Yes, you can get government job in Indian Railways after passing Intermediate with Science Group through Special Class Railway Apprentices' (SCRA) Exam. You need to crack the SCRA Exam which is conducted by the Union Public Service Commission

Tentative Schedule
Notification of Examination February
Conduct of Examination July

Age - limits:
Age should be in between 17-21 years on 1st August of the year of examination

Educational Qualification

-Must have passed in the first or second division, the Intermediate or an equivalent examination of a university or board approved by the Government of India with Mathematics
-Must have atleast one of the subjects Physics and Chemistry as subjects of the examination.