1
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The general solution of the differential equation $$\frac{d x}{d t}=\frac{x \log x}{t}$$ is

A
$$\log x-x=c$$
B
$$e^{c t}+x=0$$
C
$$\log t=x+c$$
D
$$e^{c t}=x$$
2
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$3 \sin \theta=2 \sin 3 \theta$$ and $$0< \theta<\pi$$, then $$\sin \theta=$$

A
$$\frac{\sqrt{2}}{\sqrt{5}}$$
B
$$\frac{\sqrt{3}}{2 \sqrt{2}}$$
C
$$\frac{\sqrt{2}}{3}$$
D
$$\frac{\sqrt{3}}{\sqrt{5}}$$
3
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The maximum value of the objective function $$z=2 x+3 y$$ subject to the constraints $$x+y \leq 5,2 x+y \geq 4$$ and $$x \geq 0, y \geq 0$$ is

A
15
B
10
C
20
D
25
4
MHT CET 2021 23th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The particular solution of differential equation $$(x+y) d y+(x-y) d x=0$$ at $$x=y=1$$ is

A
$$\log \left|\frac{x^2+y^2}{2}\right|=\frac{\pi}{2}-2 \tan ^{-1}\left(\frac{y}{x}\right)$$
B
$$\log \left|x^2+y^2\right|=\frac{\pi}{2}-2 \tan ^{-1}\left(\frac{y}{x}\right)$$
C
$$\log \left|x^2+y^2\right|=\frac{\pi}{2}-2 \tan ^{-1}\left(\frac{y}{x}\right)$$
D
$$\log \left|\frac{x^2+y^2}{2}\right|=\frac{\pi}{4}-2 \tan ^{-1}\left(\frac{y}{x}\right)$$
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