Are there any problems which can be solved by human brain in a very less time but a computer may take a lot of time or a computer could never solve it ?
The now standard simple example of this is CAPTCHAs which stands for "Completely Automated Public Turing test to tell Computers and Humans Apart" which was intentionally devised in the theoretical community partly to detect and deflect automated spammers. However, the technology can be subverted somewhat by some systems such as mechanical turk. The term "CAPTCHA" was coined in 2000 by Luis von Ahn, Manuel Blum, Nicholas J. Hopper, and John Langford (all of Carnegie Mellon University). CAPTCHAs have gotten increasingly visually complex over the years as computer algorithms for character recognition have improved, in other words its evolving and something of a red queen race, i.e. evolutionary "arms race".
Every kid learns how to use language within his first 1-3 years. Computers still don't understand simple language structures, not to mention ambiguity, sarcasm, subtleties, etc.
Facial recognition. Human does better and quicker here than computers.
If you consider computability, human brain is not stronger than Turing machine. Turing machine could have infinite memory (arbitrarily extendable tape) while our memory is not (limit in storing information).
But in some current applications it seems human brain works better according to performance than current computers like Natural language learning, Image/Voice recognition,...
Von Neumann suggested his famous computer architecture as a way to simulate the laws of (classical) physics. Furthermore, it was shown that these laws can be simulated efficiently.
If you believe that the human brain works under the constraints of classical physics (also, to an extent, under quantum physics), then the brain is no stronger than a Turing Machine.
In this sense - no, the brain cannot do anything that a computer can't.
You may want to read this.