$(i)$ $P, Q, R, S, T$ 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 paying guests $(PG)$ 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 combinations of subject and place of stay is not correct?

There are six persons $A, B, C, D, E,$ and $F$ in a school. Each of the teachers teaches two subjects: one compulsory subject and the other optional subject. $D's$ optional subject was History,while three others have it as a compulsory subject. $E$ and $F$ have Physics as one of their subjects. $F's$ compulsory subject is Mathematics,which is an optional subject for both $C$ and $E.$ History and English are $A's$ subjects,but in terms of compulsory and optional subjects,they are the reverse of those of $D's.$ Chemistry is an optional subject for only one of them. The only female teacher in the school has English as her compulsory subject. Which of the following has the same compulsory and optional subjects as those of $F$? (Note: The question asks for the person with the same subject distribution as $F$.)

$(i)$ 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 $I$.
Who among the following is seated between $E$ and $H$?

Six persons $A, B, C, D, E$ and $F$ are sitting in two rows,with three persons in each row. $E$ is not at the end of any row. $D$ is second to the left of $F$. $C$,the neighbor of $E$,is sitting diagonally opposite to $D$. $B$ is the neighbor of $F$. Which of the following are in the same row?

$A$ 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?

$(i)$ $P, Q, R, S, T$ 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 paying guests $(PG)$ 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.
Who studies English?