Consider the following statements:
1. The first woman President of the Indian National Congress was Sarojini Naidu.
2. The first Muslim President of the Indian National Congress was Badruddin Tyabji.
Which of the statements given above is/are correct?

The correct option is 2 only.

Let us analyze each statement step-by-step to understand why this option is correct:

Analysis of Statement 1:
Statement 1 asserts that the first woman President of the Indian National Congress (INC) was Sarojini Naidu.
Historically, the first woman President of the Indian National Congress was Annie Besant, who presided over the Calcutta session of the INC in 1917.
Sarojini Naidu was indeed a prominent leader and became the first Indian woman President of the INC at the Kanpur session in 1925, but she was not the first woman President overall.
Therefore, Statement 1 is incorrect.

Analysis of Statement 2:
Statement 2 asserts that the first Muslim President of the Indian National Congress was Badruddin Tyabji.
Badruddin Tyabji presided over the Madras session of the Indian National Congress in 1887 (the third annual session of the congress). He was indeed the first Muslim to serve as the President of the INC.
Therefore, Statement 2 is correct.

Since Statement 1 is incorrect and Statement 2 is correct, the overall correct choice is "2 only".