In a question paper there are five questions to be attempted and answer to each question has two choices—True (T) or False (F). It is given that no two candidates have given the answers to the five questions in an identical sequence. For this to happen the maximum number of candidates is:

Correct Option (D)

Each of the five questions in the paper presents two independent choices: True (T) or False (F). To determine the total number of unique answer sequences possible for these five questions, the number of choices for each question is multiplied.

The calculation is as follows:

• Number of choices for Question 1 = 2
• Number of choices for Question 2 = 2
• Number of choices for Question 3 = 2
• Number of choices for Question 4 = 2
• Number of choices for Question 5 = 2

Therefore, the total number of distinct answer sequences possible is 2 × 2 × 2 × 2 × 2 = 2⁵ = 32.

Given the condition that no two candidates have provided an identical sequence of answers, the maximum number of candidates that can participate is equal to the total number of distinct answer sequences possible, which is 32.

Incorrect Options:

Options A (10), B (18), and C (26) represent values that are less than the total number of unique answer sequences (32) that can be generated from five questions, each with two choices. Consequently, these options do not represent the maximum possible number of candidates under the stipulated condition that all candidates must have distinct answer sequences.