well well well...ur problem is a bit "hat ke"....
hmmm see i dun knw the perfect answer for ur query...but still m giving a try (i mean m asking u to try this)..
first of all....make ur study room...like a study room....i mean tv , pc and other entertainment stuff must nt be present there.....then set a min amt of syllabus that u have to cover (on a particular day)...u will nt sleep untill that much amt of syllabus is completed...but u can do more than that...

the thing u r lacking is confidence i suppose.....u have to gain it (as there is nt much time left...).....
forget all those songs...u must have only 1 aim...getting into IIT at any cost.....IIT must come 1st for u than any other thing....5 months of hardwork...can make ur life cool....(just concentrate on these things 1ce)
also meditation , u can do that too...lit will help u a lot
play any sport for 1 hour...it keeps u fresh..
ALL THE BEST :) :)