List of top Mathematics Questions on Application of derivatives asked in COMEDK UGET

The approximate value of $ f(5.001) $, $\text{where} $ $f(x) = x^3 - 7x^2 + 10 $

A ladder $5\,m$ long is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall, at the rate of $2m/sec$. The speed at which its height on the wall decreases when the foot of the ladder is $4\, m$ away from the wall is
A spherical balloon is being inflated at the rate of $35\, cc$ per minute, When its radius is $7\, cm$, its surface area increases at the rate of
Let $x$ be a number which exceeds its square by the greatest possible quantity, then $x$ =
The subtangent at $x = \pi/2$ on the curve $y = x \sin x $ is
If the tangent to the curve $2y^3 = ax^2 + x^3$ at the point $(a, a)$ cuts off intercepts $\alpha$ and $\beta$ on the coordinate axes where $\alpha^2 + \beta^2 = 61$, then the value of $a$ is
Lengthof the subtangent at $(a, a)$ on the curve $y^2 = \frac{x^2}{2a +x}$ is equal to
If $f\left(x\right) = \frac{x^{2} -1}{x^{2} +1} ,x\in R$ then the minimum value of $f$ is
If the area of a circle increases at a uniform rate, then its perimeter varies
The length of the subtangent to the curv $x^2y^2 = a^4$ at $(-a, a)$ is
The surface area of a ball is increasing at the rate of $2 \pi \, s cm/sec$. The rate at which the radius is increasing when the surface area is $16 \pi \, s cm$ is
The slopes of the tangent and normal at $(0, 1)$ for the curve $y = \sin x + e^x$ are respectively
A stone is thrown up vertically and the height $'x'$ ft reached by it in time $'t'$ secs is given by $x = 80t - 16t^2$ . The stone reaches the maximum height in time ?
If for the curve $y = 1 + bx - x^2$, the tangent at $(1 - 2)$ is parallel to $x$-axis, then $b =$
The subtangent at $x = \pi /2$ on the curve $y = x \sin x$ is
The maximum value of $\left(\frac{1}{x}\right)^{2x^2}$ is
Let $x$ be a number which exceeds its square by the greatest possible quantity, then $x$ =
The value of $x$ for which $f(x) = x^3 - 6x^2 - 36x + 7 $ is increasing, belong to