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?

There are five friends $-$ Sachin,Kunal,Mohit,Anuj,and Rohan.
Sachin is shorter than Kunal but taller than Rohan.
Mohit is the tallest.
Anuj is a little shorter than Kunal and a little taller than Sachin.
Who is the shortest?

$(i)$ $P, Q, R, S, T$ 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?

$A, B, C, D,$ and $E$ are five persons standing in a bus queue. $A$ is a teacher standing to the right of $D$,who is an advocate. $B$ is a scientist and is standing to the left of $E$,who is an electrician. There are two persons between $B$ and $A$. $C$,who is a banker,stands to the right of $A$. Who is at the extreme right?

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 Shailja do not know how to play on the violin. Shailja and Tanuja are among the dancers. Jalaja,Vanaja,Shailja and Tanuja 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?