Find an angle \(\theta\) which increases twice as fast as its sine.

2

(a)

If the area of a circle increase at a uniform rate, then prove that perimeter varies inversely as the radius.

2

(a)

The volume of a cube increases at a constant rate. Prove that the increase in its surface area varies inversely as the length of the side.

2

(a)

Aspherical ball of salt is dissolving in water in such a manner that the rate of decreasing of the volume at any instant is proportional to the surface. Prove that the radius is decreasing at a constant rate.

2

(a)

Show that \(f(x)=2 x+\cot ^{-1} x+\log \left(\sqrt{1}+x^{2}-x\right)\) is increasing in R.

2

(a)