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QUEST TUTORIALS
Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
1. Distance between the lines
represented by the equation,
x2 + 2
3
xy + 3y2 − 3x − 3
3
y − 4 = 0
is :
(A)
5
2
(B)
5
4
(C) 5 (D) 0
2. The values of h for which the equation
3x2 + 2 hxy − 3y2 − 40x + 30y − 75 = 0
represents a pair of straight lines, are
(A) 4, 4 (B) 4, 6
(C) 4, - 4(D) 0, 4
3. If pairs of straight lines,
x2 − 2 mxy − y2 = 0 & x2 − 2 nxy − y2 = 0
be such that each pair bisects the
angle between the other pair, then mn
is equal to :
(A) 1 (B) - 1
(C) 0 (D) -
1
2
4. The nature of straight lines
represented by the equation,
4x2 + 12 xy + 9 y2 = 0 is :
(A) Real and coincident
(B) Real and different
(C) Imaginary and different
(D) None of the above
5. The equation to the pair of straight
lines through the origin which are
perpendicular to the lines,
2x2 - 5 xy + y2 = 0, is :
(A) 2x2 + 5 xy + y2 = 0
(B) x2 + 2 y2 + 5 xy = 0
(C) x2 - 5 xy + 2 y2 = 0
(D) 2 x2 + y2 - 5 xy = 0
6. Acute angle between the lines
represented by, (x2 + y2)
3
= 4 xy is
(A)
π
6
(B)
π
4
(C)
π
3
(D) None of these
7. The equation of the pair of straight
lines, each of which makes an angle
α with the line y = x, is :
(A) x2 + 2 xy sec 2 α + y2 = 0
(B) x2 + 2 xy cosec 2 α + y2 = 0
(C) x2 - 2 xy cosec 2 α + y2 = 0
(D) x2 - 2 xy sec 2 α + y2 = 0
8. The equation, xy + a2 = a (x + y)
represents :
(A) A parabola
(B) A pair of straight lines
(C) An ellipse
(D) Two parallel straight lines
9. The combined equation of the
bisectors of the angle between the
lines represented by (x2 + y2)
3
= 4xy
is :
(A) y2 - x2 = 0 (B) xy = 0
(C) x2 + y2 = 2 xy (D)
x y
2 2
3
−
=
xy
2
10. The lines joining the origin to the
points of intersection of the line,
y = mx + c and the circle x2 + y2 = a2
will be mutually perpendicular, if :
(A) a2 (m2 + 1) = c2
(B) a2 (m2 − 1) = c2
(C) a2 (m2 + 1) = 2c2
(D) a2 (m2 - 1) = 2c2
11. The straight lines joining the origin
to the points of intersection of the line
2x+ y = 1 & curve 3x2 + 4xy − 4x + 1 = 0
Pair Of Straight Lines
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