Hey

Through Madhyamik, the students are selected to various institutes and universities for higher education. For engineering, you can apply for all the engineering entrances such as -:

JEE ( Joint entrance examination)

BITSAT( Birla Institute of technology and science admission test)

WBJEE ( West Bengal Joint entrance examination)

For Nerist: https://nerist.ac.in/sites/default/files/pdf/Information%20Brochure_NEE%202017.pdf

 

So, All the best.

Since you are telling 10th board as madhyamik, I consider you belong to West Bengal. Well after 10 th you can't persue B. Tech. in engineering but can persue diploma in engineering which is of three years course. For diploma in engineering you have to appear for JEXPO 2018 as you belong to West Bengal. After diploma you can apply for lateral entry and complete engineering in 3 years.

Hope your queries get cleared.
Best of luck.