Buy a new cycle or assemble new parts? My budget is $300 - $400. I live in India.
My doubt is whether, its better buying a new bike or just assemble different good company spare parts (used or new).
I am very new to cycling, so please help...
Don't know about India, but assembling from parts in my end of the world costs a lot more than a new bike. I know of many instances where people buy a "donor" bike for good new parts at a reasonable price. If you can get parts at the right price, it may be worth it, but problems with compatibility between components can lead to a  lot of blood, sweat and tears, as well as expense, especially for a beginner. It seems every year has at least one small but significant change that is incompatible with last years model.... Something as simple as seat posts - One post recently someone counted 39 different sizes -size increments are 0.1mm - measuring the hole that accurately is not possible for most of us. 

I don't know about India. but where I live you can get great secondhand bikes for good prices, if you do homework and take care. My 14 year old neighbor just got a "new condition" second hand bike for $850 -  a new one with equivalent components would have been $2.5K. The previous owner was obviously a fanatic on maintenance and all of the important bits look anything more than a few 100km old. It's not risk free, but its the best way to ride a better bike than you would otherwise be able to. 

The other option is end of season and last years bikes - often 1/2 retail price just because the color changed. This is a good way to get into a new bike cheaply.