Topic: Engineering Mathematics
There are 20 locks and 20 matching keys. Maximum number of trials required to match all the locks is
- A. 190
- B. 210
- C. 400
- D. 40
Answer: B. 210
Explanation: To guarantee finding the matching key, the first lock might require checking up to 20 keys. Once matched, the second lock might require checking up to 19 keys, and so forth, down to the final lock. This sequence forms an arithmetic progression: 20, 19, 18, ..., 1. The sum of this progression is given by the formula n(n+1)/2. For n = 20, the maximum number of trials is (20 * 21) / 2 = 210.