Rahim died ____ cholera.

রোগে ভুগে মারা যাওয়া বোঝাতে die এর পর সব্বসময় of ব্যবহৃত হয়। 
die of (disease): He died of cholera/ Karim died of cancer ইত্যাদি। 
সুতরাং, সঠিক উত্তর হবে - of.

die from (effect ): He died from snake bite/ over eating.
die for (shake / cause): He died for his country .
die in (accident): He died in an accident.
die in (place / month / year): He died in 1950./ He died in London. / He died in a hospital in Dhaka.
die in (accident): He died in a train accident.
die on (name of day /spot death): He died on the spot./ He died on Monday.
die at (time): He died at 9–30 am.
die between (time): He died between 9 a m to 9–30 am.
die within (time): He died within five minutes.