1
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
If $A=\frac{1}{\pi}\left[\begin{array}{cc}\sin ^{-1} \frac{1}{2} & \tan ^{-1} \frac{x}{\pi} \\ \sin ^{-1} \frac{x}{\pi} & \cot ^{-1} \sqrt{3}\end{array}\right] \quad B=\frac{1}{\pi}\left[\begin{array}{cc}-\cos ^{-1} \frac{1}{2} & \tan ^{-1} \frac{x}{\pi} \\ \sin ^{-1} \frac{x}{\pi} & -\tan ^{-1} \sqrt{3}\end{array}\right]$ and I is an identity matrix of order $2 \times 2$, then $A-B=$
A
2I
B
$\frac{1}{2}I$
C
I
D
0
2
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
If $A=\left[\begin{array}{ccc}0 & -1 & 2 \\ 1 & 0 & 3 \\ -2 & -3 & 0\end{array}\right]$, then $A+2 A^T=$
A
$-A^T$
B
$A^T$
C
$2 A^2$
D
$A$
3
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0
If $A(\operatorname{adj} A)=\left[\begin{array}{lll}5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{array}\right]$, then the value of $|A|+|\operatorname{adj} A|$ is equal to :
A
5
B
25
C
125
D
30
4
COMEDK 2025 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

The cost of 4 kg onion, 3 kg wheat and 2 kg rice is ₹ 500 .

The cost of 1 kg onion, 2 kg wheat and 3 kg rice is ₹ 300 .

The cost of 6 kg onion, 2 kg wheat and 3 kg rice is ₹ 575 .

The above situation can be represented in matrix form as $\mathrm{AX}=\mathrm{B}$. Then $\left|5 A^{-1}\right|=$

A
5
B
125
C
1
D
25
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