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?

$A$ training college has to conduct a refresher course for teachers of seven different subjects: Mechanics,Psychology,Philosophy,Sociology,Economics,Science,and Engineering from $22^{nd}$ July to $29^{th}$ July.
$1.$ The course should start with Psychology.
$2.$ $23^{rd}$ July,being Sunday,should be a holiday.
$3.$ Science subject should be on the previous day of the Engineering subject.
$4.$ The course should end with Mechanics.
$5.$ Philosophy should be immediately after the holiday.
$6.$ There should be a gap of one day between Economics and Engineering.
Which subject is followed by Science?

Six students $A, B, C, D, E$ and $F$ are sitting in the field. $A$ and $B$ are from Nehru House while the rest belong to Gandhi House. $D$ and $F$ are tall while the others are short. $A, C$ and $D$ are wearing glasses while the others are not.
Which short student of Gandhi House is not wearing glasses?

$(i)$ 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 $I$.
In the above sitting arrangement,which of the following statements is superfluous?

$(i)$ Eight persons $E, F, G, H, I, J, K$ and $L$ are seated around a square table,two on each side.
$(ii)$ There are three lady members and they are not seated next to each other.
$(iii)$ $J$ is between $L$ and $F$.
$(iv)$ $G$ is between $I$ and $F$.
$(v)$ $H$,a lady member,is second to the left of $J$.
$(vi)$ $F$,a male member,is seated opposite $E$,a lady member.
$(vii)$ There is a lady member between $F$ and $I$.
How many persons are seated between $K$ and $F$?

Seven executives $P, Q, R, S, T, U$ and $W$ reach office in a particular sequence. $U$ reaches immediately before $P$ but does not immediately follow $S.$ $R$ is the last one to reach office. $T$ follows immediately after $P$ and is subsequently followed by $W.$
Who ranks fourth in the sequence of reaching office?