$A, B, C, D, E,$ and $F$ (not necessarily in that order) are sitting in $6$ chairs regularly placed around a round table. It is observed that:
$1$. $A$ is between $D$ and $F$.
$2$. $C$ is opposite to $D$.
$3$. $D$ and $E$ are not on neighbouring chairs.
Which one of the following must be true?

$(i)$ Five friends $P, Q, R, S$ and $T$ travelled to five different cities of Chennai,Calcutta,Delhi,Bangalore and Hyderabad by five different modes of transport of Bus,Train,Aeroplane,Car and Boat from Mumbai.
$(ii)$ The person who travelled to Delhi did not travel by boat.
$(iii)$ $R$ went to Bangalore by car and $Q$ went to Calcutta by aeroplane.
$(iv)$ $S$ travelled by boat whereas $T$ travelled by train.
$(v)$ Mumbai is not connected by bus to Delhi and Chennai.
Who among the following travelled to Delhi?

There are six cities $A, B, C, D, E$ and $F$. $A$ is not a hill station. $B$ and $E$ are not historical places. $D$ is not an industrial city. $A$ and $D$ are not historical cities. $A$ and $B$ are not alike. Which two cities are neither historical places nor industrial centres?

$(i)$ 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 honest nor hard-working but is ambitious?

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 $T$?

$(i)$ 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 $A$.
Who is to the right of $C$?