Look for the pair where the sport does not match the athlete, and that is Somdev Devvarman listed against badminton. Devvarman actually built his reputation on the tennis court. In 2010 he had a standout year, taking home singles and doubles gold at the Commonwealth Games held in New Delhi and adding a singles gold at the Asian Games in Guangzhou, after having already made a name for himself as an NCAA singles champion in college tennis in the US. Badminton was never his game.
Every other pairing checks out. Gagan Narang shoots the 10 metre air rifle event and has a long list of Commonwealth, Asian Games and World Cup medals to his name. Arjun Atwal made history in golf in 2010 as the first Indian to win a US PGA Tour title, lifting the Wyndham Championship trophy. Anita Sood is correctly identified as a swimmer who competed for India. Because the tennis player Devvarman is wrongly tagged as a badminton player, that is the pair that does not belong, making option 1 the answer.