Let $X = \{n \in N : 1 \leq n \leq 50\}$. If $A = \{n \in X : n \text{ is a multiple of } 2\}$ and $B = \{n \in X : n \text{ is a multiple of } 7\}$,then the number of elements in the smallest subset of $X$ containing both $A$ and $B$ is

Given two finite sets $A$ and $B$ such that $n(A) = 2$ and $n(B) = 3$. Then,the total number of relations from $A$ to $B$ is:

If $A = \{2, 3, 5\}$ and $B = \{2, 5, 6\}$,then $(A - B) \times (A \cap B)$ is:

The function $f:R \to R$ is defined by $f(x) = \cos^2 x + \sin^4 x$ for $x \in R$,then $f(R) \in $

$A$ 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?

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: