In a March Past,seven persons are standing in a row. $Q$ is standing left to $R$ but right to $P$. $O$ is standing right to $N$ and left to $P$. Similarly,$S$ is standing right to $R$ and left to $T$. Find out who is standing in the middle.

$(i)$ 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?

$A$ 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 will be on Tuesday?

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

Prashant Arora has three children $-$ Sangeeta,Vimal and Ashish. Ashish married Monika,the eldest daughter of Mr. and Mrs. Roy. The Roys married their youngest daughter to the eldest son of Mr. and Mrs. Sharma,and they had two children named Amit and Shashi. The Roys have two more children,Roshan and Vandana,both elder to Veena. Sameer and Ajay are sons of Ashish and Monika. Rashmi is the daughter of Amit.
How is Mrs. Roy related to Ashish?

$(i)$ There are seven books,one each on Psychology,Hindi,English,Sociology,Economics,Education,and Accountancy,lying on a table one above the other.
$(ii)$ Sociology is on the top of all the books.
$(iii)$ Accountancy is immediately below Education,which is immediately below Sociology.
$(iv)$ Economics is immediately above Psychology but not in the middle.
$(v)$ Hindi is immediately below Psychology.
Economics is between which of the following books?