Better rank assignment in multiple-choice entrance exams

The Indian educational system administers many multiple-choice exams wherein a small percentage of candidates must receive unique ranks. But discrete marking causes ties, usually resolved by essentially arbitrary criteria. I suggest a better alternative via a probability model for the exam, participants' talent levels, and question difficulties. Monte Carlo simulations suggest that ranking accuracy improves if marks on each question are scaled by the population standard deviation for that question. Maximum marks obtained in the test should approach 100% without any ties. Finally, consideration of a guess-oriented test strategy suggests a target value for the lowest successful score.