Union Finance Minister Arun Jaitely picked up the slip bearing Yuki's name at the draw ceremony, which was also attended by Sports Minister Sarbananda Sonowal apart from AITA and ITF officials.
The second singles will be played between India's number two player Somdev Devvarman (ranked 164) and Czech number one Jiri Vesley, who is ranked 40 in the world.
The reverse singles will be played on Sunday.
Yuki, who had stated that he would prefer playing in cooler conditions, said, "I want to make a good start and put the Czechs under pressure. I can play freely at 0-0."
Indian captain Anand Amirtraj said the draw has come out "the way we wanted".
"It's slightly easier to play first match and Som had to see and wait how it goes (and plan accordingly)," Anand said.
Paes, who is the most experienced player in the team, said Indians must capitalise on hot conditions but the players have their own individual style of doing it.
"Every player has his own individual style of preparing for matches. It is not necessary that what works for me will work for Somdev. We have developed our own styles how to handle the heat and stay away from cramping. Davis Cup is five set matches. That's not an easy task. The boys have to keep hydrating," Paes, who is the fourth most successful player in the Davis Cup history with 89 wins, said.
Vesley is yet to win a live singles rubber but Somdev said that does not make the Czech a lesser player.
"He is top-50. I don't see him an inexperienced player by any means. It's going be tricky. He is pretty solid.
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