Dear friend, 
The dillema of what to do and what not to do is always there in the minds of newly grown up students who start thinking to take off towards their goal in life.
Since you are in 11th class, you are new to the world of competitions and had many illusions regarding it.
I will be very happy to guide you if at all i can. According to me, if you take both the coaching classes for competition preparation and also the academic preparation, you can let this acheive side by side. You need not to waste one extra year for getting into engineering college of national repute. You can do wonders if you have the urge to do that and this is not the time to look for negative loopholes rather than tighten your nerves to get stick to the running time and prepare hard for your both exams.
Also, i want to tell you one thing is that generally the toppers of entrance examination are freshers rather than being droppers.
So get ready to start hard work and just stick to your desire and dont look mfor the results at this time 

Best of luck