MCQ
$\tan \left[ {2{{\tan }^{ - 1}}\left( {\frac{1}{5}} \right) - \frac{\pi }{4}} \right] = $
- A$\frac{{17}}{7}$
- B$ - \frac{{17}}{7}$
- C$\frac{7}{{17}}$
- ✓$ - \frac{7}{{17}}$
$ = \tan \left[ {{{\tan }^{ - 1}}\frac{5}{{12}} - {{\tan }^{ - 1}}(1)} \right] = \tan {\tan ^{ - 1}}\left( {\frac{{\frac{5}{{12}} - 1}}{{1 + \frac{5}{{12}}}}} \right) = - \frac{7}{{17}}$.
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| Column $I$ | Column $II$ |
| $(A)$ $\int_{-1}^1 \frac{\mathrm{dx}}{1+\mathrm{x}^2}$ | $(p)$ $\frac{1}{2} \log \left(\frac{2}{3}\right)$ |
| $(B)$ $\int_0^1 \frac{\mathrm{dx}}{\sqrt{1-\mathrm{x}^2}}$ | $(q)$ $2 \log \left(\frac{2}{3}\right)$ |
| $(C)$ $\int_2^3 \frac{\mathrm{dx}}{1-\mathrm{x}^2}$ | $(r)$ $\frac{\pi}{3}$ |
| $(D)$ $\int_1^2 \frac{d x}{x \sqrt{x^2-1}}$ | $(s)$ $\frac{\pi}{2}$ |