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1
MHT CET 2026 15th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
The solution of the differential equation $\dfrac{dy}{dx} = e^{x-y} + x^2 e^{-y}$ is...
A
$y = e^x + c$
B
$e^y = e^x + x^3 + c$
C
$e^y = e^x + \dfrac{x^3}{3} + c$
D
$e^y = e^x + 2x + c$
2
MHT CET 2026 15th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
If the differential equation $\begin{vmatrix} f(x) & f'(x) \\ f'(x) & f''(x) \end{vmatrix} = 0$ for all $x$ and $f(0) = 1, f'(0) = 2$, then...
A
$f'(x) = -f(x)$
B
$f'(x) = f(x)$
C
$f'(x) = 2f(x)$
D
$f'(x) = 0$
3
MHT CET 2026 15th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
The solution of the differential equation $x^2 \dfrac{dy}{dx} - xy = 1$ is...
A
$2xy - 2cx^2 - 1 = 0$
B
$2xy + 2cx^2 + 1 = 0$
C
$2xy - 2cx^2 + 1 = 0$
D
$2x^2 y - 2cx + 1 = 0$
4
MHT CET 2025 5th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The population $p$ of the city at time $t$ is given by $\frac{\mathrm{dp}}{\mathrm{dt}}=\frac{\mathrm{p}}{2}-100$. If initial population is 100 then $\mathrm{p}=$

A

$200+100 \mathrm{e}^{\frac{\mathrm{t}}{2}}$

B

$200-100 \mathrm{e}^{\frac{1}{2}}$

C

$300-100 \mathrm{e}^{\frac{1}{2}}$

D

$300+100 \mathrm{e}^{\frac{1}{2}}$

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