Which Planet/Star is it? I live in north India. About 24° latitude. I can see a very Bright star in sky. Its towards east and high up. Is it Venus , Jupiter, star or anything else?

Its not Sirius. I used Orion belt for that.

Date: 24 March , 2016

Time : 8 :00 p.m.

At 11: 00 pm.
Its directly upwards. Angle b/w moon and sun ~60°.
The site in-the-sky.org has a wide variety of functions and options. In Planetarium mode, I chose a random city at about 24N and in the middle, which helps to get the correct UTC + 05:30 India Time Zone, and then just put in the time and date and turned on alt/az grid.  

So it is likely to have been Jupiter, as you suspect. Below are two screen shots - 20:00 and 23:00 local time, with Jupiter climbing from 41 to about 73 degrees above the horizon.