Hello,
Both stream are very good actually. After done petroleum engineering you can join any gas or any oil company. The job is great but risky also. But salary high in this department. Approximately 8lpa get any petroleum engineer. And after completing engineering as chemical engineer you can join fuel company, drug company, food company and so many authority also. Job is not that much risky. But salary is little much low than petroleum engineer. Salary will be 6 lpa approximately. Now come to private and government engineering college. If you want to study only government institution like IIT or NIT then you can join it. But this is not matter to you any private college also good for you or your favourite stream matter to you then go for private institution. I'll tell you everything now choice is totally yours. Think and decide it.
All the best.
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