Colleges in Lucknow

GITAM is better ranked than Dinbandhu Andrews Institute. Some of the important points while selecting an institute are accreditation of the institute, institute's infrastructure, teaching faculty, specialization offered, past placements records, tuition fees, city preference, and industry interface. As both, the institutes are having the campus in Bangalore and Kolkata, industry exposure is good for students in either of the college. If possible a visit to college is better option to get a reality check. Also, get in touch with college alumni's through the social network to get information about the latest changes if any.
You can compare the course fee, placements, students review, facilities offered, seats offered on the below link:- https://www.shiksha.com/resources/college-comparison-55734-230776.

Eligibility Of the Bachelor of Science [B.Sc] (Physics)
To seek admission in B.Sc Physics, the student must have cleared 10+2 with science subjects (PCM/PCB).
The percentage in 10+2 required for being eligible for the course may vary from college to college.
How to Get Admission in Bachelor of Science [B.Sc] (Physics)
Most of the colleges in India that offer B.Sc Physics give direct admission on the basis of marks obtained in 10+2, which is determined by the cut-off lists generated by each college. The student can seek admission if his marks match with the cut off announced by a college.
Distance Mode Admission
NIMS University, IGNOU, School of Open Learning are some institutions that offer distance learning for those who cannot attend full time classes.
Normal eligibility for B.Sc Physics is 10+2 which may vary in some institutes.

Yes, you can prepare for CAT at home. First, clear your basics and then move forward.
Here are some books that you can refer for your preparation:-
1) Quants - First solve the NCERT from 6th to 10th standard and then solve M.Tyra and Rs Aggarwal. These books will strengthen your foundation. Once you complete these books you can go for Arun Sharma.
2) Verbal/ RC- Start reading as much as you can. Read newspaper, novels, magazine etc, this will increase your ability to understand the context. Also, refer to verbal ability and reading comprehension book by Arun Sharma.
After all this, you need to have a good command over vocabulary, for vocabulary you can refer to word power made easy by Norman Lewis.
Also, join test series of any coaching. It will provide you real-time tracking of your preparation.