The range of $f(x) = \sec \left( \frac{\pi}{4} \cos^2 x \right)$ for $-\infty < x < \infty$ is

Let $A = \{1, 2, 3, 4, 5\}$ and $B = \{2, 3, 6, 7\}$. Then the number of elements in $(A \times B) \cap (B \times A)$ is

If $f(x) = \cos([\pi^2]x) + \cos([- \pi^2]x)$,then which of the following is true?

Let $U = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}$,$A = \{ 1, 2, 5 \}$,and $B = \{ 6, 7 \}$. Then $A \cap B'$ is:

In a class of $100$ students, the number of students who passed in English only is $46$, in Maths only is $46$, and in Commerce only is $58$. The number of students who passed in English and Maths is $16$, in Maths and Commerce is $24$, and in English and Commerce is $26$. The number of students who passed in all three subjects is $7$. Find the number of students who failed in all the subjects.

In a class of $100$ students,$55$ students have passed in Mathematics and $67$ students have passed in Physics. Then the number of students who have passed in Physics only is