List of top Mathematics Questions on Application of derivatives asked in MHT CET

If \[ y=(x-1)(x-2)(x-3)\cdots(x-100) \] and the value of \( \dfrac{dy}{dx} \) at \(x=0\) is equal to \[ \lambda\left(\frac{100!}{^{100}C_5}\right) \] then \( \lambda \) is:
Given \( f(x) = x - 1 \), \( h(1) = 4 \), and \( h'(1) = -2 \). If \( g(x) = (f[4(h(x)) + 3])^2 \), find the value of \( g'(1) \).
If two curves $x^2 - 4y^2 = 2$ and $8x^2 = 40 - my^2$ are orthogonal to each other then m =
The equation of tangent to the curve $y = \cos(x + y)$ where $-2\pi \le x \le 2\pi$ and which is parallel to the line $x + 2y = 0$, is
The perpendicular distance between the lines given by \( (x - 2y + 1)^2 + \text{k(x - 2y + 1) = 0 \) is \( \sqrt{5} \), then k =}
If two curves $x^2 - 4y^2 = 2$ and $8x^2 = 40 - my^2$ are orthogonal to each other then m =
The equation of tangent to the curve $y = \cos(x + y)$ where $-2\pi \le x \le 2\pi$ and which is parallel to the line $x + 2y = 0$, is
The perpendicular distance between the lines given by \( (x - 2y + 1)^2 + \text{k(x - 2y + 1) = 0 \) is \( \sqrt{5} \), then k =}

If the line ax+by+c=0 is a normal to the curve xy=1, then 
 

The area spherical balloon of radius 6 cm increases at the rate of 2 then find the rate of increase in the volume. 

The radius of a cylinder is increasing at the rate 2 cm/sec and its height is decreasing at the rate 3 cm/sec, then find the rate of change of volume when the radius is 3cm and the height is 5 cm.

20 meters of wire is available to fence of a flowerbed in the form of a circular sector. If the flowerbed is to have maximum surface area, then the radius of the circle is

If y = 4x – 5 is tangent to the curve y2 =px3 +q at (2, 3), then

\(y = tan^{-1} (\frac{4 sin 2x}{cos 2x - 6sin^2x})\) then \(\frac{dy}{dx}\) at \(x=0\).
If lines represented by the equation $px^2 - qy^2 = 0$ are distinct, then
If $f(x) = [8x] - 3$, where $[x]$ is the greatest integer function of $x$, then $f(\pi) =$ (where $\pi = 3.14$)
The slant height of a right circular cone is $\sqrt{3}\text{ cm}$. The height of the cone for maximum volume is
The maximum value of $f(x) = \frac{\log \, x }{x} (x \neq 0 , x \neq 1)$ is
The approximate value of $f\left(x\right)= x^{3}+5x^{2}-7x +9$ at $x=1.1 $ is
Let $f(x) = \int \frac{x^2 - 3x + 2}{x^4 + 1} \, dx$, then the function decreases in the interval
If $f'(x) = \tan^{-1}(\sec x + \tan x)$, $-\frac{\pi}{2}<x<\frac{\pi}{2}$ and $f(0) = 0$, then $f(1)$ is