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It was second meeting between the 25-year-old Indian and world number 133 Ymer, who had beaten Yuki in the first clash in 2015 at Aptos.
The Indian Davis Cupper had qualified for the Indian Wells Masters and had shcoked world number 12 Lucas Pouille in the second round.
In his first round, Yuki has drawn Lucky Loser Mirza Basic, the world number 75 from Bosnia.
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If Yuki crosses first hurdle, he will run into world number 11 and eighth seed American Jack Sock.
Yuki, of late, has created excellent results against top players. Yuki is lone Indian in the singles draw with Ramkumar Ramanathan,
In the doubles, Rohan Bopanna and his Edouard Vasselin have been pitted against Adrian Mannarino and Daniil Medvedev.