You purchased the car on May 24th, 2015.
Filed an application for transferring the RC in your name - May 28th, 2015 (assuming as not mentioned by you)
Met with an accident May 28th, 2015
Got new RC in your name - May 29th, 2015
Insurance transfered in your name - June 1st, 2015

So on the date of accident the RC and insurance both are not in your name so you are not covered and cannot claim.