A bulb is placed at the centre of a circular track of radius 10 m. A vertical wall is erected touching the track at a point P. A man is running along the track with a speed of 10 m/sec. Starting from P the speed with which his shadow is running along the wall when he is at an angular distance of 60$$^\circ$$ from P is

Let f(x) > 0 for all x and f'(x) exists for all x. If f is the inverse function of h and $${h'(x) = {1 \over {1 + \log x}}}$$. Then, f'(x) will be

Let f(x) be a derivable function, f'(x) > f(x) and f(0) = 0. Then,

Let $$f(x) = {x^4} - 4{x^3} + 4{x^2} + c,\,c \in R$$. Then