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The question is about matching personalities with their area of work or distinction.
Option 1 suggests E. C. G. Sudarshan is associated with physics, but wrongly matches V. Shanta with theater, and Mahesh Dattani with cancer treatment.
Option 2 incorrectly matches all the personalities: E. C. G. Sudarshan with violin, V. Shanta with cancer treatment, T. N. Krishnan with water-harvesting, and Mahesh Dattani with theater.
Option 3 accurately matches E. C. G. Sudarshan with physics research, V. Shanta with cancer treatment, T. N. Krishnan with violin, and Mahesh Dattani with theater which is the right match for all personalities.
Option 4 again is incorrect on all fronts: E.C.G. Sudarshan for violin, V.Shanta for theater, T.N.Krishnan for water-harvesting, and Mahesh Dattani for cancer treatment.
Therefore, the correct answer is option 3.