List of top Mathematics Questions on Continuity asked in KEAM

If $f(x)=\frac{1}{2x-4}$ then the point(s) of discontinuity of $f(f(x))$ is/are

If the function $f(x)=\begin{cases}\dfrac{2x^2+3x-5}{x-1}, & x \ne 1 \\ k, & x=1\end{cases}$ is continuous at $x=1$, then the value of $k$ is:

Let \( f(x) = \begin{cases} 3x + 6, & \text{if } x \ge c \\ x^{2} - 3x - 1, & \text{if } x<c \end{cases} \), where \( x \in \mathbb{R} \) and \( c \) is a constant. The values of \( c \) for which \( f \) is continuous on \( \mathbb{R} \) are:

The set of all points where the function $f(x)=\frac{x}{x^2-4},\ x\in\mathbb{R}$ is discontinuous, is:

The function $f(x)=\begin{cases}\dfrac{3x^2-12}{x-2}, & x\neq 2 \\ \lambda, & x=2 \end{cases}$ is continuous for $x\in\mathbb{R}$, then the value of $\lambda$ is:

Let $f(x)=[x]$, $x\in(0,6)$, where $[x]$ is the greatest integer function. Then the number of discontinuities of $f(x)$ is:

The function $f(x)=x(\sqrt{x+2}+\sqrt{x+1})$ is continuous on

Let \(f(x) = \begin{cases} x + \alpha, & \text{if } x < 0 \\ \max(2\cos x, 2\sin x), & \text{if } x \geq 0 \end{cases}\). If \(f\) is continuous at \(x = 0\), then the value of \(\alpha\) is equal to

Let $f(x) = \begin{cases} \cos x & \text{if } x \geq 0 \\ -\cos x & \text{if } x<0 \end{cases}$. Which one of the following statements is not true?

The number of points at which the function \( f(x)=\frac{1{\log_e|x|} \) is discontinuous is}

Let \( R \) be the set of all real numbers. Let \( f: R \to R \) be a function such that \( |f(x) - f(y)|^2 \le |x - y|^3, \forall x, y \in R \). Then \( f'(x) = \)

Let \( R \) be the set of all real numbers. Let \( f: R \to R \) be a function such that \( |f(x) - f(y)|^2 \le |x - y|^3, \forall x, y \in R \). Then \( f'(x) = \)

Let \( R \) be the set of all real numbers. Let \( f: R \to R \) be a function such that \( |f(x) - f(y)|^2 \le |x - y|^3, \forall x, y \in R \). Then \( f'(x) = \)