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He will meet President Pratibha Patil, who will host a banquet in his honour. Apart from call-ons by Vice President Hamid Ansari and other Indian dignitaries, Wangchuck will hold talks with Prime Minister Manmohan Singh.
This is the first visit abroad of the king after the Royal Wedding on October 13 and the fourth trip to India since his coronation in November 2008.
The couple will also go to Jaipur, Jodhpur and Udaipur during their stay.
The visit is in keeping with the tradition of regular high-level visits and exchanges between India and Bhutan.