Yes Shashi, Monad University is a government recognized university. It is a state private university established by the Uttar Pradesh State Govt. Act 23 of 2010 & U/S 2 (f) of 1956.

Established in 2010, the university is affiliated to UGC. A  letter of authorization from the Government of Uttar Pradesh has also been issued in 2011 to the university. Subsequently, the university is also recognized by Association of Indian Universities (AIU), Pharmacy Council of India (PCI), Bar Council of India (BCI), Council of Architecture (COA) and National Council for Teacher Education (NCTE).

You can visit their official website for more information. You can also find the letter of consent of affiliation from these councils on their website: http://www.monad.edu.in/government-recognition