List of top Mathematics Questions on Continuity and differentiability asked in MHT CET

If $y = \tan^{-1}\left(\sqrt{\frac{1 + \sin x}{1 - \sin x}}\right)$, where $0 \le x < \frac{\pi}{2}$, then $\frac{dy}{dx}$ at $x = \frac{\pi}{6}$ is

If $y^2 = ax^2 + bx + c$, where $a, b, c$ are constants, then $y^3 \frac{d^2y}{dx^2}$ is equal to

If $x^y \cdot y^x = 16$, then $\frac{dy}{dx}$ at $(2,2)$ is

If $y = \tan^{-1}\left(\sqrt{\frac{1+\cos x}{1-\cos x}}\right)$, then $\frac{dy}{dx} =$

If $f(x) = \csc^{-1} \left[ \frac{10}{6 \sin(2^x) - 8 \cos(2^x)} \right]$, then $f'(x) =$

If \( y = \tan^{-1} \left\{ \frac{a \cos x - b \sin x}{b \cos x + a \sin x} \right\} \), then \( \frac{dy}{dx} = \)

If \( y = \tan^{-1} \left( \frac{a \cos x - b \sin x}{b \cos x + a \sin x} \right) \), then \( \frac{dy}{dx} = \)

If $e^{-y} \cdot y = x$, then $\frac{dy}{dx}$ is

The function $f(x)=[x]\cdot \cos\left(\frac{2x-1}{2}\pi\right)$ where $[\cdot]$ denotes the greatest integer function, is discontinuous at

If $y = \left[(x+1)(2x+1)(3x+1)\cdots(nx+1)\right]^n$, then $\frac{dy}{dx}$ at $x=0$ is

If $\cos^{-1} x + \cos^{-1} y + \cos^{-1} z = 3\pi$, then the value of $x^{2025} + x^{2026} + x^{2027}$ is

Let \( f:\mathbb{R}\rightarrow \mathbb{R} \) be a function such that \( f(x)=x^{3} + x^{2}f^{\prime}(1) + x f^{\prime\prime}(2) + 6 \) for \( x \in \mathbb{R} \), then \( f(2) \) equals

If $y = (\sin^{-1}x)^2 + (\cos^{-1}x)^2$, then $(1 - x^2)\,y'' - x\,y' = $

If $\sin (\alpha +\beta )=6\sin (\alpha -\beta )$ and $k=\frac{\tan \alpha }{\tan \beta }$, then, what is the value of $k$ ?

It is known from past experience that in a certain plant there are on the average $4$ industrial accidents per month. Find the probability that there will be less than $4$ accidents in a given month. Given: $({\mathrm{e}}^{-4}=0.0183)$