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.
The three ladies are

$(i)$ 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 of person and mode is not correct?

In a car exhibition,seven cars of seven different companies viz. Cardilac,Ambassador,Fiat,Maruti,Mercedes,Bedford and Fargo were displayed in a row,facing east such that:
$(1)$ Cardilac car was to the immediate right of Fargo.
$(2)$ Fargo was fourth to the right of Fiat.
$(3)$ Maruti car was between Ambassador and Bedford.
$(4)$ Fiat,which was third to the left of Ambassador car,was at one of the ends.
Which of the following is definitely true?

There is a group of five persons $A, B, C, D$ and $E$. In the group,there are a Professor of Philosophy,a Professor of Psychology,and a Professor of Economics. $A$ and $D$ are ladies who have no specialization in any subject and are unmarried. No lady is a philosopher or an economist. There is a married couple in the group of which $E$ is the husband. $B$ is the brother of $C$ and is neither a psychologist nor an economist. Who is the Professor of Economics?

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?

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 second tallest?