How I can verifies particular distance university is it recognized university by UGC and approved by DEC.

I'd suggest you to visit the college or university's website and check for the registration number or you can directly ask the college for registration proofs or simply to check UGC's website for the white and black listed colleges and universities. And similarly checking recognition from other inst

The Distance Education Council (DEC) is responsible for the promotion and coordination of the open university and distance education system and for determination of its standards. The Council provides academic guidelines to promote excellence, encourage use of innovative technologies and approaches,