Dear Jitender, your 10th class Pass Certificate will act as as a proof of your Date of Birth. Apart from this no Birth certificate is needed. However, if you want to carry your Birth certificate along with you, that is absolutely fine. No harm
But Birth Certificate necessarily needn't be produced.

Hii Jitender!! Birth certificate is not a mandatory requirement. universities need this certificate as a proof for date of birth which can be also done by providing marksheet of 12th. Hope this helped. Good luck!!!!