1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The sum of three numbers is 6 . Twice the third number, when added to the first number gives 7 , On adding the sum of the second and third numbers to thrice the first number, we get 12 . The above situation can be represented in matrix form as $A X=B$. Then the $|\operatorname{adj} A|$ is equal to
A
$-$4
B
4
C
$-$64
D
16
2
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{1}{\sqrt{9+8 x-x^2}} d x=\varphi(x)+c$ then $\varphi(x)=$
A
$\frac{1}{5} \sin ^{-1}\left(\frac{x-4}{5}\right)$
B
$\sin ^{-1}\left(\frac{x-4}{5}\right)$
C
$\frac{1}{10} \log \left|\frac{4-x}{4+x}\right|$
D
$\log \left|\frac{4-x}{4+x}\right|$
3
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
$\frac{1}{24}$
4
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
$-2 \tan \left(5-\frac{x}{2}\right)-x+c$
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