MCQ
The domain of the function $\text{f(x)}=\sqrt{2-2\text{x}-\text{x}^2}$ is:
- A$\big[-\sqrt{3},\sqrt{3}\big]$
- B$\big[-1,-\sqrt{3},-1+\sqrt{3}\big]$
- C$\big[-2,2\big]$
- D$\big[-2-\sqrt{3},-2+\sqrt{3}\big]$
Solution:
$\text{f(x)}=\sqrt{2-2\text{x}-\text{x}^2}$
Since,
$2-2\text{x}-\text{x}^2\geq0$$\text{x}^2+2\text{x}-2\leq0$
$\Rightarrow\text{x}^2-2\text{x}-2+1-1\leq0$
$\Rightarrow(\text{x}-1)^2-\big(\sqrt{3}\big)^2\leq0$
$\Rightarrow\big[\text{x}-\big(1-\sqrt{3}\big)\big]\big[\text{x}-\big(1+\sqrt{3}\big)\big]\leq0$
$\Rightarrow\big(-1-\sqrt{3}\big)\leq\text{x}\leq(-1+\sqrt{3})$
Thus, domain
$(\text{f})=\big[-1-\sqrt{3},-1+\sqrt{3}\big]$Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Choose the correct answer.
If A and B are mutually exclusive events, then:
Mean deviation for n observations x1, x2, ...... , xn from their mean x is given by:
$\sum\limits^{\text{n}}_{\text{i}=1}(\text{x}_\text{i}-\bar{\text{x}})$
$\frac{1}{\text{n}}\sum\limits^{\text{n}}_{\text{i}=1}|\text{x}_\text{i}-\bar{\text{x}}|$
$\sum\limits^{\text{n}}_{\text{i}=1}(\text{x}_\text{i}-\bar{\text{x}})^2$
$\frac{1}{\text{n}}\sum\limits^{\text{n}}_{\text{i}=1}(\text{x}_\text{i}-\bar{\text{x}})^2$