Math Chapter Wise

EnglishRajasthan TGT 2016 PGT 2009

Q161.Parabola y2 = 4ax has

Aone asymptote Btwo asymptotes Cno asymptote DNone of these

Show answer

EnglishPGT 2009

Q162.If any equation (polar equation) of the curve remains unchanged when θ is changed to –θ in the equation, the curve is said to be symmetrical about

Athe initial line Babout the line θ 2 = x or y–axis Cabout the line θ 4 = x or y–axis DNone of these

Show answer

EnglishPGT 2005

Q163.If y = 2x+c touches the parabola y2 = 8(x+2), then:

Ac = 5 Bc = 3 Cc = 2 Dc= 1

Show answer

EnglishPGT 2005

Q164.The line lx+my+n = 0 is a normal to the ellipse 2 2 x y 1 a b + = + = is:

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

Show answer

EnglishPGT 2005

Q165.The angle between the asymptotes of 2 2 x y 1 a b − = − = will be equal to:

A2tan–1/(b/a) Btan–1/(a/b) C2tan–1/(a/b) Dtan–1/(b/a)

Show answer

EnglishPGT 2005

Q166.The curve 2 1 1 r 2 4 = − + = − + = − + = − + cosθ is

Aparabola Bhyperbola Cellipse Dstraight line

Show answer

EnglishPGT 2005

Q167.The radius of the circle 3x(x–2)+3y(y+1) = 4 is:

A15/4 B31/12 C2 D3

Show answer

EnglishPGT 2005

Q168.The points on the curve xy2 = 2, which are nearest to the origin, are:

A() 2,1 ± B1, 2 2 ± C() 1, 2 ± D(2±1)

Show answer

EnglishPGT 2004

Q169.Centre of the circle r2 = 2 - 6r cos θ + 4r sin θ is

A(3, 2), (2), (3, -2) B(3, -2) C(-3, 2) DNone of the above

Show answer

EnglishPGT 2004

Q170.The equation of the cone with vertex at the origin and base, the circle x = a, y2 + z2 = b2, is

A2 2 2 2 2 () 0 b y z a x + − = B2 2 2 2 2 () 0 a y z b x + + = C2 2 2 2 2 () 0 a y z b x + − = D2 2 2 2 2 () 0 b y z a x + + =

Show answer

EnglishPGT 2004

Q171.If (a secθ, b tanθ) and (a sec φ, b tan φ) are the co-ordinates of the ends of a focal chord of hyperbola 2 2 1 x y a b − = − =, then tan 2 θ. tan 2 φ will be equal to

A1 e − + B1 e − + C1 e + − D1 e + −

Show answer

EnglishPGT 2004

Q172.The equation of the common tangent to y2 = 8x and xy = -1 is

A3y = 9x + 2 By = 2x + 1 C2y = x + 8 Dy = x + 2

Show answer

EnglishPGT 2004

Q173.If y2 = 4x and xy = k cut orthogonally each other, the value of k2 is

A16 B36 C32 D8

Show answer

EnglishPGT 2004

Q174.If e is the eccentricity of hyperbola 2 2 1 x y a b − = − =, then the angle between it asymptotes will be

A2 1 2 cos− + e B2 1 2 2 1 tan 2 − e C2 1 2 2 1 tan 2 − + − e DNone of the above

Show answer

EnglishPGT 2003

Q175.The locus of the variable point P (at2, 2at) is

Ay2 =ax Bx2 =ay Cy2 =4ax Dx2 =4ay

Show answer

EnglishPGT 2003

Q176.If the straight line 4ax+3 by=12c be a normal to the ellipse 2 2 2 y x 1 a b = + = + then

Ac=a2 e2 Bc=5a2 e2 C5c=a2 e2 DNone of these

Show answer

EnglishPGT 2002

Q177.If e1 and e2 are the eccentricities of a hyperbola and its conjugate hyperbola then 2 1 e =

A2 1 e + B2 1 e − C2 1 e = − DNone of these

Show answer

EnglishPGT 2002

Q178.The circle x2 +y2 –6x–10y+p=0 does not touch or intersect the axes and the point (1,4) is inside the circle, then:

A0<p<29 B25<p<35 C25<p<29 DNone of these

Show answer

EnglishPGT 2002

Q179.The line x–y+2=0 touches the parabola y2 = 8x at the point:

A(2,–4) B() 1,2 2 C() 4, 4 2 D(2,4)

Show answer

EnglishPGT 2000

Q180.If the parabola y2 =4ax pass through (3,2). Then the length of its latus rectum is:

A2/3 B4/3 C1/3 D4

Show answer