If $S$ and $T$ are two sets such that $S$ has $21$ elements,$T$ has $32$ elements,and $S \cap T$ has $11$ elements,how many elements does $S \cup T$ have?

The domain of the function $\sqrt{\log \left( \frac{5x - x^2}{6} \right)}$ is

Which of the following pairs of sets are not equivalent?

The number of elements in the set $\{ (a, b) : 2a^2 + 3b^2 = 35, a, b \in \mathbb{Z} \}$,where $\mathbb{Z}$ is the set of all integers,is

$A$ class has $175$ students. The following data shows the number of students obtaining one or more subjects: Mathematics $100$,Physics $70$,Chemistry $40$; Mathematics and Physics $30$,Mathematics and Chemistry $28$,Physics and Chemistry $23$; Mathematics,Physics and Chemistry $18$. How many students have offered Mathematics alone?

Domain of $f(x) = \log |\log x|$ is