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53
MCQ (Single Correct Answer)

The matrix $P=\left[\begin{array}{lll}0 & 0 & 4 \\ 0 & 4 & 0 \\ 4 & 0 & 0\end{array}\right]$ is a

A
square matrix
B
diagonal matrix
C
unit matrix
D
None of these
54
MCQ (Single Correct Answer)

Total number of possible matrices of order $3\times3$ with each entry 2 or 0 is

A
9
B
27
C
81
D
512
55
MCQ (Single Correct Answer)

$\left[\begin{array}{ll}2 x+y & 4 x \\ 5 x-7 & 4 x\end{array}\right]=\left[\begin{array}{cc}7 & 7 y-13 \\ y & x+6\end{array}\right]$, then the value of $x+y$ is

A
$x=3, y=1$
B
$x=2, y=3$
C
$x=2, y=4$
D
$x=3, y=3$
56
MCQ (Single Correct Answer)

If $A=\frac{1}{\pi}\left[\begin{array}{cc}\sin ^{-1}(x \pi) & \tan ^{-1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & \cot ^{-1}(\pi x)\end{array}\right]$ and $B=\frac{1}{\pi}\left[\begin{array}{cc}-\cos ^{-1}(x \pi) & \tan ^{-1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & -\tan ^{-1}(\pi x)\end{array}\right]$, then $A-B$ is equal to

A
$I$
B
0
C
$2 I$
D
$\frac{1}{2} I$
57
MCQ (Single Correct Answer)

If $A$ and $B$ are two matrices of the order $3 \times \mathrm{m}$ and $3 \times n$, respectively and $m=n$, then order of matrix $(5 A-2 B)$ is

A
$m \times 3$
B
$3 \times 3$
C
$m \times n$
D
$3 \times n$