The School has its yearbooks online at
http://earchives.lib.purdue.edu/cdm/...lection/debris
A search for the phrase Zeta Beta Tau got *one* hit, from 1946 (a students Senior Bio included Zeta Beta Tau), by comparison (my guess is a transfer to Purdue) , a search for Lambda Chi Alpha got 95 hits (and that indicates how many yearbooks had it)
My honest guess given that is that the Letters were assigned to Purdue and either no chapter came into existence, or the group never chartered.
My fraternity (Alpha Phi Omega) had a chapter like that, in 2001 they thought they were rechartering the chapter at Ferrum (which had chartered in 1970), but on further investigation found out the group had never actually gone through the chartering ceremony, so instead the group chartered the chapter, but with the letters that had been assigned in 1970.