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

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 =}

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