Carr, Tagore & Company was the first joint stock company incorporated in India (may be it had the registered office in India. It may have been incorporated in England.
The Assam Company was incorporated in London in 1839 with a share capital of GBP 500,000. Devendranath Tagore, grandfather of Rabindranath Tagore was a shareholder, his company Carr, Tagore & Co. managed the Bengal Tea Association as Managing Agent and the Bengal Tea Association in turn held the shares of Indian Shareholders of the Assam Company. On 30th May, 1839, the first Board Meeting of Assam Company was held.
On 7 July 1854, Cowasji Davar floated Bomaby Spinning and Weaving Company. The mill began production on 7 February 1856.
Company registration began in India only in 1851. The Statistical Tables of Registrations published in 1882 had a list of 1,149 companies registered up to March 1882.
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References
History of Assam Company
http://www.assamco.com/Annual%20Reports/Assam_Company_Annual_Report_2010.pdf
The Rise of Business Corporations in India, 1851-190
CUP Archive, 1970 - Corporations - 320 pages