Download App

Algebra of Matrices — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices1 Mark
MCQ
If $\text{A}=\frac{1}{\pi}\begin{bmatrix}\sin^{-1}(\pi\text{x})&\tan^{-1}(\frac{\text{x}}{\pi})\\\sin^{-1}(\frac{\text{x}}{\pi})&\cot^{-1}(\pi\text{x})\end{bmatrix},$ $\text{B}=\frac{1}{\pi}\begin{bmatrix}-\cos^{-1}(\pi\text{x})&\tan^{-1}(\frac{\text{x}}{\pi})\\\sin^{-1}(\frac{\text{x}}{\pi})&-\tan^{-1}(\pi\text{x})\end{bmatrix},$ then $A - B$ is equal to:
  • A
    $I$
  • B
    $0$
  • C
    $2I$
  • ✓
    $\frac{1}{2}\text{I}$
✓

Answer

Correct option: D.
$\frac{1}{2}\text{I}$
Given $\text{A}=\frac{1}{\pi}\begin{bmatrix}\sin^{-1}(\pi\text{x})&\tan^{-1}(\frac{\text{x}}{\pi})\\\sin^{-1}(\frac{\text{x}}{\pi})&\cot^{-1}(\pi\text{x})\end{bmatrix}$ $\text{B}=\frac{1}{\pi}\begin{bmatrix}-\cos^{-1}(\pi\text{x})&\tan^{-1}(\frac{\text{x}}{\pi})\\\sin^{-1}(\frac{\text{x}}{\pi})&-\tan^{-1}(\pi\text{x})\end{bmatrix}$
$\text{A}-\text{B}=\frac{1}{\pi}\begin{bmatrix}\sin^{-1}(\text{x}\pi)+\cos^{-1}(\pi\text{x})&0\\0&\cot^{-1}(\pi\text{x})+\tan^{-1}(\pi\text{x})\end{bmatrix}$
$=\frac{1}{\pi}\begin{bmatrix}\frac{\pi}{2}&0\\0&\frac{\pi}{2}\end{bmatrix}$
$=\frac{1}{2}\begin{bmatrix}1&0\\0&1\end{bmatrix}$
$=\frac{1}{2}\text{I}$

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 "MCQ" from Algebra of Matrices→Algebra of Matrices — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If the sides of a triangle are $p, q$ and $\sqrt{p^2+p q+q^2}$, then the biggest angle is
→
The combined equation of the co-ordinate axes is _________.
→
If the binary operation $\odot$ is defined on the set $Q^+$ of all positive rational numbers by $\text{a}\odot\text{b}=\frac{\text{ab}}4$. Then, $3\odot\Big(\frac{1}5\odot\frac{1}2\Big)$ is equal to:
→
The value of $\int_0^{\pi / 2} \frac{d x}{1+\tan ^3 x}$ is
→
A fair die is tossed eight times. The probability that a third six is observed in the eight throw is:
→
If $\overline{ a }$ is a non-zero vector and $| k \overline{ a }|=1$, then $k =$
→
The inverse of $\left[\begin{array}{cc}1 & \sin \alpha \\ -\sin \alpha & -1\end{array}\right]$ is
→
The principal value of $\cos ^{-1}\left(-\frac{1}{2}\right)$ is
→
If $\int_0^k \frac{1}{2+8 x^2} d x=\frac{\pi}{16}$, then the value of $k$ is.....
→
If the rate of change of area of a circle is equal to the rate of change of its diameter, then its radius is equal to:
→