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

$(I)$ 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?

Sangeeta remembers that her father's birthday was certainly after $8^{th}$ but before $13^{th}$ of December. Her sister Natasha remembers that their father's birthday was definitely after $9^{th}$ but before $14^{th}$ of December. On which date of December was their father's birthday?

Manisha ranked sixteenth from the top and twenty-ninth from the bottom among those who passed an examination. Six boys did not participate in the competition and five failed in it. How many boys were there in the class?

If the $25^{th}$ of August in a year is Thursday,the number of Mondays in that month is

$A$ number is greater than $3$ but less than $8.$ Also,it is greater than $6$ but less than $10.$ The number is