$$\therefore$$ By Roll's theorem $$f'(x)=0$$ has root be-
tween $$\left( {0,\alpha } \right)$$
Hence $$f'(x)$$ has a positive root smaller than $$\alpha .$$
2
AIEEE 2005
MCQ (Single Correct Answer)
A spherical iron ball $$10$$ cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of $$50$$ cm$$^3$$ /min. When the thickness of ice is $$5$$ cm, then the rate at which the thickness of ice decreases is
The normal to the curve
$$x = a\left( {\cos \theta + \theta \sin \theta } \right),y = a\left( {\sin \theta - \theta \cos \theta } \right)$$ at any point
$$\theta\, '$$ is such that
A
it passes through the origin
B
it makes an angle $${\pi \over 2} + \theta $$ with the $$x$$-axis
C
it passes through $$\left( {a{\pi \over 2}, - a} \right)$$