Q1: The c.g. of the shaded area of the below figure whose curve OM is a parabola from y-axis, is

ANS:B -

We all know the equation of a parabola given by Y^2= 4aX the centre of gravity for y coordinate is given by y = integral of y^2/2 from 0 to a divided by the integral of y from 0 to a.

After doing the calculations the answer will be 3a/4. Consider it to a triangle instead of a parabola, then the distance of C.G. from Y-axis would be 2*a/3=0.66*a.

But now, it's a parabola, so the centroid has shifted away from Y-axis, so the answer should be > 0.66*a.

Now, option A gives 0.25*a which is less than 0.66*a, so option A eliminated.
option C is eliminated since the distance is asked from Y-axis and not X-axis.
Option D = 0.3*a<0.66*a, so eliminated,
Option E = 0.6*a<0.66*a, so eliminated.
Hence, correct answer is option B = 0.75*a.