If 2 and a b A A b a éù é ù a b = = êú ê ú ëû ë û b a , then

Question:

If $A=\left[\begin{array}{ll}a & b \\ b & a\end{array}\right]$ and $A^{2}=\left[\begin{array}{cc}\alpha & \beta \\ \beta & \alpha\end{array}\right]$, then

  1. $\alpha=2 a b, \beta=a^{2}+b^{2}$

  2. $\alpha=a^{2}+b^{2}, \beta=a b$

  3. $\alpha=a^{2}+b^{2}, \beta=2 a b$

  4. $\alpha=a^{2}+b^{2}, \beta=a^{2}-b^{2}$.


Correct Option: 3

JEE Main Previous Year 1 Question of JEE Main from Mathematics Inverse Trigonometric Functions chapter.
JEE Main Previous Year 2005

Solution:

Related Questions

  • If $\alpha=\cos ^{-1}\left(\frac{3}{5}\right), \beta=\tan ^{-1}\left(\frac{1}{3}\right)$, where $0<\alpha, \beta<\frac{\pi}{2}$, then $\alpha-\beta$ is equal to:

    View Solution

  • A value of $x$ satisfying the equation $\sin \left[\cot ^{-1}(1+x)\right]=\cos$ $\left[\tan ^{-1} x\right]$, is :

    View Solution

  • The principal value of $\tan ^{-1}\left(\cot \frac{43 \pi}{4}\right)$ is:

    View Solution

  • The number of solutions of the equation, $\sin ^{-1} x=2 \tan ^{-1} x$ (in principal values) is :

    View Solution

  • A value of $\tan ^{-1}\left(\sin \left(\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\right)\right.$ is

    View Solution

  • A value of $\tan ^{-1}\left(\sin \left(\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\right)\right.$ is

    View Solution

  • The largest interval lying in $\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$ for which the function, $f(x)=4^{-x^{2}}+\cos ^{-1}\left(\frac{x}{2}-1\right)+\log (\cos x)$, is defined, is

    View Solution

  • The domain of the function $f(x)=\frac{\sin ^{-1}(x-3)}{\sqrt{9-x^{2}}}$ is

    View Solution

  • The trigonometric equation $\sin ^{-1} x=2 \sin ^{-1} a$ has a solution for

    View Solution

  • $$

    \cot ^{-1}(\sqrt{\cos \alpha})-\tan ^{-1}(\sqrt{\cos \alpha})=x

    $$ then $\sin x=$

    View Solution

Leave a Reply

Your email address will not be published.

error: Content is protected !!
Download App