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 \(f(0)=3\).

If \[ f(x) = \begin{cases} x^3 - x^2 + 1, & \text{if } x > 0 \\ e^x \sin x + i x + \lambda \log 4, & \text{if } x \leq 0 \end{cases} \]
is continuous at \( x = 0 \), then the value of 500\(\lambda\) is:

If $f(x) = \frac{\cos ax - \cos bx}{\cos cx - \cos bx}$ for $x \ne 0$ and $f(0) = -1$ is continuous at $x = 0$, then $a^2, b^2, c^2$ are in ______.

Let $f(x)=\begin{cases}\frac{x^{4}-5x^{2}+4}{|(x-1)(x-2)|}&,x\ne1,2\\ 6&,x=1
12&,x=2\end{cases}$. Then $f(x)$ is continuous on the set}

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 $f(x)=[x]$, $x\in(-\frac{7}{2},100)$

Let $$\begin{array}{ll} f(x) = |x| + 3, & \text{if } x \le -3 \\ f(x) = -2x, & \text{if } -3 < x < 3 \\ f(x) = 6x - 2, & \text{if } x \ge 3 \end{array}$$ then

Let $$f(x) = \begin{array}{cc} x + a\sqrt{2}\sin x & , 0 \le x \lt \frac{\pi}{4} \\ 2x\cot x + b & , \frac{\pi}{4} \le x \lt \frac{\pi}{2} \\ a\cos 2x - b\sin x & , \frac{\pi}{2} \le x \le \pi \end{array}$$ If $f(x)$ is continuous for $0 \le x \le \pi$, then

If $f(x) = \frac{1 - \sin x + \cos x}{1 + \sin x + \cos x}$, for $x \neq \pi$ is continuous at $x = \pi$, then the value of $f(\pi)$ is

If the function given by
$f(x) = -2 \sin x$ for $-\pi \le x < -\frac{\pi}{2}$
$f(x) = a \sin x + b$ for $-\frac{\pi}{2} < x < \frac{\pi}{2}$
$f(x) = \cos x$ for $\frac{\pi}{2} \le x \le \pi$
is continuous in $[-\pi, \pi]$, then the value of $(3a + 2b)^3$ is

If the function $$f(x) = \begin{array}{cc} 3ax + b, & \text{for } x < 1 \\ 11, & \text{for } x = 1 \\ 5ax - 2b, & \text{for } x > 1 \end{array}$$ is continuous at $x = 1$, then the values of $a$ and $b$ are

If the function $$f(x) = \begin{cases} 1 + \sin\frac{\pi}{2}, & -\infty < x \le 1 \\ ax + b, & 1 < x < 3 \\ 6 \tan\frac{x\pi}{12}, & 3 \le x < 6 \end{cases}$$ is continuous in $(-\infty, 6)$, then the values of $a$ and $b$ are respectively.

Let $f(x)$ be a function defined as: $$f(x) = \begin{cases} \frac{\sqrt{1 + px} - \sqrt{1 - px}}{x}, & \text{if } -1 \leq x < 0 \\ \frac{2x + 1}{x - 2}, & \text{if } 0 \leq x \leq 1 \end{cases}$$ If $f(x)$ is continuous in the interval $[-1, 1]$, then $p =$

If $f(x) = \frac{4^{x - \pi} + 4^{\pi - x} - 2}{(x - \pi)^2}$, for $x \ne \pi$, is continuous at $x = \pi$, then $f(\pi)$ is

If $f(x) = [x]$, for $x \in (-1, 2)$, then $f$ is discontinuous at (where $[x]$ represents floor function)

If the function $$f(x) = \begin{cases} 1 + \sin\frac{\pi}{2}, & -\infty < x \le 1 \\ ax + b, & 1 < x < 3 \\ 6 \tan\frac{x\pi}{12}, & 3 \le x < 6 \end{cases}$$ is continuous in $(-\infty, 6)$, then the values of $a$ and $b$ are respectively.