$A, B, C, D, E,$ and $F$ (not necessarily in that order) are sitting in $6$ chairs regularly placed around a round table. It is observed that:
$1$. $A$ is between $D$ and $F$.
$2$. $C$ is opposite to $D$.
$3$. $D$ and $E$ are not on neighbouring chairs.
Which one of the following must be true?

Five men $A, B, C, D$ and $E$ read a newspaper. The one who reads first gives it to $C.$ The one who reads last had taken from $A. E$ was not the first or last to read. There were two readers between $B$ and $A.$ Who read the newspaper last?

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 Psychology?

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?

$1.$ There are five friends: Sonal,Ratheesh,Manoj,Ashok,and Gireesh.
$2.$ Sonal is shorter than Ratheesh but taller than Gireesh.
$3.$ Manoj is the tallest.
$4.$ Ashok is a little shorter than Ratheesh and a little taller than Sonal.
If they stand in the order of increasing heights,who will be the second?

The sum of the incomes of $A$ and $B$ is more than that of $C$ and $D$ taken together. The sum of incomes of $A$ and $C$ is the same as that of $B$ and $D$ taken together. Moreover,$A$ earns half as much as the sum of the incomes of $B$ and $D$. If $A$'s income is $Rs\, 80,000$ per annum and the difference between the income of $B$ and $D$ is the same as $A$'s income,what is $B$'s income?