We presume the birth details shared by you are that of your child. Your child is a serious contender in everything and generally would not lag in anything.
The current ongoing period is moderately conducive and the outcome would much depend on the extent and intensity of hard work, study and/or preparation that has gone in for the exam.
So depending on your preparation, chances are good that you could clear your entrance exam.
Vrishabha Lagna with the Lagna lord Venus posited in the second house conjunct Sun; Mercury posited in the Lagna; Ketu Maha Dasha ongoing with rahu Antar Dasha and Saturn Pratyantar Dasha currently; Saturn is benefic for Vrishabha Lagna.