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The correct answer is option 3 - Vijay Kelkar.
Option 1: Vijay Tendulkar is an Indian playwright and novelist, known for his works in Marathi and Hindi literature. However, he is not the Chairman of the 13th Finance Commission.
Option 2: M. Damodaran is an Indian administrator and retired civil servant. He has held various positions in the Indian government, but he is not the Chairman of the 13th Finance Commission.
Option 3: Vijay Kelkar is an Indian economist and bureaucrat. He served as the Chairman of the 13th Finance Commission from 2007 to 2010. He is known for his contributions to fiscal policy in India.
Option 4: Y.V. Reddy is an Indian economist and a former Governor of the Reserve Bank of India. While he has made significant contributions to the financial sector in India, he is not the Chairman of the 13th Finance Commission.
Therefore, the correct answer is option 3 - Vijay Kelkar.