MHT CET 2025 19th April Morning Shift | Differential Equations Question 54 | Mathematics

In a bank, the principal increases continuously at a rate of $x \%$ per year. Then the rate $x$, if ₹$100$ double itself in 10 years, is ( $\log 2=0.6931$)

$6.93 \%$

$9.63 \%$

$6.09 \%$

$3.69 \%$

MHT CET 2025 19th April Morning Shift

MCQ (Single Correct Answer)

-0

The solution of the differential equation $x \frac{\mathrm{~d}^2 y}{\mathrm{~d} x^2}=1$ at $x=y=1$ with $\frac{\mathrm{d} y}{\mathrm{~d} x}=0$ at $x=1$, is

$y=x \log x+x+2$

$y=x \log x-x+2$

$x=x \log x+2$

$x \log x-x=y$

MHT CET 2024 16th May Evening Shift

MCQ (Single Correct Answer)

-0

The slope of tangent at $(x, y)$ to a curve passing through $\left(1, \frac{\pi}{4}\right)$ is $\frac{y}{x}-\cos ^2 \frac{y}{x}$, then the equation of curve is

$y=\tan ^{-1}\left(\log \left(\frac{\mathrm{e}}{x}\right)\right)$

$y=x^2\left(\tan ^{-1}\left(\log \frac{\mathrm{e}}{x}\right)\right)$

$y=x\left(\tan ^{-1}\left(\log \frac{\mathrm{e}}{x}\right)\right)$

$y=\frac{1}{x}\left(\tan ^{-1}\left(\log \frac{\mathrm{e}}{x}\right)\right)$

MHT CET 2024 16th May Evening Shift

MCQ (Single Correct Answer)

-0

The function $y(x)$ represented by $x=\sin t$, $y=a e^{t \sqrt{2}}+b e^{t \sqrt{2}}, t \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$ satisfies the equation $\left(1-x^2\right) y^{\prime \prime}-x y^{\prime}=\mathrm{k} y$, then the value of k is k is

$-$1

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