Is there an entrance exam for B.Tech?

Yes, there are so many entrance exams like JEE Mains and advance for NITs and IITs. UPSEE for colleges in Uttar Pradesh. And, various private engineering college entrance exams are also there. You can refer this link too. http://bit.ly/2B5LAI3.

If you want to pursue a B-Tech from IIT's and NIT's, then you have to give JEE Mains and then JEE Advanced. Every state has its own CET examination for government engineering colleges in the respective state. Many private colleges also have their own examinations like VITEEE for VIT, Vellore; SRMJEE