The solution set of inequality ( ^ - 1 x ) ( ^ - 1 x ) - ( ^ - 1 … - Vidyadip

MCQ

The solution set of inequality $\left( {{{\tan }^{ - 1}}x} \right)\left( {{{\cot }^{ - 1}}x} \right) - \left( {{{\tan }^{ - 1}}x} \right)\left( {1 + \frac{\pi }{2}} \right) - 2{\cot ^{ - 1}}x + 2\left( {1 + \frac{\pi }{2}} \right)\,$$ > \mathop {\lim }\limits_{x \to \infty } \left[ {{{\sec }^{ - 1}}x - \frac{\pi }{2}} \right]\,$ is (where [.] denotes the greatest integer function)

A
$(tan\ 1, tan\ 2)$
B
$(-cot\ 1, cot \ 2)$
✓
$(-tan\ 1, tan\ 2)$
D
$(-tan\ 1, \infty)$

✓

Answer

Correct option: C.

$(-tan\ 1, tan\ 2)$

c
$\left(\tan ^{-1} x-2\right)\left(\cot ^{-1} x-1-\frac{\pi}{2}\right)>0$

$\Rightarrow\left(\tan ^{-1} x+1\right)\left(\tan ^{-1} x-2\right)<0$

$\Rightarrow-1<\tan ^{-1} x<2$

$ \Rightarrow - \tan 1 < x < \tan 2$

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

Explore more

More "M.C.Q (1 Marks)" from 2. inverse trigonometric function→2. inverse trigonometric function — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

A five-digit number is written down at raddom. The probability that the number is divisible by 5, and no two consecutive digits are identical, is:

$\frac{1}{5}$
$\frac{1}{5}\big(\frac{9}{10}\big)^3$
$\big(\frac{3}{5}\big)^4$
$\text{None of these}$

If $\overrightarrow {AO} + \overrightarrow {OB} = \overrightarrow {BO} + \overrightarrow {OC} ,$ then $A, B, C$ form

Suppose the vectors $x_{1}, x_{2}$ and $x_{3}$ are the solutions of the system of linear equations, $Ax = b$ when the vector $b$ on the right side is equal to $b _{1}, b _{2}$ and $b _{3}$ respectively. If $x =\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right], x _{2}=\left[\begin{array}{l}0 \\ 2 \\ 1\end{array}\right], x _{3}=\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right], b _{1}=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ $b _{2}=\left[\begin{array}{l}0 \\ 2 \\ 0\end{array}\right]$ and $b _{3}=\left[\begin{array}{l}0 \\ 0 \\ 2\end{array}\right],$ then the determinant of $A$ is equal to

The position of the points $\mathrm{O}(0,0)$ and $\mathrm{P}(2,-1)$ is $\ldots \ldots . .,$ in the region of the inequality $2 y-3 x\,<\,5$

The projections of a line on the co-ordinate axes are $4, 6, 12$. The direction cosines of the line are

If $f\left( x \right) = \left[ x \right] - \left[ {\frac{x}{4}} \right],\,x \in R$ , where $[x]$ denotes the greatest integer function, then

Choose the correct answer
If $\theta$ is the angle between two vectors $\vec{\text{a}}\ \text{and}\ \vec{\text{b}},\ \text{then}\ \vec{\text{a}}\cdot\vec{\text{b}}\geq0$ only when,

$0<\theta<\frac{\pi}{2}$
$0\leq\theta\leq\frac{\pi}{2}$
$0<\theta<\pi$
$0\leq\theta\leq\pi$

Maximize Z = 6x + 4y, subject to $\text{x}\leq2,\text{x}+\text{y}\leq3,-2\text{x}+\text{y}\leq1,\text{x}\geq0,\text{y}\geq0.$

12 at (2, 0)
16 at (2, 1)
$\frac{140}{3}$ at $\Big(\frac{2}{3},\frac{1}{3}\Big)$
4 at (0, 1)

The interval on which the function f(x) = 2x³ + 9x² + 12x - 1 is decreasing is:

The differential coefficient of ${\tan ^{ - 1}}\left( {{{\sqrt {1 + {x^2}} - 1} \over x}} \right)$ with respect to ${\tan ^{ - 1}} x$ is