$A$ man is facing north-west. He turns $90^{\circ}$ in the clockwise direction and then $135^{\circ}$ in the anticlockwise direction. Which direction is he facing now?

$A$ clock gaining $2 \, \text{minutes}$ every hour was synchronized at midnight with a clock losing $1 \, \text{minute}$ every hour. How many minutes behind will the second clock be at $11:00 \, \text{AM}$ the following morning compared to the clock gaining $2 \, \text{minutes}$ every hour?

If the digits of a watch are replaced by every alternate letter of the alphabet beginning from $12$ in the reverse order,i.e.,$12$ is replaced by $A$,$11$ is replaced by $C$,and so on,then on which alphabet would the small hand be when the time is $5:00 \, P.M.$?

After walking a distance of $50 \, m$ to the south of her house,Lakshmi turns left and walks another $20 \, m$. Then she turns north and walks $30 \, m$ and then starts walking to her house. In which direction is she walking now?

Sumesh went $15 \, km$ to the north from his house. Then he turned west and covered $10 \, km$. Then he turned south and covered $5 \, km$. Finally,he turned to the east and covered $10 \, km$. In which direction is he from his house?

If South-east becomes North,North-east becomes West and so on,what will West become?