$1.$ There is a group of six persons $A, B, C, D, E$ and $F$ from a family. They are Professor,Manager,Lawyer,Jeweller,Doctor,and Engineer.
$2.$ The Doctor is the grandfather of $F$,who is a Professor.
$3.$ The Manager $D$ is married to $A$.
$4.$ $C$,the Jeweller,is married to the Lawyer.
$5.$ $B$ is the mother of $F$ and $E$.
$6.$ There are two married couples in the family.
How is $A$ related to $E$?

Eight friends $A, B, C, D, E, F, G$ and $H$ are sitting in a circle facing the centre. $B$ is sitting between $G$ and $D$. $H$ is third to the left of $B$ and second to the right of $A$. $C$ is sitting between $A$ and $G$ and $B$ and $E$ are not sitting opposite to each other.
Who is third to the left of $D$?

Six roads lead to a country. They may be indicated by letters $X, Y, Z$ and digits $1, 2, 3$. When there is a storm,$Y$ is blocked. When there are floods,$X, 1$ and $2$ will be affected. When road $1$ is blocked,$Z$ also is blocked. At a time when there are floods and a storm also blows,which road$(s)$ can be used?

$(i)$ 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?

$(i)$ 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.
Which three books are between Accountancy and Hindi?

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?