Sixth seed Sindhu, who had beaten Bingjiao at the Denmark Open last week, could not get past her rival this time and lost 20-22 17-21 to the Chinese in a 41-minute match.
In the men's singles, India's H S Prannoy also failed to cross the second round as he lost 19-21 16-21 to fifth seed Chou Tien Chen of Chinese Taipei in the match that lasted 42 minutes.
In the second game, Bingjiao did not give Sindhu much chance to make a comeback as she led from the front, moving to 11-6 at the break and then surging to a 18-9 lead. Sindhu tried her bit and narrowed down the gap to 17-19 before the Chinese shut the door on the Indian.
In the men's singles match, Prannoy was ahead at 8-5 and 18-15 but he faltered at the final stages to allow Chou pocket the opening game.
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