Given the following information:
$(A)$ Gopal is shorter than Ashok but taller than Kunal;
$(B)$ Navin is shorter than Kunal;
$(C)$ Jayesh is taller than Navin;
$(D)$ Ashok is taller than Jayesh.
Which of the given statements is not necessary to determine the relative heights of all individuals?

$1.$ 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 left of $B$?

$Mr. A, Miss B, Mr. C$ and $Miss D$ are sitting around a table and discussing their trades.
$(1)$ $Mr. A$ sits opposite to the cook.
$(2)$ $Miss B$ sits to the right of the barber.
$(3)$ The washerman is on the left of the tailor.
$(4)$ $Miss D$ sits opposite $Mr. C$.
What are the trades of $A$ and $B$?

There are five different houses,$A$ to $E$,in a row. $A$ is to the right of $B$,and $E$ is to the left of $C$ and right of $A$. $B$ is to the right of $D$. Which of the houses is in the middle?

$(i)$ $P, Q, R, S, T$ and $U$ are six students pursuing their Master's degree in six different subjects $-$ English,History,Philosophy,Physics,Statistics and Mathematics.
$(ii)$ Two of them stay in a hostel,two stay as paying guests $(PG)$ and the remaining two stay at their home.
$(iii)$ $R$ does not stay as a $PG$ and studies Philosophy.
$(iv)$ The students studying Statistics and History do not stay as $PG$.
$(v)$ $T$ studies Mathematics and $S$ studies Physics.
$(vi)$ $U$ and $S$ stay in a hostel. $T$ stays as a $PG$ and $Q$ stays at home.
Which of the following combinations of subject and place of stay is not correct?

$(i)$ 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?