The number of $4$-digit numbers that are less than or equal to $2800$ and are either divisible by $3$ or by $11$ is equal to $............$.

Consider a three-digit number $N = 100x + 10y + z$,where $x, y, z$ are the digits at the hundreds,tens,and units places respectively. The number satisfies the following properties:
$I$. If its digits in the units place and tens place are interchanged,the number increases by $36$.
$II$. If its digits in the units place and hundreds place are interchanged,the number decreases by $198$.
If the digits in the tens place and hundreds place are interchanged,then the number:

If $n(U) = 600$,$n(A) = 100$,$n(B) = 200$,and $n(A \cap B) = 50$,then $n(\bar{A} \cap \bar{B})$ is: ($U$ is the universal set and $A$ and $B$ are subsets of $U$)

The sum of the integers from $1$ to $100$ which are not divisible by $3$ or $5$ is

In a class of $60$ students,$25$ students play cricket and $20$ students play tennis,and $10$ students play both the games. The number of students who play neither is:

$A$ certain $12$-hour digital clock displays the hour and the minute of a day. Due to a defect in the clock,whenever the digit $1$ is supposed to be displayed,it displays $7$. What fraction of the day will the clock show the correct time?