of the foot of perpendicular drown from the point (2,3) on the line 4x–5y+8 = 0 will be.

A(0,0) B(1,1) C41 128, 78 75 D78 128, 41 41

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