How many numbers from $11$ to $50$ are there which are exactly divisible by $7$ but not by $3$?

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

How many numbers from $11$ to $50$ are there which are exactly divisible by $7$ but not by $3$?

Nitin was counting down from $32$. Sumit was counting upwards starting from $1$ and he was calling out only the odd numbers. What common number will they call out at the same time if they were calling out at the same speed?

$(I)$ 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?

$M$ is older than $R$. $Q$ is younger than $R$ and $N$. $N$ is not as old as $M$. Who among $M, N, R$,and $Q$ is the oldest?