Math Chapter Wise

EnglishPGT 2005

Q181.If the equation ax2 + 2hxy + by2 +2gx +2fy+c=0 represents a pair of parallel lines, then the distance between them is

A2 2 2 − + g ac h a B() 2 − + g ac a a b C() 2 − + g ac a a b D() 2 + g ac a a b

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EnglishPGT 2004

Q182.The straight line y = mx + c will be normal to the circle (x + a)2 + (y + b)2 = r2, if

Aa = bm + c Bc = am - b Cb = am + c Dc = bm - a

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EnglishPGT 2004

Q183.If m1 and m2 are slopes of the two tangents that are drawn from the point (2, 3) to the parabola y2 = 4x, then the value of 1 2 1 1 m m + + is

A3 B–3 C2/3 D3/2

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EnglishPGT 2004

Q184.The distance between the pair of lines represented by the equation x2 – 6xy + 9y2 + 3x – 9y – 4 = 0 is

A15/10 B1/2 C5/2 D1/10

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EnglishPGT 2003

Q185.The equation of the straight lines through the origin each of which makes an angle a with the straight line y=x is

Ax2 –xy cos 2a +y2 = 0 Bx2 –xy sec 2a +y2 = 0 Cx2 –2xy sec 2a +y2 = 0 Dx2 –2xy sec a +y2 = 0

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EnglishPGT 2003

Q186.The pair of straight lines x2 –2pxy–y2 =0 and x2 – 2qxy–y2 =0 be such that each pair bisects the angles between the other pair, then

Apq = 1 Bpq = –1 Cpq = 0 DNone of these

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EnglishPGT 2003

Q187.The conic given by 3x2 –8xy–3y2 +10x–13y+8=0

ARepresents an ellipse BRepresents a hyperbola CRepresents a parabola DRepresents a pair of straight lines

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EnglishPGT 2002

Q188.Two tangents are drawn from the point (–2,–1) to the parabola y2 =4x, If α is the angle between them, then tan α =

A3 B2 4 5 C2 D1/2

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EnglishPGT 2002

Q189.The orthocenter of the triangle with vertices 3 1 1 1 2,,, 2 2 2 − and 1 2, 2 − is:

A() 3 3 3, 2 6 − B1 2, 2 − C() 3 2 5, 4 4 − D1 1, 2 2 −

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EnglishPGT 2002

Q190.If the lines joining the origin to the points of intersection of y=mx+1 with x2 +y2 =1 are perpendicular, then:

Am = 1 Bm = ±1 Cm = 0 DNone of these

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EnglishPGT 2002

Q191.The pair of lines joining the origin to the points of intersection of the curves ax2 +2hxy+by2 +2gx=0 and a'x2 +2h'xy+b' y2 +2g'x=0 will be at right angles to one other if:

Ag(a'+b')=g'(a+b) Bg(a+b)=g'(a'+b') Cgg'=(a+b)(a'+b') Dnone of these

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EnglishPGT 2002

Q192.The curve described parametrically by x = t2 +t+1, y=t2 –t+1 represents:

Aa pair of straight lines Ban ellipse Can parabola Da hyperbola

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EnglishPGT 2000

Q193.The equation y2 –x2 +2x–1= 0 represent:

Aa circle Ban ellipse Cpair of straight line Da parabola

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EnglishRajasthan TGT 2016

Q194.The equation of the locus of a point which moves so that its distance from (4,0) and y-axis are equal, is given by

Ay2 +4x+16=0 By2 +8x+16=0 Cy2 –8x+16=0 Dy2 –8y+4=0

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EnglishRajasthan TGT 2016

Q195.If the equation hxy+gx+fy+c=0; h≠0 represents a pair of straight lines, then

Afc= gh Bfh=cg Cfh= c2 g2 Dgf=ch

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EnglishRajasthan TGT 2016

Q196.If A(0,3), B(–2, 0) and C(6,1) are vertices of triangle ABC and P(2x,x) be any point, then A and P lies on same side of BC when

Ax>1/2 Bx>1/3 Cx>2 Dx>3

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EnglishRajasthan TGT 2016

Q197.The co-ordinates of the three consecutive vertices of a parallelogram ABCD are A(3, –1, 2), B(1, 2, –4) and C(–1, 1, 2), then co-ordinates of the vertex D are

A(1,2,8) B(2, 8, 1) C(1,–2,8) D(1, 2, –8)

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EnglishRajasthan TGT 2015

Q198.The line joining the points (1,3) and (2,7) is divided by the line 3x y 9 + = + = in the ratio-

A3:4 externally B3:4 internally C4:3 externally D4:3 internally

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EnglishRajasthan TGT 2015

Q199.The lines 2x 3y 5 − = − = and 3x 4y 7 − = − = are the diameters of a circle of area 154 square units, then equation of this circle is-

A2 2 x y 2x 2y 62 + + − = B2 2 x y 2x 2y 47 + + − = C2 2 x y 2x 2y 47 + − + = D2 2 x y 2x 2y 62 + − + =

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EnglishRajasthan TGT 2015

Q200.If the tangent at any point on the curve 4 4 4 x y a + = + = cuts off intercepts p and q on the axes, then 4 4 3 3 p q − − + + is equal to-

A4 3 a − B1 2 a − C1 3 a − D1 4 a −

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