The number of choices to be filled in JoSAA counseling depends upon whether you did pass in JEE Advanced or not. Because, if you don’t pass into JEE Advanced you’ll have IIT’s out of your options. IIT’s take admission only through JEE Advanced.
In case you fail JEE Advanced you can fill around 300–350 choices and if you’ve passed JEE Advanced the number is more than it. So, don’t hesitate to fill more options. But be careful while filling the options as once they are filled these options cannot be changed and if you’ve alloted one college the options filled below that college get removed automatically and you’ll get a college filled above it or the same.
For example, you’ve filled IIT DELHI Electrical as option 10, IIT BOMBAY Electrical option 7 and IIT KHARAGPUR Electrical as option 11 and you’ve been alloted option 10 in first round. Then in the next rounds you cannot get options below 10. You can get alloted only between option 1 to 10. And rest all the options are automatically removed.