MHT CET 2023 12th May Morning Shift | Differential Equations Question 16 | Mathematics

The decay rate of radio active material at any time $$t$$ is proportional to its mass at that time. The mass is 27 grams when $$t=0$$. After three hours it was found that 8 grams are left. Then the substance left after one more hour is

$$\frac{27}{8}$$ grams

$$\frac{81}{4}$$ grams

$$\frac{16}{3}$$ grams

$$\frac{16}{9}$$ grams

MHT CET 2023 12th May Morning Shift

MCQ (Single Correct Answer)

-0

The differential equation $$\cos (x+y) \mathrm{d} y=\mathrm{d} x$$ has the general solution given by

$$y=\sin (x+y)+c$$, where $$\mathrm{c}$$ is a constant.

$$y=\tan (x+y)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant

$$y=\tan \left(\frac{x+y}{2}\right)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant

$$y=\frac{1}{2} \tan (x+y)+\mathrm{c}$$, where $$\mathrm{c}$$ is a constant

MHT CET 2023 12th May Morning Shift

MCQ (Single Correct Answer)

-0

If $$\frac{\mathrm{d} y}{\mathrm{~d} x}=y+3$$ and $$y(0)=2$$, then $$y(\log 2)=$$

$$-$$2

MHT CET 2023 11th May Evening Shift

MCQ (Single Correct Answer)

-0

The solution of $$\frac{\mathrm{d} x}{\mathrm{~d} y}+\frac{x}{y}=x^2$$ is

$$\frac{1}{y}=\mathrm{c} x-x \log x$$, where $$\mathrm{c}$$ is a constant of integration.

$$\frac{1}{x}=\mathrm{c} y-y \log y$$, where $$\mathrm{c}$$ is a constant of integration.

$$\frac{1}{x}=\mathrm{c} x-x \log y$$, where $$\mathrm{c}$$ is a constant of integration.

$$\frac{1}{y}=\mathrm{c} x-y \log x$$, where $$\mathrm{c}$$ is a constant of integration.

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