IIT

The answer would be zero.
Yes, it is possible that you won't get placed even after going to IIT.
Many of the newer IITs have decent placements but none has 100% placements. So it is possible that you won't get placed if you waste the four years during your engineering completely.
Assuming that you won't completely waste four years and just be an average student I think you can expect an average package of around Rs 6 lakhs per annum (approx). But lowest package can also be around Rs 3.5 to Rs 4 lakhs per annum for newer IITs.
Again, don't select a college based on only placements or package but consider everything right from your own interest in a particular branch to the infrastructure and quality of education provided. If you are in top IITs you may expect a median salary around Rs 8 lakhs per annum.
So if you secure good rank in JEE advance stop worrying about the package and start worrying about where your passion lies and work hard in that particular field. If you are genuinely interested in what you study and are brilliant you may get phenomenal packages like Rs 1 crore and all. But the effort you need to put in would also be as high as the package you want.

Hello Pratap,
Half a year is really a great time to crack JEE Mains if spent in the right way.
There are two parts namely JEE Mains and JEE Advanced.
In Mains, the questions are not that tough but they require high conceptual knowledge and solving skills.
The questions are from PCM only based on classes 11th&12th syllabi (NCERT).
First, you can go through the concepts in PCM as they play a major role in any of the exams.
The questions in JEE Mains will be generally easy but you need to master the concepts to be fast in answering as the time is not more.
You can prefer NCERT books for getting conceptual clarity. Then you can prefer TMH(Tata Mc Graw Hill) and Arihant books for PCM concepts as well as problems.
They are really good books for JEE preparation and they provide good quality of exercises for practice.
You can solve as many problems as you can within the time limit so that they will provide you with a better way of preparation for JEE Mains.
For Advanced, you may require coaching as it is not very easy to clear with self-preparation.
You may follow the above tips but you need to go for more advanced concepts.
The previous year papers would help you to know the quality of questions in JEE Advanced and then practice more.
I hope you have more time and guidance.
Focus on what you do and do with full interest.
All the best.

Devoting one full year for competitive exam preparation has its own merits and demerits. Dropping a year means that you will get sufficient amount of time to prepare for competitive exams. It will allow you take mock up test and help to score good ranking in competitive exams. However, one year is a long time so the possibility of you may change your goals and objectives. You may become lethargic because of availability of time and lesser pressure. You may waste time. If you are confident of keeping the momentum, dedication, determination, readiness to work on a plan, will to achieve your objective and support of family; you may consider dropping a year for competitive exams. IIT JEE is the most competitive examination. It is worth try option to crack JEE for admission in IITs because graduation from IITs is a jump pad for a successful Engineering career.