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1
MHT CET 2023 14th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The differential equation of $$y=\mathrm{e}^x(\mathrm{a} \cos x+\mathrm{b} \sin x)$$ is

A
$$\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}-2 \frac{\mathrm{d} y}{\mathrm{~d} x}-y=0$$
B
$$\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}+2 \frac{\mathrm{d} y}{\mathrm{~d} x}+2 y=0$$
C
$$\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}-2 \frac{\mathrm{d} y}{\mathrm{~d} x}+y=0$$
D
$$\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}-2 \frac{\mathrm{d} y}{\mathrm{~d} x}+2 y=0$$
2
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$x d y=y(d x+y d y), y(1)=1, y(x)>0$$, then $$y(-3)$$ is

A
1
B
2
C
3
D
4
3
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The solution of $$(1+x y) y d x+(1-x y) x d y=0$$ is

A
$$\log \left(\frac{x}{y}\right)+\frac{1}{x y}=k$$, where $$k$$ is constant of integration
B
$$\log \left(\frac{x}{y}\right)=\frac{1}{x y}+k$$, where $$k$$ is constant of integration
C
$$\log \left(\frac{x}{y}\right)+{x y}=k$$, where $$k$$ is constant of integration
D
$$\log \left(\frac{x}{y}\right)={x y}+k$$, where $$k$$ is constant of integration
4
MHT CET 2023 13th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A radioactive substance, with initial mass $$m_0$$, has a half-life of $$h$$ days. Then, its initial decay rate is given by

A
$$\frac{m_0}{h} \log 2$$
B
$$m_0 h \log 2$$
C
$$-\frac{m_0}{h} \log 2$$
D
$$-m_0 h \log \cdot 2$$
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