Give one example where it takes Non- deterministically exponential time to solve the problem?
There are problems that cannot be solved in polynomial time on a nondeterministic machine. Indeed, there are problems that cannot be solved on any Turing machine, such as the halting problem.

We know from the nondeterministic version of the time hierarchy theorem that there are things that can be done in exponential time on a nondeterministic TM that cannot be done in polynomial time.  That is, $\mathrm{NP}\subsetneq\mathrm{NEXP}$.

Wikipedia gives several examples of $\mathrm{NEXP}$-complete problems: these are examples of problems that are provably not in $\mathrm{NP}$.