To raise the temperature of a certain mass of gas by $50^{\circ} C$ at a constant pressure, $160$ calories of heat is required. When the same mass of gas is cooled by $100^{\circ} C$ at constant volume, $240$ calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal) $?$
JEE MAIN 2020, Medium
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