Yes, definitely u will get a government job by pursuing Computer science. Today, everything is digitalized and knowledge of computer science is the most important thing. Central government can provide various opportunities for CS students. You can appear for many civil services exams like IAS, IPS, IFS etc. Other than this, a computer graduate can apply for many other government companies.

For taking  admission in government colleges, you can appear in JEE mains examination as well as other entrance exams of government  institutions for undergraduate courses. 

There are very such possibilities for a cse branch students since evry government organisation is getting digitalized and evry governmnet office need the software enginners so there will be definetly great demand in future also , so to get a job in governmnet sector you have ato get qualified in GATE so that you can get a government job in the software sector and all the best for your future and hope you will definetly get succeded in you futute

Hi aspirant 

A cse graduate can get a government in the following ways:

 PSUs JOBS(After qualifying GATE, you will be eligible to apply for psus )

 STAFF SELECTION COMMISSION (SSC):This is a kind of officer job.You need to qualify SSC-CGL to get various officer post.

RAILWAYS :After graduating you will be eligible for all railway exams.Even for DMRC(Delhi metro)

 BANKING Jobs:Each and every bank takes their own exam time to time you may apply them to do banking jobs.

You may take JEE main or state level entrances through which you can take admission in any government college of your state.

All the best.