The Managing Director entered the conference room $10 \, \text{minutes}$ before $12:30 \, \text{hours}$ for interviewing. He came $20 \, \text{minutes}$ before the chairman who was $30 \, \text{minutes}$ late. At what time was the interview scheduled?

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

$A$ monkey climbs $30$ feet at the beginning of each hour and rests for a while,during which he slips back $20$ feet before he again starts climbing at the beginning of the next hour. If he begins his ascent at $8:00 \, a.m.$,at what time will he first touch a flag at $120$ feet from the ground?

Abhishek ranks thirteenth in a class of thirty-one students. What is his rank from the last (in $19^{th}$)?

$(I)$ 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?

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