1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
A person writes four letters and address four envelopes. If the letters are placed in the envelopes at random, then the probability that not all letters are placed in the right envelope is
A
$\frac{15}{24}$
B
$\frac{11}{24}$
C
$\frac{23}{24}$
D
$\frac{1}{24}$
2
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \tan ^2\left(5-\frac{x}{2}\right) d x=$
A
$-\frac{1}{2} \tan \left(5-\frac{x}{2}\right)-x+c$
B
$-2 \tan \left(5-\frac{x}{2}\right)+c$
C
$\tan \left(5-\frac{x}{2}\right)+c$
D
$-2 \tan \left(5-\frac{x}{2}\right)-x+c$
3
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
$-12+27 \log 3$
4
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
$A^2(-t)$
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