Correct option: (b) -2, (d) 4
Case I : When m = 0
In this case y = x - x2 .....(i)
and y = 0 .....(ii)
are two given curves, y > 0 is total region above x-axis.
Therefore, area between y = x - x2 and y = 0 is area between y = x - x2 and above the x-axis
Hence, no solution exists.
Case II: When m < 0
In this case area between
y = x - x2 and y = mx is
OABCO and points of intersection are (0,0) and {1 - m,m(1 - m)}
Case III: When m > 0
In this case y = mx and y = x - x2 intersect in (0,0) and {(1 - m), m(1 - m)} as shown in Fig.
=> (1- m)3 = - 27
=> (1 - m) = - 3
=> m = 3 + 1 = 4.
Therefore, (b) and (d) are the answers.
