Can I reach level 72 without True and Ultimate Vault hunter Mode?
I am playing this game solo.
I am going to think I am going to get alot of exp from the DLC quests in Normal. So I can reach level 72
Is this a good idea?
No, you cannot reach level 72 without True or Ultimate Vault Hunter Mode. On a normal playthrough, your level is capped at 50.
You will not be able to get higher than level 50 until you attempt playthroughs 2 or 3. Your second playthrough (New Game+, essentially) will raise your level cap by 11, to 61. Your third playthrough (New Game++) will raise your level cap by another 11, to a maximum level of 72.
Thus, without playing True or Ultimate Vault Hunter Mode, you cannot get above level 50.
See this Q&A for more detailed info about how subsequent playthroughs work.