Balance of Trade: https://tradingeconomics.com/india/balance-of-trade
Foreign Exchange Reserves: https://tradingeconomics.com/india/foreign-exchange-reserves
Remittances do help (avg. \$4B/mo) but are not enough to offset the trade deficit (avg. \$15B/mo).
India Remittances: https://tradingeconomics.com/india/remittances
Please note that the time scales in the above charts are not the same.
The central bank's accounts are not the same as entire country's accounts.
The foreign currency reserves statistic comes from the Reserve Bank of India, the central bank, when it discloses its account. The trade deficit is not a property of the central bank's accounts, although the central bank might have economists producing that statistic. The trade deficit is a property of the entire country in aggregate, which includes household, business, and government trade activity.
I saw somewhere that it's largely down to Indian employees abroad sending much of their earnings home, but I don't have the link to hand.
