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}}$

Answer

Correct option: D.
$ - \frac{7}{{17}}$
d
(d) $\tan \left[ {2{{\tan }^{ - 1}}\left( {\frac{1}{5}} \right) - \frac{\pi }{4}} \right] = \tan \left[ {{{\tan }^{ - 1}}\frac{{\frac{2}{5}}}{{1 - \frac{1}{{25}}}} - {{\tan }^{ - 1}}(1)} \right]$

$ = \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}}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

If $P(\operatorname{Not} A)=3 / 5$, then the value of $P(A)$ will be
The cosines of the angle between any two diagonals of a cube is:
Let $A$ and $B$ be two points on the line $\frac{x}{1} = \frac{y}{1} = \frac{z}{{ - 1}}$. If distance of point $P(1, 1,1.)$ from the points $A$ and $B$ is $\sqrt 3$ then distance between $A$ and $B$ is
Let $f : (-1, 1) \to R$ be a function defined by $f\left( x \right) = \left\{ { - \left| x \right|, - \sqrt {1 - {x^2}} } \right\}$. if $K$ be the set of all points at which $f$ is not differentiable, then $K$ has exactly
If $\text{A}=\begin{bmatrix}\text{n}&0&0\\0&\text{n}&0\\0&0&\text{n}\end{bmatrix}$ and $\text{B}=\begin{bmatrix}\text{a}_1&\text{a}_2&\text{a}_3\\\text{b}_1&\text{b}_2&\text{b}_3\\\text{c}_1&\text{c}_2&\text{c}_3\end{bmatrix},$ then AB is equal to:
  1. B
  2. nB
  3. Bn
  4. A + B
A body moves according to the formula $v = 1 + {t^2}$, where $v$ is the velocity at time $ t.$ The acceleration after $ 3$ sec will be .......... $cm/{\sec ^2}$. ($v$ in $cm/sec$)
Match the integrals in Column $I$ with the values in Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
Column $I$ Column $II$
$(A)$ $\int_{-1}^1 \frac{\mathrm{dx}}{1+\mathrm{x}^2}$ $(p)$ $\frac{1}{2} \log \left(\frac{2}{3}\right)$
$(B)$ $\int_0^1 \frac{\mathrm{dx}}{\sqrt{1-\mathrm{x}^2}}$ $(q)$ $2 \log \left(\frac{2}{3}\right)$
$(C)$ $\int_2^3 \frac{\mathrm{dx}}{1-\mathrm{x}^2}$ $(r)$ $\frac{\pi}{3}$
$(D)$ $\int_1^2 \frac{d x}{x \sqrt{x^2-1}}$ $(s)$ $\frac{\pi}{2}$
Which of the following is not a vector quantity:
  1. Speed
  2. Density
  3. Force
  4. Velocity
If $y=e^{3 x+7}$, then the value of $\left[\frac{d y}{d x}\right]_{x=0}$ is equal to
The rate of growth of bacteria in a culture is proportional to the number of bacteris present and the bacteria count is $1000$ at initial time $t =0 .$ The number of bacteria is increased by $20 \%$ in $2$ hours. If the population of bacteria is $2000$ after $\frac{ k }{\log _{ e }\left(\frac{6}{5}\right)}$ hours, then $\left(\frac{ k }{\log _{ c } 2}\right)^{2}$ is equal to