Six persons $A, B, C, D, E,$ and $F$ are standing in a circle. $B$ is between $D$ and $C$. $A$ is between $E$ and $C$. $F$ is to the right of $D$. Who is between $A$ and $F$?

There are five persons $P, Q, R, S$ and $T$. One is a football player,one is a chess player,and one is a hockey player. $P$ and $S$ are unmarried ladies and do not participate in any game. None of the ladies plays chess or football. There is a married couple in which $T$ is the husband. $Q$ is the brother of $R$ and is neither a chess player nor a hockey player. Who is the wife of $T$?

$(i)$ 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 $G$?

$(i)$ 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 statements is true in the context of the above sitting arrangements?

In a pile of $10$ books,there are $3$ History,$3$ Hindi,$2$ Mathematics,and $2$ English books. From the top,an English book is between a History and a Mathematics book,a History book is between a Mathematics and an English book,a Hindi book is between an English and a Mathematics book,a Mathematics book is between two Hindi books,and two Hindi books are between a Mathematics and a History book. Which subject book is at the $6^{th}$ position from the top?

$(i)$ Kailash,Govind and Harinder are intelligent.
$(ii)$ Kailash,Rajesh and Jitendra are hard-working.
$(iii)$ Rajesh,Harinder and Jitendra are honest.
$(iv)$ Kailash,Govind and Jitendra are ambitious.
Which of the following persons is neither hard-working nor ambitious?