The correct answer is option 2, which states that the second statement is correct, while the first and third statements are incorrect.

Let`s analyze each statement:

1. According to the 2011 census, 82% of Indians are literate.

This statement is incorrect. According to the 2011 census, the literacy rate in India was around 74%. Therefore, statement 1 is not correct.

2. Sex ratio of the population has increased during the period 2001-2011.

This statement is correct. The sex ratio is defined as the number of females per 1000 males in the population. The 2011 census shows that the sex ratio in India has improved from 933 females per 1000 males in 2001 to 943 females per 1000 males in 2011.

3. The gender gap in literacy has not declined during the period 2001-2011.

This statement is incorrect. The gender gap in literacy has indeed declined during the period 2001-2011. In 2001, the gap was 21.7 percentage points, but it reduced to 16.7 percentage points in 2011. Therefore, statement 3 is not correct.

In conclusion, only statement 2