There is a group of five persons $A, B, C, D$ and $E$. In the group,there is 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. Which of the following groups includes all the men?

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?

$A$ 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 precedes Mechanics?

$(i)$ $P, Q, R, S, T$ 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 a paying guest $(PG)$ 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 a $PG$.
$(v)$ $T$ 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 subject does $Q$ study?

At the end of a cricket series,when five players were arranged in the ascending order of runs scored by them,$O$ was fourth while $N$ was first. When they were arranged in descending order for wickets taken by them,$K$ replaces $O$ while $O$ replaces $L$. $M$'s position remains unchanged. $K$ has scored more runs than $M$. $L$ is having first rank in one ranking and fifth in another.
Who has taken the lowest number of wickets?

$(i)$ Eight persons $E, F, G, H, I, J, K$ and $L$ are seated around a square table,two on each side.
$(ii)$ There are three lady members and they are not seated next to each other.
$(iii)$ $J$ is between $L$ and $F$.
$(iv)$ $G$ is between $I$ and $F$.
$(v)$ $H$,a lady member,is second to the left of $J$.
$(vi)$ $F$,a male member,is seated opposite $E$,a lady member.
$(vii)$ There is a lady member between $F$ and $I$.
Who among the following is to the immediate left of $F$?