MHT CET 2024 10th May Morning Shift | Differential Equations Question 24 | Mathematics

A radio-active substance has a half-life of h days, then its initial decay rate is given by (where radio-active substance has initial mass $\mathrm{m}_0$)

$\frac{\mathrm{m}_0}{\mathrm{~h}}(\log 2)$

$\left(\mathrm{m}_0 \mathrm{~h}\right)(\log 2)$

$-\frac{\mathrm{m}_0}{\mathrm{~h}}(\log 2)$

$-\left(m_0 h\right)(\log 2)$

MHT CET 2024 9th May Evening Shift

MCQ (Single Correct Answer)

-0

The general solution of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{y+\sqrt{x^2-y^2}}{x}$ is

$\sin ^{-1} y=\log x+c$, where c is a constant of integration.

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

$\frac{y}{x}=\sqrt{x^2-y^2}+\mathrm{c}$, where c is a constant of integration.

$\sin ^{-1}\left(\frac{y}{x}\right)=\log x+\mathrm{c}$, where c is a constant of integration.

MHT CET 2024 9th May Evening Shift

MCQ (Single Correct Answer)

-0

In a certain culture of bacteria, the rate of increase is proportional to the number present. If there are $10^4$ at the end of 3 hours and $4 \cdot 10^4$ at the end of 5 hours, then there were _________ the beginning.

$10^4$

$\frac{10^4}{4}$

$410^4$

$\frac{10^4}{8}$

MHT CET 2024 9th May Evening Shift

MCQ (Single Correct Answer)

-0

Integrating factor of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}+y=\frac{1+y}{x}$ is

$\frac{x}{\mathrm{e}^x}$

$x e^x$

$e^x$

$\frac{\mathrm{e}^x}{x}$

PREVIOUS NEXT

MHT CET Subjects