MCQ
For any $2 \times 2$ matrix $ A$, if $A(adj.\,\,A)$= $\left[ {\begin{array}{*{20}{c}}{10}&0\\0&{10}\end{array}} \right]$, then $|A|\, = $
- A$0$
- ✓$10$
- C$20$
- D$100$
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(There are two questions based on $PARAGRAPH "II"$, the question given below is one of them)
($1$) The value of $2 \int^{\frac{\pi}{2}} f(x) g(x) d x-\int^{\frac{\pi}{2}} g(x) d x$ us
($2$) The value of $\frac{16}{\pi^3} \int_0^{\frac{\pi}{2}} f(x) g(x) d x$ is
Give the answer or quetion ($1$) and ($2$)
If $\text{A}=\frac{1}{\pi}\begin{bmatrix}\sin^{-1}(\text{x}\pi)&\tan^{-1}\Big(\frac{\text{x}}{\pi}\Big)\\\sin^{-1}\Big(\frac{\text{x}}{\pi}\Big)&\cot^{-1}(\pi\text{x})\end{bmatrix}$ and $\text{B}=\frac{1}{\pi}\begin{bmatrix}-\cos^{-1}(\text{x}\pi)&\tan^{-1}\Big(\frac{\text{x}}{\pi}\Big)\\\sin^{-1}\Big(\frac{\text{x}}{\pi}\Big)&\tan^{-1}(\pi\text{x})\end{bmatrix}$ then A - B is:
$\text{I}$
$0$
$2\text{I}$
$\frac{1}{2}\text{I}$