If $f: R \to R$,then the range of the function $f(x) = \frac{x^2}{x^2 + 1}$ is

Set $A$ has $m$ elements and Set $B$ has $n$ elements. If the total number of subsets of $A$ is $112$ more than the total number of subsets of $B$,then the value of $m \times n$ is

$A$ survey shows that $63\%$ of the Americans like cheese whereas $76\%$ like apples. If $x\%$ of the Americans like both cheese and apples,then

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

The relation $R$ defined on the set of natural numbers as $\{(a, b) : a\}$ differs from $b$ by $\{3\}$,is given by

Consider the two sets:
$A = \{m \in R : \text{both the roots of } x^{2} - (m+1)x + m+4 = 0 \text{ are real}\}$ and $B = [-3, 5)$.
Which of the following is not true?