Yes, some good engineering exams are open now. You can apply for SRMJEEE Phase 2 before June 6, 2025, for SRM University. Also, JoSAA counselling starts June 3, 2025, for admission to IITs, NITs, and IIITs based on JEE Main scores. BITSAT session 2 is in June for BITS Pilani. You can also apply for VITEEE and Delhi University B.Tech admission, which are open now. Make sure to apply before deadlines. Good luck!