Pdf image of the Harvard Entrance Exam -
18991869 (thanks, iitmsriram, for the correction). [Via Terry Tao who comments, "The mathematics portion has aged reasonably well; the classics and geography sections, less so."]
Dheeraj Sanghi: IIT Joint Entrance Examination Completes Half Century of Secrecy
Charu Sudan Kasturi in HT: IIT Professor Admits Errors in JEE Math Paper: "Prof. K.D. Joshi of IIT Bombay told HT he has found over 10 marks-worth of errors in this year’s math papers in the IIT Joint Entrance Examination."