MHT CET 2026 16th April Evening Shift | Differential Equations Question 25 | Mathematics

If water at $100^\circ\text{C}$ cools in 10 minutes to $80^\circ\text{C}$ and to $65^\circ\text{C}$ in the next 10 minutes, then the room temperature will be ...

$30^\circ\text{C}$

$15^\circ\text{C}$

$25^\circ\text{C}$

$20^\circ\text{C}$

MHT CET 2026 16th April Evening Shift

MCQ (Single Correct Answer)

-0

The equation of the curve passing through the point (0, 1) and having a slope of the tangent at point $P(x, y)$ is equal to $\dfrac{y}{x + y}$, is

$x = e^{-\frac{y}{x}}$

$y = e^{-\frac{y}{x}} + 1$

$x = e^{\frac{x}{y}} - 1$

$y = e^{\frac{x}{y}}$

MHT CET 2026 16th April Evening Shift

MCQ (Single Correct Answer)

-0

If $f(x)$ is a polynomial such that $f(x) = [f'(x)]^2$ and $f(2) = 0$, then $f(-2) = \ldots$

$1$

$-1$

$4$

$-4$

MHT CET 2026 16th April Morning Shift

MCQ (Single Correct Answer)

-0

The integrating factor of the differential equation $(1 + t^2) + \left(x - e^{\tan^{-1}t}\right)\dfrac{dt}{dx} = 0$ is

$e^{\tan^{-1}t}$

$-e^{\tan^{-1}t}$

$e^{-\tan^{-1}t}$

$-e^{-\tan^{-1}t}$

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