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?

$(i)$ There are six friends $A, B, C, D, E$ and $F$.
$(ii)$ Each one is proficient in one of the games,namely Badminton,Volleyball,Cricket,Hockey,Tennis and Polo.
$(iii)$ Each owns a different coloured car,namely yellow,green,black,white,blue and red.
$(iv)$ $C$ does not play either Tennis or Hockey and owns neither blue nor yellow coloured car.
$(v)$ $D$ plays Polo and owns a yellow coloured car.
$(vi)$ $E$ owns a white car and plays Badminton.
$(vii)$ $B$ does not play Tennis,he owns a red coloured car.
$(viii)$ $A$ plays Cricket and owns a black car.
Which of the following combinations of colour of car and game played 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 of 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 $D$. Chemistry is an optional subject of only one of them. The only female teacher in the school has English as her compulsory subject. Disregarding which is the compulsory and which is the optional subject,who has the same two-subject combination as $F$?

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. Who among the teachers was teaching the maximum number of subjects?

There is a group of five persons $A, B, C, D$ and $E$. In the group,there are a Professor of Philosophy,a Professor of Psychology,and a Professor of Economics. $A$ and $D$ are ladies who have no specialization in any subject and are unmarried. No lady is a philosopher or an economist. There is a married couple in the group of which $E$ is the husband. $B$ is the brother of $C$ and is neither a psychologist nor an economist. Who is the Professor of Psychology?

Consider the following:
$1.$ Saxena,David,Jain,and Kumar were District Collectors at places $P, Q, R,$ and $S$ respectively in $1970$.
$2.$ In $1972$,they were transferred; Saxena and Jain interchanged places. Kumar and David also interchanged places.
$3.$ One year later in $1973$,they were again transferred such that David and Jain interchanged places,and Saxena and Kumar were also interchanged.
What should be the next round of transfers so that all the four persons could have been posted at all the four places?