Saiyeev ranks seventh from the top and twenty-eighth from the bottom in a class. How many students are there in the class?

Sajith ranked thirteenth from the top and twenty-sixth from the bottom among those who have passed in the annual examination in a class. If six students have failed in the annual examination, what was the total number of students in that class?

$(I)$ Kamal is available at home from $12$ noon to $4 \,p.m.$ on Tuesday,Thursday,and Sunday.
$(II)$ His younger brother Navin is available at home on Monday,Thursday,Friday,and Sunday between $10 \,a.m.$ to $2 \,p.m.$
$(III)$ The eldest brother Rajiv is available between $9 \,a.m.$ to $12$ noon on Monday,Wednesday,and Thursday and $2 \,p.m.$ to $4 \,p.m.$ on Friday,Saturday,and Sunday.
For how many days is only one brother available at a particular time in a week?

How many $18$s are there in the following sequence which are immediately preceded by $9$ but not immediately followed by $7$?
$7, 1, 9, 1, 1, 7, 1, 8, 9, 1, 7, 1, 2, 1, 3, 1, 4, 5, 7, 1, 3, 9, 1, 7$

In the series,$6, 4, 1, 2, 2, 8, 7, 4, 2, 1, 5, 3, 8, 6, 2, 1, 7, 1, 4, 1, 3, 2, 8, 6$,how many pairs of successive numbers have a difference of $2$ each?

Among $P,$ $Q,$ $R,$ $S,$ and $T,$ $S$ is older than $R$ but not as old as $T.$ $Q$ is older than only $P.$ Who among them is the youngest?