MHT CET 2025 21st April Evening Shift | Differential Equations Question 26 | Mathematics

The equation of the curve passing through the origin and satisfying the equation $\left(1+x^2\right) \frac{\mathrm{d} y}{\mathrm{~d} x}+2 x y=4 x^2$, is

$3\left(1+x^2\right) y=4 x^3$

$3\left(1-x^2\right) y=4 x^3$

$3\left(1+x^2\right)=x^3$

$\quad 4\left(1-x^2\right)=x^3$

MHT CET 2025 21st April Evening Shift

MCQ (Single Correct Answer)

-0

The differential equation of all circles having their centres on the line $y=5$ and touching ( X -axis) is $\qquad$

$\quad(5-y) \frac{\mathrm{d} y}{\mathrm{~d} x}+y^2-10 y=0$

$\quad(5-y)^2 \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}+y^2-10 y=0$

$\quad(5-y) \frac{\mathrm{d} y}{\mathrm{~d} x}+y-10=0$

$\quad(5-y)^2\left(\frac{\mathrm{~d} y}{\mathrm{~d} x}\right)^2+y^2-10 y=0$

MHT CET 2025 21st April Evening Shift

MCQ (Single Correct Answer)

-0

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)

-0

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

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

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

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

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

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