In the given figure,$P$ is $300 \, km$ eastward of $O$ and $Q$ is $400 \, km$ north of $O$. $R$ is exactly in the middle of $Q$ and $P$. The distance between $Q$ and $R$ is (in $, km$)

Reaching the place of meeting on Tuesday $15 \text{ minutes}$ before $8:30 \text{ hours}$,Anuj found himself half an hour earlier than the man who was $40 \text{ minutes}$ late. What was the scheduled time of the meeting? (in $\text{hours}$)

$A$ man walked $30 \, m$ towards south. Then,he turned to his right and walked $30 \, m$. Then,he turned to his left and walked $20 \, m$. Again,he turned to his left and walked $30 \, m$. How far is he from his initial position?

Nitin correctly remembers that Nidhi's birthday is after Tuesday but before Friday. Derek correctly remembers that Nidhi's birthday is after Wednesday but before Saturday. On which of the following days does Nidhi's birthday definitely fall?

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 $5:00 \, P.M.$?

Anuj started walking positioning his back towards the sun. After sometime,he turned left,then turned right and then towards the left again. In which direction is he going now?