What is the maximum number of parenthesis that will appear on the stack at any…

Answer: 3

Method: Scan the expression left to right. Push on each '(' and pop on each ')', tracking the current stack depth and the maximum depth seen.

1. 1st symbol '(' -> depth 1

2. 2nd symbol '(' -> depth 2

3. 3rd symbol ')' -> depth 1

4. 4th symbol '(' -> depth 2

5. 5th symbol '(' -> depth 3

6. 6th symbol ')' -> depth 2

7. 7th symbol ')' -> depth 1

8. 8th symbol '(' -> depth 2

9. 9th symbol '(' -> depth 3

10. 10th symbol ')' -> depth 2

11. 11th symbol ')' -> depth 1

12. 12th symbol ')' -> depth 0

Maximum depth observed: 3