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 historical places?

$(i)$ 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?

$1.$ Six friends $A, B, C, D, E$ and $F$ are sitting in a closed circle facing the centre.
$2.$ $E$ is to the left of $D$.
$3.$ $C$ is between $A$ and $B$.
$4.$ $F$ is between $E$ and $A$.
Who is to the right of $C$?

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 was the correct position of the Mercedes?

$A$ training college has to conduct a refresher course for teachers of seven different subjects: Mechanics,Psychology,Philosophy,Sociology,Economics,Science,and Engineering from $22^{nd}$ July to $29^{th}$ July.
$1.$ The course should start with Psychology.
$2.$ $23^{rd}$ July,being Sunday,should be a holiday.
$3.$ Science subject should be on the previous day of the Engineering subject.
$4.$ The course should end with Mechanics.
$5.$ Philosophy should be immediately after the holiday.
$6.$ There should be a gap of one day between Economics and Engineering.
Which subject is followed by Science?

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 $F$?