# Let 1 2 3 4 A æ ö = ç ÷ è ø and 0 0 a B b æ ö = ç ÷ è ø, ab N , Î . Then

Question:

Let $A=\left(\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right)$ and $B=\left(\begin{array}{cc}a & 0 \\ 0 & b\end{array}\right), a, b \in N$. Then

1. there cannot exist any $\mathrm{B}$ such that $\mathrm{AB}=\mathrm{BA}$

2. there exist more than one but finite number of $B^{\prime} s$ such that $\mathrm{AB}=\mathrm{BA}$

3. there exists exactly one $\mathrm{B}$ such that $\mathrm{AB}=\mathrm{BA}$

4. there exist infinitely many $\mathrm{B}^{\prime}$ s such that $\mathrm{AB}=\mathrm{BA}$

Correct Option: 4

JEE Main Previous Year 1 Question of JEE Main from Mathematics Inverse Trigonometric Functions chapter.
JEE Main Previous Year 2004

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

error: Content is protected !!
Download App