If $U = \{a, b, c, d, e, f\}$ and $A = \{a, b, c\}$,find $(U \cup A^{\prime})$.

In a school,$20$ teachers teach either mathematics or physics. If $12$ of them teach mathematics and $4$ teach both subjects,then the number of teachers teaching physics is:

In an examination,$30 \%$ of the total students failed in Hindi,$45 \%$ failed in English,and $20 \%$ failed in both the subjects. Find the percentage of those who passed in both the subjects. (in $\%$)

Let $A = \{1, 2, \{3, 4\}, 5\}$. Which of the following statements are true?

Range of the function $f(x) = \frac{1}{2 - \sin 3x}$ is

Let $f:R \to R$ be defined by $f(x) = 2x + |x|$,then $f(2x) + f(-x) - f(x) = $