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 $2$ are affected. When road $1$ is blocked,$Z$ is also blocked. At a time when there are floods and a storm also blows,which road$(s)$ can be used?

The sum of the incomes of $A$ and $B$ is more than that of $C$ and $D$ taken together. The sum of incomes of $A$ and $C$ is the same as that of $B$ and $D$ taken together. Moreover,$A$ earns half as much as the sum of the incomes of $B$ and $D$. If $A$'s income is $Rs\, 80,000$ per annum and the difference between the income of $B$ and $D$ is the same as $A$'s income,what is $B$'s income?

$(i)$ 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 $I$.
Which of the following groups of friends is sitting to the right of $G$?

In a group of six women,there are four table tennis players,four postgraduates in economics,one postgraduate in commerce,and three bank employees. Vimala and Kamala are among the bank employees,while Amala and Komala are unemployed. Komala and Nirmala are among the table tennis players. Amala,Kamala,Komala,and Nirmala are postgraduates in economics,of whom two are bank employees. If Shyamala is a postgraduate in commerce,who among the following is both a table tennis player and a bank employee?

Five friends $A, B, C, D$ and $E$ are sitting on a bench.
$1.$ $A$ is sitting next to $B$.
$2.$ $C$ is sitting next to $D$.
$3.$ $D$ is not sitting with $E$.
$4.$ $E$ is on the left end of the bench.
$5.$ $C$ is on the second position from the right.
$6.$ $A$ is on the right side of $B$ and to the right side of $E$.
$7.$ $A$ and $C$ are sitting together.
Where is $A$ sitting?

$(i)$ Six friends $A, B, C, D, E$ and $F$ are sitting in a closed circle facing the centre.
$(ii)$ $E$ is to the left of $D$.
$(iii)$ $C$ is between $A$ and $B$.
$(iv)$ $F$ is between $E$ and $A$.
Which of the above given statements is superfluous?