The 39-year-old Bangalore-based is the sixth shooter to have earned the country a quota place for next year's quadrennial extravaganza.
He finished the qualification with a score of 567 that put him in second spot. Nanjappa was eliminated after the eighth final shot with 70.1 points. Nevertheless, he won applauses of the spectators crowding Gabala's finals hall.
Ranked 52nd in the world, with 567 points, he turned out to be the second-best athlete in the qualifications.
Besides Nanjappa and Rai, Olympic champion Abhinav Bindra, bronze winner Gagan Narang, Apurvi Chandela and Gurpreet Singh are the other quota winners for the 2016 Games.
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Nanjappa, who won a bronze medal in the 2013 ISSF World Cup in Changwon, South Korea, in the 10 metre air pistol event, suffered from a paralytic attack the same year in the right side of his face, during the World Cup in Granada.
Following his recovery, in October 2013, Nanjappa won the silver medal in the 50 metre pistol event in the Asian Air Gun Championship in Tehran.