Yes you can definitely buy Call (CE) AND pe (PE) of the same stock on same day.
If you buy at the money strikes
ATM CE + ATM PE
This strategy is called as Long straddle, such strategies are used only when you are expecting a huge move in the market due to any event or announcement but are not sure in which direction.
You make loss in one, and gains in other.
due to large movement, the gains are greater than loss and one makes money.
Remember this strategy only works when the move id strong (more than 4%), else you will end up in losses.
So if you are confident about the movement in the stock but don’t know the direction ,then prefer straddle.
Similarly by using different strikes for call and put you can make your own strategies like strangle, etc