Here is a <A HREF="https://archive.org/details/mathematicalprob00wolsrich">collection</A>, with solutions, from the period 1864-1878 (published by Joseph Wolstenholme). An earlier period, 1800-1820, was collected by <A HREF="https://books.google.nl/books?id=KBtRAAAAYAAJ&pg=PR6&lpg=PR6&dq=wright+tripos+problems+cambridge&source=bl&ots=q43kp2QPwr&sig=K9vI6WDS29xFu4FQgDV4YfxmGYA&hl=nl&sa=X&redir_esc=y#v=onepage&q&f=false">I.M.F. Wright.</A>

These are transcriptions of the problem sets, not copies of the original documents, some of which you can find <A HREF="https://archive.org/details/papersetinmathtr00cambrich">here (1913-1917)</A> (freely accessible) and <A HREF="https://babel.hathitrust.org/cgi/pt?id=uc1.b2825298">here (1908-1912)</A> (only accessible in the US because of copyright restrictions).