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 question in an identical sequence. For this to happen the maximum number of candidates is:

The correct option is 32.

To find the maximum number of candidates such that no two candidates have given the answers in an identical sequence, we need to calculate the total number of unique answer sequences possible for the five questions.

Each question has exactly two choices: True (T) or False (F).
Let us analyze the number of choices for each question:
Question 1 has 2 choices (T or F).
Question 2 has 2 choices (T or F).
Question 3 has 2 choices (T or F).
Question 4 has 2 choices (T or F).
Question 5 has 2 choices (T or F).

According to the fundamental counting principle, if there are 5 questions and each question has 2 possible answers, the total number of different sequences of answers is given by multiplying the choices for each question:

$$\text{Total unique sequences}=2\times 2\times 2\times 2\times 2$$

This can be simplified as:
$2^5=32$

Since no two candidates have given the same sequence of answers, each candidate must have a unique sequence. Therefore, the maximum number of candidates possible is equal to the total number of unique sequences, which is 32.