Raman ranks sixteenth from the top and forty-ninth from the bottom in a class. How many students are there 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.
On which day$(s)$ of a week,the youngest and the eldest brothers are available at home at the same time?

Some boys are sitting in a row. $P$ is sitting fourteenth from the left and $Q$ is seventh from the right. If there are four boys between $P$ and $Q,$ how many boys are there in the row?

$(I)$ 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.
On which day of the week are all three brothers available at home at the same time?

If $3^{rd}$ December,$1990$ is Sunday,what day is $3^{rd}$ January,$1991$?

In a queue of children,Kashish is fifth from the left and Mona is sixth from the right. When they interchange their places among themselves,Kashish becomes thirteenth from the left. Now what will be Mona's position from the right (in $^{th}$)?