Dollar closed at 63.6000 against its opening at 63.6800. Dollar in the offshore market traded up tracking the spike in the spot pair on buying by nationalised banks amid month-end dollar demand by oil importers. The greenback traded higher against its major peers ahead of the Federal Open Market Committee (FOMC) two-day monetary policy outcome as investors covered their short positions taking advantage of the sharp plunge. Market participants expect the Fed to hold short-term interest rates steady while the central bank's policy statement could signal whether officials intend to raise rates at a quicker pace than expected this year. Dollar may get a boost on expectations of rising rates, making the currency more attractive to yield-seeking investors.

On the US economic front, the Commerce Department reported that the personal income increased by slightly more than expected in the month of December. The Commerce Department said personal income rose by 0.4% in December after climbing by 0.3% in November.
 
BSE Sensex closes just over 36000 points, while the Nifty ended at 11,050 mark.
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Asian shares fell, taking a cue from Wall Street and on mixed regional data and concerns about the dollar ahead of President Trump's State-of-the-Union speech later which could include more on recent trade spats.
 
 
Labor demand in Japan rose in December to its highest in more than 40 years, which could help workers pressing for bigger pay increases at annual wage negotiations and push stubbornly slow consumer price growth towards policymakers' inflation target.
 
 
The European Union offered to let Britain keep its membership benefits for 21 months after Brexit to help businesses adapt but it rejected the idea that London could block new EU laws during the transition.
 
 
Gold fell for a second straight session as the dollar strengthened and U.S. bond yields rose, while traders awaited a U.S. Federal Reserve policy meeting for any indications on interest rate hikes this year.
 
 
Oil prices fell on Tuesday for a second day as rising U.S. output and a strengthening dollar sapped demand for crude, pushing Brent below $70 a barrel.