The reasons for the failure of the Background Verification (BGV) are not clear. You can submit a bank statement to prove that you received a salary from a particular organisation. Secondly, if there is a PF trust, then you may go back to the ex-company and ask them to provide a certificate that provides details of the PF trust.
Nevertheless, both the grounds do not appear to be genuine. What if the candidate does not work in a company that provides a PF facility? Does it mean that Cognizant will not hire such persons?
From India, Bangalore