$1.$ Six friends $A, B, C, D, E$ and $F$ are sitting in a closed circle facing the centre.
$2.$ $E$ is to the left of $D$.
$3.$ $C$ is between $A$ and $B$.
$4.$ $F$ is between $E$ and $A$.
Which of the above given statements is superfluous?

$(i)$ $P, Q, R, S, T$ 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 $PG$.
$(v)$ $T$ 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 of the following pairs of students stay at home?

In a group of six women,there are four dancers,four vocal musicians,one actress and three violinists. Girija and Vanaja are among the violinists while Jalaja and Shailaja do not know how to play the violin. Shailaja and Thanuja are among the dancers,Jalaja,Vanaja,Shailaja and Thanuja are all vocal musicians and two of them are also violinists. If Pooja is an actress,who among the following is both a dancer and a violinist?

There are five bus stops $A, B, C, D,$ and $E$ at equal intervals. $C$ is not the middle stop. $A$ and $E$ are not terminal stops. $C$ comes twice as many stops before $D$ in the upward journey as $B$ comes after $A$. $D$ is the first stop in the downward journey. Which of the following gives the correct sequence of the stops in the downward journey?

There are five persons $P, Q, R, S$ and $T$. One is a football player,one is a chess player,and one is a hockey player. $P$ and $S$ are unmarried ladies and do not participate in any game. None of the ladies plays chess or football. There is a married couple in which $T$ is the husband. $Q$ is the brother of $R$ and is neither a chess player nor a hockey player. Who is the hockey player?

$(i)$ Eleven students,$A, B, C, D, E, F, G, H, I, J$ and $K$ are sitting in the first row of the class facing the teacher.
$(ii)$ $D$,who is to the immediate left of $F$,is second to the right of $C$.
$(iii)$ $A$ is second to the right of $E$,who is at one of the ends.
$(iv)$ $J$ is the immediate neighbour of $A$ and $B$ and third to the left of $G$.
$(v)$ $H$ is to the immediate left of $D$ and third to the right of $I$.
Which of the following groups of friends is sitting to the right of $G$?