Hello dear aspirant .

The second year year you are talking about is if 12th then you can surely be able to give JEE mains exam. If you are talking about second year of your college might be graduation then for your kind information JEE mains gives you three chances one is when you are appearing in class 12th second year when you pass your 12 next year. Third one is in next to next year. Means in continuation of three years . If you are fulfilling this criteria you can surely apply for JEE mains.

Good luck