1
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

If the matrix $A$ is such that $$A\left(\begin{array}{cc}-1 & 2 \\ 3 & 1\end{array}\right)=\left(\begin{array}{cc}-4 & 1 \\ 7 & 7\end{array}\right)$$ then $$A$$ is equal to

A
$$\left(\begin{array}{cc}1 & 1 \\ 2 & -3\end{array}\right)$$
B
$$\left(\begin{array}{cc}-1 & 1 \\ 2 & 3\end{array}\right)$$
C
$$\left(\begin{array}{cc}1 & 1 \\ -2 & 3\end{array}\right)$$
D
$$\left(\begin{array}{cc}1 & -1 \\ 2 & 3\end{array}\right)$$
2
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $$A=\left[\begin{array}{ccc}0 & x & 16 \\ x & 5 & 7 \\ 0 & 9 & x\end{array}\right]$$ is a singular matrix then $$x$$ is equal to

A
$$-12$$
B
21
C
$$-144$$
D
144
3
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } A=\left[\begin{array}{cc} 1 & -2 \\ 4 & 5 \end{array}\right] \text { and } f(t)=t^2-3 t+7 \text { then } f(A)+\left[\begin{array}{cc} 3 & 6 \\ -12 & -9 \end{array}\right] \text { is } $$

A
$$ \left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right] $$
B
$$ \left[\begin{array}{ll} 1 & 1 \\ 0 & 0 \end{array}\right] $$
C
$$ \left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right] $$
D
$$ \left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right] $$
4
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

$$ \left|\begin{array}{ccc} \cos (\alpha+\beta) & -\sin (\alpha+\beta) & \cos 2 \beta \\ \sin \alpha & \cos \alpha & \sin \beta \\ -\cos \alpha & \sin \alpha & \cos \beta \end{array}\right| $$ is independent of

A
$$\beta$$
B
$$\alpha$$ and $$\beta$$
C
Neither $$\alpha$$ nor $$\beta$$
D
$$\alpha$$
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