1
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
The general solution of the differential equation $(x-y) d y=(x+y) d x$ is
A
$\tan ^{-1}\left(\frac{y}{x}\right)=c \sqrt{x^2+y^2}$
B
$\tan ^{-1}\left(\frac{y}{x}\right)=x^2+y^2+c$
C
$e^{\tan ^{-1}\left(\frac{y}{x}\right)}=\frac{c \sqrt{x^2+y^2}}{x}$
D
$e^{\tan ^{-1}\left(\frac{y}{x}\right)}=c \sqrt{x^2+y^2}$
2
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
A line $L_1$ passes through the points $(h, k),(1,2)$ and $(-3,4)$. The points $(4,3)$ and $(h, k)$ lie on the line $L_2$. Given $L_1 \perp L_2$ then $(k-h)$ equals to
A
2
B
$\frac{1}{2}$
C
$-$2
D
0
3
COMEDK 2025 Morning Shift
MCQ (Single Correct Answer)
+1
-0
Let $M$ be the set of all $2 \times 2$ matrices with entries from the set R of real numbers. Then the function $f: M \rightarrow R$ defined by $f(A)=|A|$ for every $A \in M$ is
A
neither one-one nor onto
B
one-one but not onto
C
onto but not one-one
D
one-one and onto
4
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
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