Explanation:

Let's analyze the net effect of the turns. A left turn corresponds to a $-90^\circ$ rotation (counter-clockwise), and a right turn corresponds to a $+90^\circ$ rotation (clockwise). \nRakesh takes two left turns and one right turn:\nNet rotation $= (-90^\circ) + (-90^\circ) + (+90^\circ) = -90^\circ$. \nThis means the final direction is $90^\circ$ counter-clockwise from the starting direction.\nLet $D_S$ be the starting direction and $D_F$ be the final direction. $D_F = D_S - 90^\circ$ (counter-clockwise). \nWe are given that $D_F = \text{North}$. To find $D_S$, we reverse the operation: $D_S = D_F + 90^\circ$ (clockwise). $D_S = \text{North} + 90^\circ \text{ (clockwise)}$. $D_S = \text{East}$. \nLet's verify:\nIf Rakesh started facing East: 1. Started East. 2. First Left Turn: East $- 90^\circ = \text{North}$. 3. Second Left Turn: North $- 90^\circ = \text{West}$. 4. One Right Turn: West $+ 90^\circ = \text{North}$.\nThis matches the final direction given in the problem. \nOption (A) North: If Rakesh started North, he would end up West (North $\xrightarrow{L}$ West $\xrightarrow{L}$ South $\xrightarrow{R}$ West). This is incorrect.\nOption (B) South: If Rakesh started South, he would end up East (South $\xrightarrow{L}$ East $\xrightarrow{L}$ North $\xrightarrow{R}$ East). This is incorrect.\nOption (C) East: As derived, if Rakesh started East, he would end up North. This is the correct option.\nOption (D) West: If Rakesh started West, he would end up South (West $\xrightarrow{L}$ South $\xrightarrow{L}$ East $\xrightarrow{R}$ South). This is incorrect.