Is sikkim-manipal university of India is approved by ugc and hec?

Yes. Sikkim Manipal University is approved by UGC and AICTE. It was formed by the Government of Sikkim under the Section (2) of UGC act like every other Government University in India. SMU is not a Deemed University, it is a proper University formed by a state legislature act, like the Mumbai University or Pune University or Delhi University and so on. SMU is a member of Association of Indian Universities. It is one of the fastest growing and most respected Universities in India.