MHT CET 2024 16th May Morning Shift | Differential Equations Question 7 | Mathematics

The assets of a person are reduced in his business such that the rate of reduction is proportional to the square root of the existing assets. If the assets were initially ₹$10,00,000$ and due to loss they reduce to ₹$ 10,000$ after 3 years, then the number of years required for the person to go bankrupt will be

$\frac{10}{3}$

$\frac{10}{9}$

$\frac{20}{9}$

$\frac{20}{3}$

MHT CET 2024 15th May Evening Shift

MCQ (Single Correct Answer)

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The order of the differential equation, whose solution is $y=\left(C_1+C_2\right) \mathrm{e}^x+C_3 \mathrm{e}^{x+C_4}$, is

MHT CET 2024 15th May Evening Shift

MCQ (Single Correct Answer)

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The general solution of the differential equation $\frac{d y}{d x}=\frac{3 e^{2 x}+3 e^{4 x}}{e^x+e^{-x}}$ is

$y=\mathrm{e}^{-3 x}+\mathrm{c}$, where c is a constant of integration.

$y=\mathrm{e}^x+\mathrm{c}$, where c is a constant of integration.

$y=\mathrm{e}^{3 x}+\mathrm{c}$, where c is a constant of integration.

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

MHT CET 2024 15th May Morning Shift

MCQ (Single Correct Answer)

-0

The differential equation, having general solution as $A x^2+B y^2=1$, where $A$ and $B$ are arbitrary constants, is

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

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

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

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

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