Early in the morning after sunrise, Karthik is standing in front of his house in such a way that his shadow falls exactly behind him. He then starts walking straight ahead for 5 metres, turns to his left and walks 3 metres, and again turns to his left and walks 2 metres. In which direction is he now with respect to his starting point in front of the house?

Introduction / Context:
This question combines knowledge about the position of the sun with direction sense and left right turns. Karthik stands so that his shadow is directly behind him in the morning, and then he walks and turns. We must use the information about the sun's position after sunrise to infer his initial facing direction, and then track his path to determine his final direction with respect to the starting point.

Given Data / Assumptions:

• It is early morning just after sunrise, so the sun is in the east.
• Karthik stands so that his shadow falls directly behind him.
• He walks straight ahead for 5 metres from this position.
• Then he turns left and walks 3 metres.
• Again he turns left and walks 2 metres.
• We assume the directions follow the usual convention in which the sun rises in the east and shadows fall opposite to the sun.

Concept / Approach:
The first step is to find Karthik's initial facing direction. In the morning the sun is in the east, so a person whose shadow falls behind him must be facing away from the sun, that is, towards the west. Once we know he is facing west, we can interpret straight, left, and left again in terms of west, south, and east movements. Finally, we compare his ending position to the starting point and identify the overall direction such as south west or south east.

Step-by-Step Solution:
Step 1: Since it is after sunrise, the sun is in the east. Shadows fall away from the sun.Step 2: Karthik's shadow is directly behind him, which means he must be facing away from the east, that is, towards the west.Step 3: Take his starting point as the origin (0, 0). Facing west, he walks straight 5 metres to reach (−5, 0).Step 4: From facing west, a left turn means he now faces south. Walking 3 metres south leads to (−5, −3).Step 5: From facing south, another left turn makes him face east. Walking 2 metres east takes him to (−3, −3).Step 6: His final position is 3 metres west and 3 metres south of his starting point.Step 7: Therefore, with respect to the starting point, he is in the south west direction.

Verification / Alternative check:
We can quickly verify the initial facing direction by visualising. In the morning, the sun is in front if a person faces east and shadows fall behind towards the west. For the shadow to be behind while the sun is east, Karthik must face west. Once this is clear, the left turns can be tracked using a simple compass sketch: from west, left leads to south, and from south, left leads to east. The final coordinate calculation confirms that his displacement has both a south and west component, which identifies the south west direction uniquely.

Why Other Options Are Wrong:
If he were to the west of the starting point but not south, only pure west would be correct, but here he is also 3 metres south. North east and south east would have him east of the start, which does not match the negative x coordinate. Pure east is clearly incorrect because his main movement began towards the west. South east would place him in the opposite horizontal direction. Only south west fits both the horizontal and vertical displacement signs.

Common Pitfalls:
Learners often misinterpret the effect of sunlight on shadows and may wrongly assume that facing east gives a shadow behind in the morning. Another frequent error is mixing up left and right when the person is facing west or south, which reverses directions. Drawing the four cardinal directions and following the turns step by step helps avoid confusion and ensures that both the initial orientation and turns are handled correctly.

Final Answer:
After all his movements, Karthik is located in the South-West direction from his original starting position in front of his house.