VITEEE 2013 Paper

The equation of curve is y = x - x2
⇒ x2 - x = y
⇒ (x−

1

2

)2 = - (y−

1

4

)
which is a parabola whose vertex is (

1

2

,

1

4

)

Hence, finding the point of intersection of the curve and the line,
x - x2 = mx ⇒ x (1 - x - m) = 0
i.e, x = 0 or x = 1 - m
∴

9

2

=

1−m

∫

0

(x - x2 - mx) dx
= {

x2

2

−

x3

3

−m

x2

2

}01−m
(1 - m)

(1−m)2

2

-

(1−m)3

3

=

(1−m)3

6

∴ (1−m)3 =

6×9

2

= 27
⇒ 1 - m = (27)1∕3 = 3
⇒ m = - 2
Also (1−m3) - (3)3 = 0
∴ (1−m3) = 33 ⇒ 1 - m = 3
or m = - 2