How many days of gap are there between Science and Philosophy?

$1.$ There is a group of six persons $A, B, C, D, E$ and $F$ from a family. They are Professor,Manager,Lawyer,Jeweller,Doctor and Engineer.
$2.$ The Doctor is the grandfather of $F$ who is a Professor.
$3.$ The Manager $D$ is married to $A.$
$4.$ $C,$ the Jeweller is married to the Lawyer.
$5.$ $B$ is the mother of $F$ and $E$.
$6.$ There are two married couples in the family.
Which of the following is one of the pairs of couples in the family?

Six persons $A, B, C, D, E$ and $F$ are sitting in two rows,three in each. $E$ is not at the end of any row.
$D$ is second to the left of $F$.
$C$,the neighbour of $E$,is sitting diagonally opposite to $D$.
$B$ is the neighbour of $F$.
Who is facing $B$?

Seven executives $P, Q, R, S, T, U$ and $W$ reach office in a particular sequence. $U$ reaches immediately before $P$ but does not immediately follow $S$. $R$ is the last one to reach office. $T$ follows immediately after $P$ and is subsequently followed by $W$. Among the executives,who reaches the office first?

$(i)$ $P, Q, R, S, T$ 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 pairs of students stay one each at a hostel and at home?

There are five friends $-$ Sachin,Kunal,Mohit,Anuj,and Rohan.
Sachin is shorter than Kunal but taller than Rohan.
Mohit is the tallest.
Anuj is a little shorter than Kunal and a little taller than Sachin.
If they stand in the order of increasing heights,who will be the second?