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?

The total income of $A$ and $B$ is greater than the total income of $C$ and $D$. The total income of $A$ and $C$ is equal to the total income of $B$ and $D$. Furthermore,the income of $A$ is equal to half the total income of $B$ and $D$. Which of the following statements is $NOT$ true?

$(i)$ There are seven books,one each on Psychology,Hindi,English,Sociology,Economics,Education,and Accountancy,lying on a table one above the other.
$(ii)$ Sociology is on the top of all the books.
$(iii)$ Accountancy is immediately below Education,which is immediately below Sociology.
$(iv)$ Economics is immediately above Psychology,but not in the middle.
$(v)$ Hindi is immediately below Psychology.
If Sociology and English,Accountancy and Hindi,and Education and Psychology interchange their positions,which book will be between Psychology and Sociology?

$A$ group of eight members sit in a circle. $D$ is between $A$ and $F$ and is opposite to $G$. $E$ is to the right of $A$ but on the left of $C$,whose right-hand neighbor is $G$. $B$ enjoys having $H$ to his left and $F$ to his right. Find the member who is diagonally opposite to $A$.

Eight books are kept one over the other. Counting from the top,the second,fifth and sixth books are on Plays. Two books on Plays are between two books on Composition. One book of Plays is between two books on Poetry while the book at the top of the book of Literature is a book of Composition. Which book is fourth from the top?

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?