The rupee opened on a flat note against the US dollar in the morning session on Thursday, amid a muted trend in domestic equities. Forex traders said the rupee is trading in a narrow range as rising crude oil prices, strong American currency, and sustained foreign fund outflows dented sentiments. At the interbank foreign exchange, the rupee opened at 83.13 against the dollar and touched an initial high of 83.11 and an early low of 83.14 against the greenback. On Wednesday, the rupee had settled at 83.12 against the US dollar. "Against the given odds favouring the rupee, challenges persist primarily due to the strengthening US Dollar, geopolitical tensions, and the ongoing Red Sea issue," CR Forex Advisors MD Amit Pabari said. Additionally, India's liquidity deficit has widened to Rs 3.34 trillion (USD 40.18 billion) as of January, limiting the Reserve Bank of India from allowing the rupee to appreciate towards its fair value. Despite these obstacles, the overall outlook suggests