After 2nd puc,there are many engineering entrance exams conducted across india.... some of these are- VITEEE,SRMEEE,JEE MAINS,BITSAT,COMEDK,AEEE,MUOET,JEE ADVANCED...and many more state government exams.... you can check it out on google in more details or on our website....

For Engineering, there are several entrance exams across country. Every state conducts their own entrance exam to fill their respective state level B.tech seats (Except few states Punjab, Haryana, MP, Rajasthan, Odisha states- these states consider JEE Main score/ 12th Marks to fill their state seats) So You can appear in your state level entrance exam.
There are few important national level exams below:

JEE Main- It is national level level exam to get admisison in top engineering colleges like NITs, IIITs, GFTIs, few other top  governement institutes like PEC Chandigarh, IIIT Delhi, NSIT Delhi, DTU Delhi  and some top private college/universities like Thapar University, Patiala, SASTRA University, Shiv Nadar Univeristy, JAYPEE Noida, LNMIIT Jaipur.
Also, JEE Main is the entry exam for JEE Advanced.
JEE Advanced: This exam is the gatway for admission in IIT/ISM.Top 2,24,000 candidates from JEE Main would be eligible to take JEE Advanced for IIT admission.IISc- Bangalore, IISER’s, IMU Etc. consider JEE Advanced score/rank to fill their seats.
BITSAT- .BITS Pilani conducts BITSAT for admission in 3 BITS campuses (Pilani, Hyderabad and Goa).

VITEEE - Exam for 4 VIT Campuses (Vellore, Chennai, Amaravati and Bhopal)
MUOET- Exam for 3 Manipal Institutes (Manipal, Jaipur and Sikkim Manipal).
SRMJEEE - Exam for 5 campuses of SRM (Kattankulathar, Ramapuram, Vadapalani, NCR  Delhi & Amaravati).

AEEE - Exam for 4 Amrita campuses (Amritapuri, Bengaluru, Coimbatore and Chennai).

Apart from these exams, You can appear for COMEDK UGET , IPU CET (Engineering colleges affilated to IP University) , KVPY (To get admission in IISER) Etc.

Good Luck!!