There are four friends $A, B, C, D$. One of them is a cricketer and studies Chemistry and Biology. $A$ and $B$ play football. Both football players study Maths. $D$ is a boxer. One football player also studies Physics. The boxer studies Maths and Accounts. All the friends study two subjects each and play one game each. Who is the cricketer?

$(i)$ 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.
Which of the following combinations is true for $S$?

$A$ group of eight members sit in a circle. $D$ is between $A$ and $F$ and is opposite to $G$. $E$ is to the right of $A$ but on the left of $C$,whose right-hand neighbor is $G$. $B$ enjoys having $H$ to his left and $F$ to his right. Find the member who is diagonally opposite to $A$.

$(i)$ $A, B, C, D, E, F$ and $G$ are sitting on a wall and all of them are facing east.
$(ii)$ $C$ is on the immediate right of $D$.
$(iii)$ $B$ is at an extreme end and has $E$ as his neighbour.
$(iv)$ $G$ is between $E$ and $F$.
$(v)$ $D$ is sitting third from the south end.
Which of the conditions $(i)$ to $(v)$ given above is not required to find out the place in which $D$ is sitting?

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 city is a hill station and an industrial centre but not a historical place?

There are six persons $A, B, C, D, E$ and $F$ in a school. Each of the teachers teaches two subjects,one compulsory subject and the other optional subject. $D$'s optional subject was History while three others have it as a compulsory subject. $E$ and $F$ have Physics as one of their subjects. $F$'s compulsory subject is Mathematics,which is an optional subject of both $C$ and $E$. History and English are $A$'s subjects,but in terms of compulsory and optional subjects,they are the reverse of those of $D$. Chemistry is an optional subject of only one of them. The only female teacher in the school has English as her compulsory subject. Which of the following groups has History as the compulsory subject?