(a) a fixed point (b) a variable point
(c) origin (d) none of these

25. If u ≡ a 1 x + b 1 y + c 1 = 0 and v ≡ a 2 x + b 2 y + c 2 = 0

and a
a

b

b

c

c

1

2

1

2

1

2

==, then the curve u + kv = 0 is

(a) the same straight line u
(b) different straight line
(c) it is not a straight line
(d) none of these

26. If a + b + c = 0 and p ≠ 0, the lines ax + (b + c)y = p,
    bx + (c + a)y = p and cx + (a + b)y = p
    (a) do not intersect (b) intersect
    (c) are concurrent (d) none of these


27. The equation of the straight line passing through
    the point (4, 3) and making intercepts on the
    co-ordinate axes whose sum is – 1, is

(a) xy x y
23

1

21

− = 1

−

and +=

(b)

xy x y

23

1

21

− =− 1

−

and +=−

(c) xy xy
23

1

21

− =+= and 1

(d) xy x y
23

1

21

+=− 1

−

and +=−

28. The line which is parallel to x-axis and crosses the

curve yx= at an angle of 45° is equal to
(a) x = 1/4 (b) y = 1/
(c) y = 1/2 (d) y = 1

29. The line parallel to the x-axis and passing through
    the intersection of the lines ax + 2by + 3b = 0 and
    bx – 2ay – 3a = 0, where (a, b) ≠ (0, 0) is
    (a) above the x-axis at a distance of 3/2 from it
    (b) above the x-axis at a distance of 2/3 from it
    (c) below the x-axis at a distance of 3/2 from it
    (d) below the x-axis at a distance of 2/3 from it


30. The equation to the line bisecting the join of (3, –4)
    and (5, 2) and having its intercepts on the x-axis and the
    y-axis in the ratio 2 : 1 is
    (a) x + y – 3 = 0 (b) 2x – y = 9
    (c) x + 2y = 2 (d) 2x + y = 7


31. The line lx + my + n = 0 will be parallel to x-axis,
    if
    (a) l = m = 0 (b) m = n = 0
    (c) l = n = 0 (d) l = 0
    32. To which of the following types the straight lines
    represented by 2x + 3y – 7 = 0 and 2x + 3y – 5 = 0
    belong?
    (a) parallel to each other
    (b) perpendicular to each other
    (c) inclined at 45° to each other
    (d) coincident pair of straight lines
    33. The line passes through (1, 0) and (, )− 23 makes
    an angle of ...... with x-axis.
    (a) 60° (b) 120° (c) 150° (d) 135°
    34. Angle between x = 2 and x – 3y = 6 is
    (a) ∞ (b) tan–1(3)
    (c) tan–1(1/3) (d) none of these
    35. A straight line through origin bisect the line
    passing through the given points (acosα, asinα) and
    (acosβ, asinβ), then the lines are
    (a) perpendicular
    (b) parallel
    (c) angle between them is π/
    (d) none of these
    36. In ΔABC, P is any point inside a triangle such that
    area of ΔBPC, ΔAPC, ΔAPB are equal. Line AP cut BC
    at M, area of ΔPMC is 5 sq. units, then area of ΔABC is
    (a) 20 sq. units (b) 25 sq. units
    (c) 30 sq. units (d) 10 sq. units
    Multiple Correct Answer Type
    37. Let uaxbyab≡ ++ =^30 , vbxayba≡−+=^3 0,
    a, b ∈ R be two straight lines. The equation of the
    bisectors of the angle formed by L 1 ≡ (tanθ 1 )u – (tanθ 2 )v = 0
    and L 2 ≡ (tanθ 1 )u + (tanθ 2 )v = 0 for θθ 12 0 π
    2

, ∈⎛⎝⎜, ⎞⎠⎟ is

(a) u = 0

(b) (tanθ 2 )u + (tanθ 1 )v = 0

(c) (tanθ 2 )u – (tanθ 1 )v = 0

(d) v = 0

38. Equations of bisectors of angles between
    intersecting lines xyxy−^3535 = + − = +
    cos sin

,

θθφφcos sin

are

xy− (^35) = + xy− (^35) = +
cosαα βγsin
and
then
(a) α=θφ+
2
(b) β^2 + γ^2 = 1
(c) tanα β
γ
=− (d) tanα
β
γ