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:

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

Let $Z$ be the set of integers. If $A = \{ x \in Z : 2^{(x + 2)(x^2 - 5x + 6)} = 1 \}$ and $B = \{ x \in Z : -3 < 2x - 1 < 9 \}$,then the number of subsets of the set $A \times B$ 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 group of $50$ people, $35$ speak Hindi, $25$ speak both Hindi and English, and all the people speak Hindi or English or both. The number of people who speak English only is

There are $80$ families in a small extension area. $20$ percent of these families own a car each. $50$ percent of the remaining families own a motor cycle each. How many families in that extension do not own any vehicle?