Governor N N Vohra administered the oath to the legislators at Raj Bhavan. It was the second expansion of the council of ministers since Mehbooba Mufti formed the government in the state with the BJP.
Tassaduq Mufti, 45, previously served as the head of Mehbooba Mufti's grievance cell. He returned to the state's politics after their father Mufti Mohammad Sayeed died in 2016.
A noted cinematographer, Tassaduq Mufti joined the PDP at a gathering organised to commemorate his father Mufti Mohammed Sayeed's first death anniversary on January 7 this year.
He is expected to get the tourism portfolio.
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"I will work hard for peace, progress and prosperity of Jammu and Kashmir. My focus will infuse life in the tourism sector in J&K," Tassaduq told reporters here.
Javed Mustafa Mir, an MLA from the Chadoora Assembly constituency, is a two-time minister.
He was a minister of state in the Mufti Mohammad Sayeed government in 2002 and a cabinet minister under him in 2015.
The BJP, a coalition partner in the ruling alliance in the state, welcomed the minor expansion of the cabinet.
BJP leader and Deputy Chief Minister Nirmal Singh said the expansion will give thrust to the council of ministers.
But the Congress party questioned BJP's silence over Tassaduq Mufti's induction. Its state chief G A Mir said the saffron party had made dynasty rule an issue in its election campaigns but it was now "keeping its eyes closed."
The PDP appeared to discourage any suggestion of differences withing the party over the induction of Tassaduq Mufti.
On December 22, when Tassaduq was nominated as a member of the state legislative council, then minister of state for Haj and Auquaf, Syed Farooq Andrabi, had resigned from the council of ministers, citing "personal reasons".
Andrabi had submitted his resignation to his niece Mehbooba Mufti and it was forwarded to the governor, who accepted it.