MHT CET 2021 20th September Morning Shift | Differential Equations Question 57 | Mathematics

An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half the quantity of ice melts in 20 minutes, $$x_0$$ is the initial quantity of ice. If after 40 minutes the amount of ice left is $$\mathrm{Kx}_0$$, then $$\mathrm{K}=$$

$$\frac{1}{2}$$

$$\frac{1}{8}$$

$$\frac{1}{4}$$

$$\frac{1}{3}$$

MHT CET 2020 16th October Morning Shift

MCQ (Single Correct Answer)

-0

The differential equation obtained from the function $$y=a(x-a)^2$$ is

$$8 y^2=\left(\frac{d y}{d x}\right)^2\left[x+\frac{1}{4 y}\left(\frac{d y}{d x}\right)^2\right]^2$$

$$4 y^2=\left(\frac{d y}{d x}\right)^2\left[x-\frac{1}{4 y}\left(\frac{d y}{d x}\right)^2\right]^2$$

$$2 y^2=\left(\frac{d y}{d x}\right)^2\left[x-\frac{1}{4 y}\left(\frac{d y}{d x}\right)^2\right]^2$$

$$8 y^2=\left(\frac{d y}{d x}\right)^2\left[x-\frac{1}{4 y}\left(\frac{d y}{d x}\right)^2\right]^2$$

MHT CET 2020 16th October Morning Shift

MCQ (Single Correct Answer)

-0

The differential equation of all lines perpendicular to the line $$5 x+2 y+7=0$$ is

$$2 d y-5 d x=0$$

$$5 d y-2 d x=0$$

$$2 d y-3 d x=0$$

$$3 d y-2 d x=0$$

MHT CET 2020 16th October Morning Shift

MCQ (Single Correct Answer)

-0

The bacteria increases at the rate proportional to the number of bacteria present. If the original number '$$N$$' doubles in $$4 \mathrm{~h}$$, then the number of bacteria in $$12 \mathrm{~h}$$ will be

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