Hello dear

The top institutes for B.sc Astrophysics course are

1.Indian institute of science, Bangalore

2.Indian institute of Astrophysics, bangalore

3.Raman research institute

4.inter university center for astronomy and astrophysics, pune

5.pune university

6.osmania university

7.tata institute of fundamental research

The entrance exams for B.sc in Astrophysics are indian institute of science education and research (IISER)which is conducted in national level

BHU UET

SAAT

And for other universities you may have their own entrance based test which is common test for all courses .

The top institute for B.sc astronomy course are

1.Aryabhatta Research institute on observational sciences,nainital

2.indian institute of Astrophysics, bangalore

3.indian institute of science educators and research

4.indian institute of science

5.indian institute of space science and technology, thiruvanathapuram

6.inter university for astronomy and Astrophysics, pune

7.national centre for radio astronomy

Entrance exams for B.sc astronomy

IISER -nationl level

IIT -JEM - for iit colleges

and other universities conduct their own entrance tests .

Hope this is helpful

Good luck!