JEE is one of the premier exam in the country and people cracking it are considered generally to be better than others(it's a fact).

if you feel you can do the dedicated efforts for one year then I would definitely advise you to take a drop for jee but you have to stay motivated throughout the whole period and do hard and smart work. It is not that you can'Tt be successfull after doing bsc but mostly people prefer b.tech from a college like IIT. Regarding the basics they can be improved by thorough underrstanding of the subject and I feel that 1 year is sufficient for it. we have many people studying at an IIT now who had a similar case as yours. best wishes from my side.

Dear Chander,

According to your problem, you don't have to worry about anything as there are lots of people like you out there who completed their 10+2 but having no basic knowledge but I am giving you some advice may be this will help. See If you didn't know the basic of Physics, Chemistry and Math then ask yourself this question.

Are you going to study a lot without bunking and cover all your basic and advanced topics in all these subject in a year?  If the answer is yes, then you should go and drop the year.

But I am telling this gonna be hard as most of your friend will pursue something and sometimes you feel you are doing nothing at all. So ask yourself multiple questions whether you are able to do this if the answer is yes then drop the year. But dont drop you one year in order to get a tag of engineer then trust me you gonna frustrate with your life and also you will become a bad engineer (IF YOU CANT HANDLE PRESSURE AND ANSWER OF ALL THE ABOVE QUESTIONS IS NO). No one is going to study with you. You have to study all by yourself so if you feel like not wasting your time then you should pursue your BSC. 

Believe me, there are multiple job opportunity is waiting for you after graduation. You can pursue MBA to or MSC after it and will land to a beautiful high paying job. So trust yourself ask the question from yourself and choose the decision wisely.

Good luck.

I hope you will get through this confusing phase.

I think you can drop one year by that you will have time to build your basic and build your knowledge for jee main.Engineering is a very good career option and in engineering you can settle you career in less time than bsc.So you can drop and build yourself better and try for engineering. Best of luck.