How many $7$s are there in the following series which are immediately preceded by $6$ but not immediately followed by $4$?
$7, 4, 2, 7, 8, 4, 3, 6, 7, 5, 3, 5, 7, 8, 4, 3, 7, 6, 7, 2, 4, 0, 6, 7, 4, 3$

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

Among $B, F, J, K$ and $W$ each having a different weight, $F$ is heavier than only $J.$ $B$ is heavier than $F$ and $W$ but not as heavy as $K.$ Who is the third heaviest among them?

If Thursday was the day after the day before yesterday five days ago, what is the least number of days ago when Sunday was three days before the day after tomorrow?

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

Ashish leaves his house at $20 \text{ minutes}$ to seven in the morning,reaches Kunal's house in $25 \text{ minutes}$,they finish their breakfast in another $15 \text{ minutes}$ and leave for their office which takes another $35 \text{ minutes}$. At what time do they leave Kunal's house to reach their office?