MCQ
$\tan \left(2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{\sqrt{5}}{2}+2 \tan ^{-1} \frac{1}{8}\right)$ is equal to.
- A$1$
- ✓$2$
- C$\frac{1}{4}$
- D$\frac{5}{4}$
$=\tan \left[2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{2}\right)\right]$
$=2$
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| Column $I$ | Column $II$ |
| $(A)$ Interval contained in the domain of definition of non-zero solutions of the differential equation $(x-3)^2 y^{\prime}+y=0$ | $(p)$ $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ |
|
$(B)$ Interval containing the value of the integral $\int_1^5(x-1)(x-2)(x-3)(x-4)(x-5) d x$ |
$(q)$ $\left(0, \frac{\pi}{2}\right)$ |
| $(C)$ Interval in which at least one of the points of local maximum of $\cos ^2 x+\sin x$ lies | $(r)$ $\left(\frac{\pi}{8}, \frac{5 \pi}{4}\right)$ |
| $(D)$ Interval in which $\tan ^{-1}(\sin x+\cos x)$ is increasing | $(s)$ $\left(0, \frac{\pi}{8}\right)$ |
| $(t)$ $(-\pi, \pi)$ |