Am I eligible for admission in Ph.D. (Home Science) course after competition of Masters in Home Science (M.H.Sc)???

Yes, you can surely do Ph.D. (Home Science) course after competition of Masters in Home Science (M.H.Sc)

Ph.D. (Home Science) is Doctorate level degree and its duration is 3 Years

Eligibility:
Must have Masters degree in the similar field to join the PhD program.

List of some of the Colleges offering Ph.D. (Home Science) in India

Assam Agricultural University (AAU)
Borbheta
Jorhat, Assam

Dr. Bhim Rao Ambedkar University / Agra University
Paliwal Park
Agra, Uttar Pradesh

Government M.H. College of Home Science and Science for Women (Autonomous) Napier Town
Jabalpur, Madhya Pradesh

I.I.S. University (International College for Girls - ICG)
I.C.G. Campus, Gurukul Marg, SFS Mansarovar
Jaipur, Rajasthan

Jayoti Vidyapeeth Women's University
Vedaant Gyan Valley, Jhama, Mahla-Jobner Link Road,
Jaipur - Ajmer Express Way,
Jaipur, Rajasthan

Justice Basheer Ahmed Sayeed Womens College
No.56, K.B.Dasan Road College Avenue Anna Salai Teynampet
Chennai, Tamil Nadu

Magadh University
Gaya-Dobhi Road
Bodh Gaya, Bihar

Marathwada Agriculture University
Krishinagar
Parbhni, Maharashtra

Nagaland University
Opp. Congress Bhavan, Old Sectt. Complex
Kohima, Nagaland

NIMS University
Shobha Nagar, Jaipur-Delhi Highway (NH-11C),
Jaipur, Rajasthan