1
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
$$ \left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right] $$
2
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
$$\alpha$$
3
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If A }(\operatorname{adj} A)=5 I \text {, where I is the identity matrix of order } 3 \text {, then }|\operatorname{adj} A|= $$

A
5
B
125
C
25
D
10
4
COMEDK 2024 Afternoon Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { A square matrix } P \text { satisfies } P^2=I-P \text { where } I \text { is identity matrix. If } P^n=5 I-8 P \text {, then } n \text { is equal to } $$

A
4
B
6
C
7
D
5
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