MHT CET 2026 20th April Morning Shift | Application of Derivatives Question 4 | Mathematics

A spherical iron ball $10$ cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of $50\ \text{cm}^3/\text{min}$. When the thickness of ice is $5$ cm, the rate at which the thickness of ice decreases is...

$\dfrac{1}{18\pi}\ \text{cm}/\text{min}$

$\dfrac{1}{36\pi}\ \text{cm}/\text{min}$

$\dfrac{5}{6\pi}\ \text{cm}/\text{min}$

$\dfrac{1}{54\pi}\ \text{cm}/\text{min}$

MHT CET 2026 20th April Morning Shift

MCQ (Single Correct Answer)

-0

If the line $ax + by + 5 = 0$ is a normal to the curve $xy = 1$ then .....

$a > 0, b < 0$

$a < 0, b < 0$

$a > 0, b = 0$

$a > 0, b > 0$

MHT CET 2026 20th April Morning Shift

MCQ (Single Correct Answer)

-0

On the interval $[0, 1]$, the function $f(x) = x^{25}(1 - x)^{75}$ attains its maximum value at the point $x = $....

$0$

$\dfrac{1}{4}$

$\dfrac{1}{2}$

$\dfrac{1}{3}$

MHT CET 2025 5th May Evening Shift

MCQ (Single Correct Answer)

-0

The area of the triangle formed by the co-ordinate axes and a tangent to the curve $x y=\mathrm{a}^2$ at the point $\left(x_1, y_1\right)$ is _______ sq. units (where a, $x_1$ and $y_1$ are non-zero)

$\frac{\mathrm{a}^2 x_1}{y_1}$

$\frac{\mathrm{a}^2 y_1}{x_1}$

$2 \mathrm{a}^2$

$4 \mathrm{a}^2$

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