List of top Mathematics Questions on Continuity asked in MHT CET

Find the value of \(k\) if the function \(f(x) = \dfrac{k\sin x}{x}\) is continuous at \(x = 0\) and \(f(0)=3\).

The value of \( \sin^{-1}\left(-\frac{1}{\sqrt{2}}\right) + \cos^{-1\left(-\frac{1}{2}\right) - \cot^{-1}\left(-\frac{1}{\sqrt{3}}\right) + \tan^{-1}(-\sqrt{3}) \) is

If $f(x) = \begin{cases} mx + 1, & x \le \frac{\pi}{2} \\ \sin x + n, & x > \frac{\pi}{2} \end{cases}$ is continuous at $x = \frac{\pi}{2}, (m, n \in \mathbb{Z})$ then}

If the function \(f(x)\) is continuous in \([0, \pi]\) then \(a - b =\)

The value of \( \sin^{-1}\left(-\frac{1}{\sqrt{2}}\right) + \cos^{-1\left(-\frac{1}{2}\right) - \cot^{-1}\left(-\frac{1}{\sqrt{3}}\right) + \tan^{-1}(-\sqrt{3}) \) is

The number of discontinuities of the greatest integer function $f(x)=[x]$, $x\in(-\frac{7}{2},100)$