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The study of the dynamics of foreign exchange rates is of paramount importance to economic policy makers for developing countries like India that depend on foreign exchange to meet a large part of their import obligations. This paper uses the concepts of entropy to study the regularity/irregularity of the returns from the Indian Foreign exchange (forex) markets particularly during periods of economic instability. We use the Approximate Entropy and Sample Entropy statistics which measure the level of repeatability in the data are used to quantify the randomness in the forex returns for four major currencies namely the US Dollar, the British pound, the EURO and the Japanese Yen with respect to the Indian Rupee from the time period 2006 to 2021. These statistics are chosen as they are both statistical measures for assessing the randomness or regularity of time series data and enable researchers to objectively evaluate the degree of randomness present in the returns series and understand the crucial underlying patters or behaviors. In this research we look at two periods of major financial upheavals, the subprime crisis also known as the Global Financial Crisis (GFC) during 2006-2007 and the recent Covid-19 pandemic during 2020-2021. Our empirical results overwhelmingly confirm our working hypothesis that regularity in the returns of the major Indian foreign exchange rates increases during times of financial crisis. This is evidenced by a decrease in the values of the sample entropy and approximate entropy before and after/during the financial crisis period for the majority of the exchange rates. Our empirical results also show that Sample Entropy is a better measure of regularity than Approximate Entropy for the Indian forex rates which is in agreement with the theoretical predictions. Understanding the returns from foreign exchange rates during financial crises has important policy implications for various stakeholders, including market participants, policymakers, and regulators. It enables them to formulate better risk management and hedging strategies. It also helps policy makers in crisis management and contingency planning and safeguard the stability of the financial system. Exchange rate movements are interconnected across global markets, and crises often have cross-border implications. Collaborating on crisis management strategies across countries can help foster stability in international markets. [ABSTRACT FROM AUTHOR]