- A$p + q$
- B$p + q + 1$
- ✓$pq$
- D${p^2}$
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Let $E_2=E_1-S_1$ and $F_2=F_1 \cup S_1$. Now two elements are chosen at random, without replacement, from the set $F_2$ and let $S_2$ denote the set of these chosen elements.
Let $G _2= G _1 \cup S _2$. Finally, two elements are chosen at random, without replacement, from the set $G _2$ and let $S _3$ denote the set of these chosen elements.
Let $E_3=E_2 \cup S_3$. Given that $E_1=E_3$, let $p$ be the conditional probability of the event $S_1=\{1,2\}$. Then the value of $p$ is
$f( x )=\frac{ x ^2-3 x -6}{ x ^2+2 x +4} \text {. }$
Then which of the following statements is (are) $TRUE$ ?
$(A)$ $f$ is decreasing in the interval $(-2,-1)$
$(B)$ $f$ is increasing in the interval $(1,2)$
$(C)$ $f$ is onto
$(D)$ Range of $f$ is $\left[-\frac{3}{2}, 2\right]$