1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $f(x)=\left(\frac{3+x}{1+x}\right)^{2+3 x}$, then $f^{\prime}(0)=$
A
$12+\log 3$
B
$-12+3 \log 3$
C
$-\frac{4}{3}+3 \log 3$
D
$-12+27 \log 3$
2
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $A(t)=\left[\begin{array}{cc}\cos t & \sin t \\ -\sin t & \cos t\end{array}\right]$ then the product of $A(t)$ and $A(-t)$ is
A
Identity matrix
B
$A^2(t)$
C
Null matrix
D
$A^2(-t)$
3
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $A=\left[\begin{array}{cc}1 & -2 \\ 4 & 5\end{array}\right] ; f(t)=t^2-3 t+7$ then $f(A)+\left[\begin{array}{cc}3 & 6 \\ -12 & -9\end{array}\right]=$
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
$\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$
D
$\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
4
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
Codes used for vehicle identification consists of two distinct English alphabets followed by two distinct digits from 1 to 9 . How many of them end with an even number.
A
10400
B
2600
C
20800
D
5200
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