Serena Williams marked her first European appearance of the season with victory on the Madrid Open's striking blue clay courts on Monday, but her sister Venus crashed out in the second round.
The Indian ace lost l3-6, 0-6 to New Zealand's Marina Erakovic in the second round of the DFS Classic grass-court tournament. US-based Rao beat wildcard Naomi Cavaday of Great Britain 4-6, 6-3, 6-1 after an hour and 50 minutes.
Serbian Jelena Jankovic battled into the second round of the French Open with a 7-6, 6-2 win over Romania's Monica Niculescu on Monday.
India were beaten 1-2 by New Zealand in their second match of the Asia/Oceania Group I Federation Cup match in Bangkok, on Thursday.
World number two Roger Federer launches his bid for a sixth US Open title, and his first since 2008, with a first-round match against Argentina's Leonardo Mayer at the Arthur Ashe Stadium on Tuesday.
Victoria Azarenka defeated Spain's Silvia Soler-Espinosa 6-1, 6-3 to set up a second round meeting with Jelena Jankovic.
India's Sania Mirza is standing on the cusp of history as she is now one win away from becoming World No 1.
Serena Williams must navigate a heavily American quarter of the draw including sister Venus to complete a calendar sweep of the four Grand Slams, while two sensational quarter-finals loom on the men's side after Thursday's U.S. Open draw.
Defending champion Angelique Kerber battled her nerves and blew a match point in the second set before finally overcoming Lesia Tsurenko 6-2, 5-7, 6-2 to reach the second round.
Top seed Andy Murray could meet Roger Federer or Kei Nishikori in the third round, while Serena faces tricky Belinda Bencic in opening round
Images from all the action from Day 1 of the Wimbledon on Monday.
Roger Federer glided to victory on another hot, steamy day at the US Open, the envy of a clutch of men's players made to work overtime on Tuesday at the season's final Grand Slam.
Tournament favourite Novak Djokovic beat Finnish veteran Jarkko Nieminen 6-2, 7-5, 6-2 on Tuesday, kicking off his quest for a first ever Paris trophy to add to his eight other Grand Slams.
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