We have exchanged information before about the old Oxford dialect: Soccer; Rugger; Brekker; Wagger Pagger Bagger; and the rest. But I don't think we've swapped opinions on Divvers.
"Divvers" was part of the First Public Examination (Honour Mods or Prelims). It was a compulsory paper which consisted of an examination, both written and Viva Voce, on Scripture -- one Synoptic Gospel; S John; Acts. (Appropriate, if arcane, alternative provisions were made for candidates with Indian backgrounds.)
You had to pass it; it was the hurdle which Sir John Betjeman failed with the result that he was sent down. HisTutor (C S Lewis) was unsympathetic; Betjeman had been a far from model undergraduate. He was idle and lackadaisical, and ... worse ... tended to make cruel fun of Lewis behind his back. Lewis was unprepared to intercede on Betjeman's behalf: "You would only have got a Third".
("Divvers" had already disappeared when our generation went up in 1960. It is not to be confused with Responsions, which was an even earlier hoop one had to jump through in order to secure entry to the University in the first place.)
In 1933, this joke was still doing the rounds (Knox Silo): a man who has just been interviewed by the police says: "Never had such an easy let down since they viva'd me for Divvers at Oxford. No, not Galileo, Mr Tollard, he doesn't come in the Acts, they said. Doesn't he; I said, it's all one to me. And they let me through on it."