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:

Let $A_1, A_2, \ldots, A_m$ be non-empty subsets of $\{1, 2, 3, \ldots, 100\}$ satisfying the following conditions:
$1.$ The numbers $|A_1|, |A_2|, \ldots, |A_m|$ are distinct.
$2.$ $A_1, A_2, \ldots, A_m$ are pairwise disjoint.
(Here $|A|$ denotes the number of elements in the set $A$).
Then,the maximum possible value of $m$ is:

The lengths of the sides and the diagonal of an isosceles trapezium form a two-element set $\{a, b\}$. If $a > b$,then $a / b$ equals

In a group of students,$100$ students know Hindi,$50$ know English,and $25$ know both. Each student knows either Hindi or English. How many students are there in the group?

$2n(A \setminus B) = n(B \setminus A)$ and $5n(A \cap B) = n(A) + 3n(B)$,where $P \setminus Q = P \cap Q^C$. If $n(A \cup B) \leq 10$,then the value of $\frac{n(A) \cdot n(B) \cdot n(A \cap B)}{8}$ is:

If $X$ and $Y$ are two sets such that $X$ has $40$ elements,$X \cup Y$ has $60$ elements and $X \cap Y$ has $10$ elements,how many elements does $Y$ have?