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

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.

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

If the sets $A$ and $B$ are defined as $A = \{ (x, y) : y = e^x, x \in R \}$ and $B = \{ (x, y) : y = x, x \in R \}$,then

$A - (A - B)$ is equal to:

If $A = \{a, d\}, B = \{b, c, e\}$ and $C = \{b, c, f\},$ then $A \times (B \cup C) =$