I have a exhaust fan whose capacitor is completely burnt. I do not know the value of the capacitor which was used. How do I determine the capacitor rating

You wold be safe enough with a 4uf capacitor on an exhaust fan and it should look similar in size.

... wow!. I'm tempted to ask for tomorrow's lottery...

It is a big exhaust fan. I have used 10 MFD but not getting speed. What will happen if I use big capacitor once for all, say 50 MFD capacitor?

Go to a motor rewinding shop