B.Sc Maths

Your rank is good enough to get admission in Lucknow University. You can apply for the admission.

Yes, you can do M.Sc (Hons) Maths in Punjab University after this course.
Good luck.

Hi Shivangi,
You can shift from Science to arts definitely after class 12th.
But, one thing to make sure if you want to go for arts with maths, then you need to have had maths in your class 11th and class 12th Science grades. If you do have maths there, then I don't think there'll be any issue for enrolling for the same. But up to my knowledge you won't be able to pursue B.Sc Maths with an arts pass out after class 12th, as the requirement for B.Sc is some aggregate percentage in class 12th Science. Hope it helps.

by graduation purpose both are similar duration course.but both sallybus are totally different.and both carrier opportunities are also different.
hope it is helpful.

You should check your rank by Shiksha rank predictor. Best of luck.

http://www.oldquestionpapers.net/wp-content/uploads/2013/06/B.Sc_.Math-2012-Paper.pdf.

List of best institute provide B.Sc. Delhi University
BHU (Banaras Hindu University)
University of Hyderabad
Chennai Mathematical Institute (CMI)
Good luck.

They ask normal Maths questions and little bit physics and chemistry. Good luck.