how many entrance exams should I answer and which ones for greatest chance of getting a seat?

Hello,

There are so many entrance examination are present for different different departments. All though you are not mentioned  above that which department you are already studied in 12th class.

Like for engineering and architecture you can give JEE Mains examination, for only architecture you can give NATA examination. Medical entrance examination you can give NEET. For law entrance examination every state conduct their own examination like ts lawcet for Telengana state. You can give own college entrance examination, like so many colleges are organised their own entrance examination like BHU entrance examination etc. So you have to choose which field you have to go for study and which college you can take admission. Then you can go for entrance examination.

All the best.