MCA Entrance Previous Year Question Bank

The value of the expression $50\tan \left(3{\tan }^{-1}\left(\frac{1}{2}\right)+2{\cos }^{-1}\left(\frac{1}{\sqrt{5}}\right)\right)+4\sqrt{2}\tan \left(\frac{1}{2}{\tan }^{-1}(2\sqrt{2})\right)$ is equal to:

Let $(a,b)\subset (0,2\pi )$ be the largest interval for which \sin^{-1}(\sin \theta) - \cos^{-1}(\sin \theta) > 0, \theta \in (0, 2\pi), holds. If $\alpha x^2+\beta x+{\sin }^{-1}(x^2-6x+10)+{\cos }^{-1}(x^2-6x+10)=0$ and $\alpha -\beta =b-a$, then $\alpha$ is equal to:

Let $a_1=1,a_2,a_3,a_4,\dots$ be consecutive natural numbers. Then ${\tan }^{-1}\left(\frac{1}{1+a_1{a}_2}\right)+{\tan }^{-1}\left(\frac{1}{1+a_2{a}_3}\right)+\cdots +{\tan }^{-1}\left(\frac{1}{1+a_{2021}{a}_{2022}}\right)$ is equal to:

If the sum of all the solutions of \tan^{-1} \left( \frac{2x}{1-x^2} \right) + \cot^{-1} \left( \frac{1-x^2}{2x} \right) = \frac{\pi}{3}, \quad -1 < x < 1, \quad x \neq 0 is $\alpha -\frac{4}{\sqrt{3}}$, then $\alpha$ is equal to:

If the domain of the function $f(x)={\sec }^{-1}\left(\frac{2x}{5x+3}\right)$ is $[\alpha ,\beta )\cup (\gamma ,\delta ]$, then $|3\alpha +10(\beta +\gamma )+21\delta |$ is equal to ____.

Using the principal values of the inverse trigonometric functions the sum of the maximum and the minimum values of 16((sec^–1x)² + (cosec^–1x)²) is: