Competing in the men's 10-metre air rifle event, Beijing Games gold medal winner Bindra, London Olympian Sanjeep Rajput and Chain Singh -- all failed to qualify for the finals after finishing 15th, 19th and 25th, respectively.
The result in the 50-metre pistol men was slightly better, with Prakash Nanjappa just about managing a top-eight finish with a total score of 71.5.
Rahi Sarnobat, Sushma Singh, Anisa Sayyed, Shreya Gawande and Annu Raj Singh will look to produce a better show when they take to the range for the final of the 25-metre pistol event tomorrow.
In men's 10-metre air rifle, Bindra shot 102.4 104.2 101.2 104.9 103.2 104.0 for a total of 619.9. Rajput totalled 618.2, while Chain Singh managed 616.2.
China's Wang Tao won the gold medal with a score of 206.8 in the elimination round. Israel's Sergey Richter bagged the silver after shooting 205.6 and the bronze went to Hungary's Peter Sidi, who scored 182.2.