MCQ
Solve $\sin \left(\tan ^{-1} x\right),|x|<1$ is equal to
- A$\frac{1}{\sqrt{1+x^{2}}}$
- B$\frac{1}{\sqrt{1-x^{2}}}$
- ✓$\frac{x}{\sqrt{1+x^{2}}}$
- D$\frac{x}{\sqrt{1-x^{2}}}$
Let $\tan ^{-1} x=y .$ Then
$y=\sin ^{-1}\left(\frac{x}{\sqrt{1+x^{2}}}\right)$ $\Rightarrow \tan ^{-1} x=\sin ^{-1}\left(\frac{x}{\sqrt{1+x^{2}}}\right)$
$\Rightarrow \sin \left(\tan ^{-1} x\right)=\sin \left(\sin ^{-1}\left(\frac{x}{\sqrt{1+x^{2}}}\right)\right)=\frac{x}{\sqrt{1+x^{2}}}$
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| $x_i$ | $0$ | $1$ | $5$ | $6$ | $10$ | $12$ | $17$ |
| $f_i$ | $3$ | $2$ | $3$ | $2$ | $6$ | $3$ | $3$ |
$P$ (computer turns out to be defective given that it is produced in plant $T_1$ )
$=10 P\left(\right.$ computer turns out to be defective given that it is produced in plant $\left.T_2\right)$,
where $P(E)$ denotes the probability of an event $E$. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant $T_2$ is