differentiability of function for pair of (m,n) 
my doubt:
In this question, i think option B and option C are not correct. I need suggestions to decide which one from A and D are correct.
thanks.

Hint: Note that 
$$\left|\frac{f_{m,n}(x)-f_{m,n}(0)}{x}\right|=\left|\frac{x^m\sin\frac{1}{x^n}-0}{x-0}\right|\leq|x|^{m-1}$$
Thus $f_{m,n}$ is differentiable at $x=0$ whenever $m>1$
