Pune is bigger than Jhansi,Sitapur is bigger than Chittor. Raigarh is not as big as Jhansi,but is bigger than Sitapur. Which is the smallest?

Seven men $A, B, C, D, E, F$ and $G$ are standing in a queue in that order. Each one is wearing a cap of a different colour like violet,indigo,blue,green,yellow,orange and red. $D$ is able to see in front of him green and blue,but not violet. $E$ can see violet and yellow,but not red. $G$ can see caps of all colours other than orange. If $E$ is wearing an indigo coloured cap,then the colour of the cap worn by $F$ is

In a school,there were five teachers. $A$ and $B$ were teaching Hindi and English. $C$ and $B$ were teaching English and Geography. $D$ and $A$ were teaching Mathematics and Hindi. $E$ and $B$ were teaching History and French. Which of the following pairs was teaching both Geography and Hindi?

$A, B, C, D, E$ and $F$,not necessarily in that order,are sitting on six chairs regularly placed around a round table. It is observed that:
$1$. $A$ is between $D$ and $F$.
$2$. $C$ is opposite $D$.
$3$. $D$ and $E$ are not on neighbouring chairs.
Which of the following pairs must be sitting on neighbouring chairs?

$(i)$ $P, Q, R, S, T$ and $U$ are six students pursuing their Master's degree in six different subjects $-$ English,History,Philosophy,Physics,Statistics and Mathematics.
$(ii)$ Two of them stay in a hostel,two stay as a paying guest $(PG)$ and the remaining two stay at their home.
$(iii)$ $R$ does not stay as a $PG$ and studies Philosophy.
$(iv)$ The students studying Statistics and History do not stay as a $PG$.
$(v)$ $T$ studies Mathematics and $S$ studies Physics.
$(vi)$ $U$ and $S$ stay in a hostel. $T$ stays as a $PG$ and $Q$ stays at home.
Which subject does $Q$ study?

Seven persons $P, Q, R, S, T, U,$ and $V$ participate in and finish all the events of a series of swimming races. There are no ties at the finish of any of the events. $V$ always finishes somewhere ahead of $P$. $P$ always finishes somewhere ahead of $Q$. Either $R$ finishes first and $T$ finishes last or $S$ finishes first and $U$ or $Q$ finishes last. If in a particular race $V$ finished fifth,then which one of the following would be true?