Explanation:

Let's analyze the effect of the turns on Rakesh's direction. - A left turn changes direction by $-90^\circ$ (counter-clockwise). - A right turn changes direction by $+90^\circ$ (clockwise). \nRakesh takes two left turns and one right turn. The net change in direction is:\nTotal change = (Left Turn) + (Left Turn) + (Right Turn)\nTotal change = $(-90^\circ) + (-90^\circ) + (+90^\circ)$\nTotal change = $-180^\circ + 90^\circ = -90^\circ$. \nThis means Rakesh's final direction is $90^\circ$ counter-clockwise from his starting direction. \nLet $D_{start}$ be the starting direction and $D_{final}$ be the final direction. $D_{final} = D_{start} - 90^\circ$ (where $-90^\circ$ means $90^\circ$ counter-clockwise). \nWe are given that $D_{final} = \text{North}$.\nSo, $\text{North} = D_{start} - 90^\circ$. \nTo find $D_{start}$, we can rearrange the equation: $D_{start} = \text{North} + 90^\circ$ (where $+90^\circ$ means $90^\circ$ clockwise). \nStarting from North and turning $90^\circ$ clockwise leads to East.\nTherefore, Rakesh was facing East when he started from his house. \nLet's verify this by tracing the path if Rakesh started facing East: 1. Starts facing East. 2. First Left Turn: East $\rightarrow$ North. 3. Second Left Turn: North $\rightarrow$ West. 4. One Right Turn: West $\rightarrow$ North.\nThis matches the given final direction of North. \nAnalyzing the options: (1) North: If Rakesh started North, he would end up facing West (North $\rightarrow$ West $\rightarrow$ South $\rightarrow$ West). This is incorrect. (2) South: If Rakesh started South, he would end up facing East (South $\rightarrow$ East $\rightarrow$ North $\rightarrow$ East). This is incorrect. (3) East: This is correct. If Rakesh started East, he would end up facing North. (4) West: If Rakesh started West, he would end up facing South (West $\rightarrow$ South $\rightarrow$ East $\rightarrow$ South). This is incorrect. \nThe logically derived answer is East. Please note that the provided answer key in the document indicates option (1) North as correct, which contradicts this derivation. If Rakesh started North, he would not be facing North at the market after the given turns.