This was written by Basavappa Shastry, the court poet of Mysore Darbar during the reign of Chamaraja Wodeyar to commemorate the handing over of direct rule of Mysore State to the Wodeyars in 1881. The tune is set to Raga Dheerashankarābharanam
Kayo Sri Gowri, Karuna lahari, Thoya Jakshi, Shankareeshwari
Vaimanika Bhamarchitha Komalakara Padhe
Shreemanvitha Bhoomaspade Kamitha Phaladhe
Shumbadima Dhambhonidhi kumbaja nibha devi
Jambhahitha Sambhavithe Shambhavi shubhavee
Sri jaya jamundike Sri Jayachamendra
Namankitha Bhomeendra Lalamana Mudade
The italicized stanza was changed to
Shyamalike Chamundike Somakulaja Krishna
Namamkita Bhumindra Lalamana Mudade
during the reign of Krishna Raja Wodeyar and
Sri jaya jamundike Sri Jayachamendra
Namankitha Bhomeendra Lalamana Mudade
during the reign of Jaya Chama Raja Wodeyar.
It is also said that the inspiration to the tune of Jana Gana Mana is from this song.
Source: http://akshay-chavan.blogspot.co.uk/2012/04/mysore-state-anthem-kayo-shri-gowri.html
cbkwgl 
Wrong information. There is no similarity with Jana Gana Mana . But huge similarity with another song of Tagore- “Anandaloke Mangaloke” .
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It was not an inspiration of tune but Tagore admired Mysore state anthem as it was the only one anthem which praised divine powers not merely the kings. This anthem was taken by Sarala Debi and Tagore made Sangachhadhwang and later Anandaloke in the same tune.
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