Yes there are many entrance exams for btech in private and government college .It is conducted in the month of March to may have nearly same question pattern . One main exam from them is jee mains and advance through which you can take admission in iits and nit's . All other states have their state btech exam like wbjee for West Bengal bcece for Bihar. For more specific details please comment 

For admission to Btech Programme at all IITs you need to appear For Jee Advanced marks and try to secure ranks within 15000 for good chances.

For appearing Jee Advanced one must qualify from 2.31 lakh candidates in Jee Mains.

Hence firstly you need to appear jee mains exam and only then jee advanced can be given and after counselling admission takes place.

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