COMEDK 2026 Morning Shift | Application of Derivatives Question 7 | Mathematics

If $\mathbf{3 ~ c m} / \mathbf{s}$ is the rate at which the side of an equilateral triangle increases, then the rate of change of area, when the side is $\mathbf{1 2 ~ c m}$ is:

$9 \sqrt{3} \mathrm{~cm}^2 / \mathrm{s}$

$18 \mathrm{~cm}^2 / \mathrm{s}$

$6 \sqrt{3} \mathrm{~cm}^2 / \mathrm{s}$

$18 \sqrt{3} \mathrm{~cm}^2 / \mathrm{s}$

COMEDK 2026 Morning Shift

MCQ (Single Correct Answer)

-0

If the function $f(x)=x^4-31 x^2+\boldsymbol{a} x+5$ has a turning point at $x=1$, then the value of ' $\boldsymbol{a}$ ' is $\_\_\_\_$ and the function attains a $\_\_\_\_$ at $x=1$

$a=50$, local minima

$a=58$, local maxima

$a=58$, local minima

$a=-50$, local maxima

COMEDK 2026 Morning Shift

MCQ (Single Correct Answer)

-0

The behaviour of the function $f(x)=\sin \left(2 x+\frac{\pi}{4}\right)$ on $\left(\frac{3 \pi}{8}, \frac{5 \pi}{8}\right)$ is:

Strictly increasing on $\left(\frac{3 \pi}{8}, \frac{5 \pi}{8}\right)$

Strictly increasing on $\left(\frac{\pi}{8}, \frac{3 \pi}{8}\right)$

Strictly decreasing on $\left(\frac{3 \pi}{8}, \frac{5 \pi}{8}\right)$

${\text { Strictly decreasing on }}\left(\frac{\pi}{8}, \frac{5 \pi}{8}\right)$

COMEDK 2025 Evening Shift

MCQ (Single Correct Answer)

-0

Let $f(x)=x \sqrt{4 a x-x^2}, a>0$ then $f^{\prime}(x)$ at $x=2 a$ is :

Does not exist

Zero

Decreasing

Increasing

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