Can I pursue full time PhD after completing PG through distance mode?

Actually Govt. Universities don't allow those students who have done PG from Distance Learning for PhD programmes but some Mid and Level Private Universities so allow , better do preparation for NET JRF if you want some Good University to do PhD .

Yes, you can do it if the distance learning course was recognized by UGC and you have scored not less than 55% Marks in PG.

Yes you can pursue

You certainly can. But please check the minimum Eligible Percentage before applying.