MHT CET 2025 21st April Evening Shift | Differential Equations Question 31 | Mathematics

In a culture bacteria count is $1,00,000$ initially. The number increases by $10 \%$ in first 2 hours. In how many hours will the count reach $2,00,000$, if the rate of growth of bacteria is proportional to the number present?

$\frac{2 \log \left(\frac{11}{10}\right)}{\log 2}$

$\frac{\log \left(\frac{11}{10}\right)}{\log 2}$

$\frac{2 \log 2}{\log \left(\frac{11}{10}\right)}$

$\frac{\log (2)}{\log \left(\frac{11}{10}\right)}$

MHT CET 2025 21st April Morning Shift

MCQ (Single Correct Answer)

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A particular solution of $\frac{\mathrm{d} y}{\mathrm{~d} x}=(x+9 y)^2$, when $x=0, y=\frac{1}{27}$ is

$\quad 3 x+27 y=\tan \left[3\left(x+\frac{\pi}{12}\right)\right]$

$\quad 3 x+27 y=\tan \left(x+\frac{\pi}{4}\right)$

$3 x+27 y=\tan \left(x+\frac{\pi}{12}\right)$

$3 x+27 y=\tan \left[3\left(x+\frac{\pi}{4}\right)\right]$

MHT CET 2025 21st April Morning Shift

MCQ (Single Correct Answer)

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

$y=\mathrm{e}^{-\mathrm{e}^{x^2}} \mathrm{c}$, where c is the constant of integration

$y=\mathrm{e}^{-x^2} \mathrm{c}$, where c is the constant of integration

$y=\mathrm{e}^{\mathrm{e}^{\mathrm{e}^2}} \mathrm{c}$, where c is the constant of integration

$y=\mathrm{e}^{x^2} \mathrm{c}$, where c is the constant of integration

MHT CET 2025 21st April Morning Shift

MCQ (Single Correct Answer)

-0

Which of the following is not a homogeneous function?

$\quad y^2+2 x y$

$2 x-3 y$

$\quad \sin \left(\frac{y}{x}\right)$

$\cos x+\sin y$

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