For admission into national importance institute ie 

Iits nits IIITs and gftis 

JEE main and JEE advanced are conducted.

For admission into private colleges

BITSAT 

Viteee 

Muoet for Manipal ,lpunest,Amrita aee exam,Srmjee etc

Also some centrally based Universities conduct national level exams 

Hello

That depends if you are applying for Govt colleges specifically for IITs and NITs then there is only one exam which is JEE Mains and Advanced, if you are applying for DU cluster Innovation then there is DUJAT if you want to apply for private colleges then many like VIT have VITEEE and for SRM there is SRMJEE so there are many national level engineering exams depends on which college you want to apply for.

Hpe it helps.