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 $U$)

Out of $100$ students in a class,$55$ passed in Mathematics and $67$ passed in Physics. The number of students who passed only in Physics is:

The number of $3$-digit numbers that are divisible by either $2$ or $3$ but not divisible by $7$ is $.........$.

In a college of $300$ students,every student reads $5$ newspapers and every newspaper is read by $60$ students. The number of newspapers is:

Let $S = \{1, 2, 3, 5, 7, 10, 11\}$. The number of nonempty subsets of $S$ such that the sum of all elements is a multiple of $3$ 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?