Hello,
Yes he can apply for BCECE. Eligibility criteria for the entrance exam is :-

1. There is no age limit
2. Candidate must have passed diploma/BSc. course with minimum aggregate of 45% and for reserved category it is 40%.

there is time for now to prepare for exam. Take time seriously and practice as much as questions and previous year papers he can. To get a good score , best practice history or good memory is required. Either one is required.
For more information , please visit the link below :-
https://engineering.careers360.com/articles/bcece-le
hope it helps!

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