1
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-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

A
1
B
2
C
$-$1
D
0
2
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at $\mathrm{t}=0$. The number of bacteria is increased by $20 \%$ in 2 hours. If the population of bacteria is 2000 after $\frac{\mathrm{k}}{\log \left(\frac{6}{5}\right)}$ hours, then $\left(\frac{\mathrm{k}}{\log 2}\right)^2$ is

A
16
B
8
C
2
D
4
3
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

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

A
$\tan x=(\mathrm{c}+\sec x) y$, where c is constant of integration.
B
$\sec y=(\mathrm{c}+\tan y) x$, where c is constant of integration.
C
$\sec x=(\mathrm{c}+\tan x) y$, where c is constant of integration.
D
$\cos y=(\mathrm{c}+\tan y)$, where c is constant of integration.
4
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $y=y(x)$ be the solution of the differential equation $(x \log x) \frac{d y}{d x}+y=2 x \log x(x \geq 1)$ then $y(\mathrm{e})$ is equal to

A
2
B
2e
C
e
D
1
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