Mitali,
I agree with Cs. Ankur Garg, you can accept the share application money without being increasing the authorised capital, however, you cannot allot the shares against the share application money so received, unless the authorised share capital increased.
So before the time of allotment of shares, you need to increase the Authorised Capital.
Further as far as EGM is concerned it can be held anywhere, I say anywhere in the world like Board Meeting. It can be hold even on public holiday and out of the business hours like at 7.00 p.m. or so. The restrictions provided in Section 166 is applicable to AGM only.