Treesa Jolly and Gayatri Gopichand (women's doubles) and B Sumeeth Reddy and N Sikki Reddy (mixed doubles) suffered three-game defeats in their opening contests.
PV Sindhu and Kidambi Srikanth secured straight game wins
Kashyap, a 2014 Glasgow Commonwealth Games gold medallist, defeated Japan's Yu Igarashi 15-21, 21-16, 22-20 in the final round of the qualification to seal his place in the main draw.
Sindhu took just 33 minutes to get the better of American Lauren Lam 21-16 21-13
The Indian men's team, led by Srikanth, had beaten powerhouse and 14-time champions Indonesia in the final to win the country's maiden Thomas Cup title on Sunday.
Two-time Olympic medallist P V Sindhu stormed into the second round of the women's singles in the Syed Modi International Super 300 badminton tournament after a dominating victory over compatriot Tanya Hemanth, in Lucknow, on Wednesday.
Former World champion P V Sindhu needed 36 minutes to get the better of the 21-year-old Chaliha 21-7, 21-18 and set up a last-four meeting with Thailand's Supanida Katethong.
News of all that's transpired on and off the football field
Take a look at images from events that caught our attention in the week gone by.
The American captain struck three times inside 16 minutes as the US stormed into an unexpected and unsurmountable 4-0 lead over their shell-shocked opponents.
Brazil were knocked out of the Women's World Cup on Sunday after a surprise 1-0 defeat by Australia in the round of 16.
Fourteen photos from events that defined the world in the week gone by.