Manoj and Sachin are ranked seventh and eleventh respectively from the top in a class of $31$ students. What will be their respective ranks from the bottom in the 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?

Sanal's position in a row is $12^{th}$ from the front side and $47^{th}$ from the back side. How many persons are standing in that row?

In the following list of numerals,how many $2$'s are followed by $1$'s but not preceded by $4$?

Ram remembers that Lakshman's birthday is after $19^{th}$ but before $22^{nd}$ November,whereas Anil remembers that Lakshman's birthday is after $20^{th}$ but before $24^{th}$ November. Which day is Lakshman's birthday?

How many $8$s are there in the following number sequence which are preceded by $7$ but not immediately followed by $4$?
$2, 3, 8, 2, 5, 7, 8, 3, 7, 8, 4, 6, 9, 8, 4, 3, 2, 7, 8, 9, 5, 7, 8, 1, 5, 2, 9$