In all forms of cricket, the number of bouncers per over is limited. For example, quoting from the current One Day International playing conditions:
22.214.171.124 A fast short-pitched delivery is defined as a ball, which passes or would have passed above the shoulder height of the striker standing upright at the popping crease.
126.96.36.199 In the event of a bowler bowling more than two fast short-pitched deliveries in an over as defined in clause 188.8.131.52 above, the umpire at the bowler’s end shall call and signal No ball on each occasion.
If the batsman manages to hit a bouncer, when the bowler has already exhausted his quota of bouncers per over, and the ball is caught, will the batsman be out or is it a no ball?