Ravi wants to go to the university. He starts from his home,which is in the East,and comes to a crossing. The road to the left ends in a theatre,and straight ahead is the hospital. In which direction is the university?

$A$ man leaves for his office from his house. He walks towards east. After moving a distance of $20 \, m$,he turns towards south and walks $10 \, m$. Then he walks $35 \, m$ towards west and further $5 \, m$ towards north. He then turns towards east and walks $15 \, m$. What is the straight distance in metres between his initial and final positions?

Point $B$ is $12 \,meters$ south of point $A.$ Point $C$ is $24 \,meters$ east of point $B.$ Point $D$ is $8 \,meters$ south of point $C.$ Point $D$ is $12 \,meters$ east of point $E$ and point $F$ is $8 \,meters$ north of point $E.$ If a man is standing facing north at point $C,$ how far and in which direction is point $F$?

Sachin and Vinod want to visit the museum after their exams. Sachin's exams finish on $9^{th}$ April and he is leaving for a holiday on $12^{th}$ April. Vinod's exams will be over by $10^{th}$ April,after which he is free. On which of the following dates can the two definitely meet?

Six flats on a floor in two rows facing North and South are allotted to $P, Q, R, S, T$ and $U$.
$(i)$ $Q$ gets a North-facing flat and is not next to $S$.
(ii) $S$ and $U$ get diagonally opposite flats.
(iii) $R$,next to $U$,gets a South-facing flat and $T$ gets a North-facing flat.
Which of the other pairs,besides $SU$,are diagonally opposite to each other?

$A$ man walks $1 \, km$ towards East and then he turns to South and walks $5 \, km.$ Again he turns to East and walks $2 \, km,$ after this he turns to North and walks $9 \, km.$ Now,how far is he from his starting point? (in $\, km$)