Yes why not...
I recommend you to drop but in only one case that you must have to study hard.

In my opinion if you fill form for bitsat then you study hard for bitsat and not even think for drop.
But if you don't fill from then apply for upes
And study for it.
Soo.. Dont think for drop any time because bits pilani is much better then many iits and nits.
Upes is also good there packages are much better than many nits.
So study hard for next few months.
All the best. 

No, as per last year analysis,  u better get admission in any pvt college

If you can devote your full time in JEE preparation, then go for a year drop.
But, if you are still in 1% doubt of not clearing JEE next year, don't drop. Get some good private college or try for other state level entrance exams.
But do try again for next year JEE.

Dude this depend upon u whether to take a drop or not if u r confident enough that u can clear jee  in 1 yr that u should definitely give a try 
Best of luck

There are far more alternatives than IIT or NIT's.
What matters is how much hard work you put during your college life.
You can still join other good colleges.
I would recommend some private college.
Taking a drop might be risky but if you believe that you can, go for it.

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