MCQ
If $\sin x + \cos x = \frac{1}{5},$ then $\tan 2x$ is
- A$\frac{{25}}{{17}}$
- B$\frac{{7}}{{25}}$
- C$\frac{{25}}{7}$
- ✓$\frac{{24}}{7}$
==> ${\sin ^2}x + {\cos ^2}x + 2\sin x\cos x = \frac{1}{{25}}$
$\sin 2x = \frac{{ - 24}}{{25}}$
==> $\cos 2x = \frac{{ - 7}}{{25}}$
==> $\tan 2x = \frac{{24}}{7}$.
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| $\mathrm{x}$ | $-2$ | $-1$ | $3$ | $4$ | $6$ |
| $\mathrm{P}(\mathrm{X}=\mathrm{x})$ | $\frac{1}{5}$ | $\mathrm{a}$ | $\frac{1}{3}$ | $\frac{1}{5}$ | $\mathrm{~b}$ |
If the mean of $X$ is $2.3$ and variance of $X$ is $\sigma^{2}$, then $100 \sigma^{2}$ is equal to :