1
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { The general solution of the differential equation }(1+\tan y)(d x-d y)+2 x d y=0 \text { is } $$

A
$$y(\sin x+\cos x)=\sin x+c e^x$$
B
$$y(\sin x+\cos x)=\sin x+c e^{-x}$$
C
$$x(\sin y+\cos y)=\sin y+c e^y$$
D
$$x(\sin y+\cos y)=\sin y+c e^{-y}$$
2
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

The sum of the order and degree of the differential equation $$\left(\frac{d^2 y}{d x^2}\right)^5+\frac{4\left(\frac{d^2 y}{d x^2}\right)^3}{\left(\frac{d^3 y}{d x^3}\right)}+\frac{d^3 y}{d x^3}=x^2-1$$ is

A
4
B
5
C
6
D
8
3
COMEDK 2024 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } \frac{d y}{d x}=y+3>0 \text { and } y(0)=2 \text { then } y(\log 2) \text { is equal to } $$

A
5
B
13
C
$$-$$2
D
7
4
COMEDK 2024 Morning Shift
MCQ (Single Correct Answer)
+1
-0

The particular solution of $$\frac{d y}{d x}+\sqrt{\frac{1-y^2}{1-x^2}}=0$$, when $$x=0, y=\frac{1}{2}$$ is

A
$$\sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{6}$$
B
$$\sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{2}$$
C
$$\sin ^{-1} x-\sin ^{-1} y=\frac{\pi}{2}$$
D
$$\sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{3}$$
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