If the third day of a month is Tuesday,which of the following would be the $4^{th}$ day before the $27^{th}$ day of that month?

Gopal started walking towards east. After moving a distance of $1 \,km$,he turned southward and walked $5 \,km$. Again,he turned to east and walked $2 \,km$. Finally,he turned to the north and walked $9 \,km$. How far is he from his starting point (in $,km$)?

In a square arrangement,let the initial positions be $A$ (North-West),$B$ (North-East),$C$ (South-East),and $D$ (South-West). $C$ and $A$ move diagonally to opposite corners and then one side each clockwise and anticlockwise respectively. $B$ and $D$ move two sides each clockwise and anticlockwise respectively. Who is at the North-West corner?

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 following combinations get South-facing flats? To arrive at the answer to the above question,which of the following statements can be dispensed with?

Rupa and Saroj want to attend a seminar together between $9 \, am$ and $5 \, pm$ on Friday. Saroj cannot leave till after her lunch break which begins at $1:30 \, pm$. Rupa is free after her meeting which begins at noon. For how many hours can the two of them attend the seminar?

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 $, km$)