List of top Mathematics Questions on Continuity asked in KCET

The function $f(x) = |\cos x|$ is:
The function f(x) = cot x is discontiuous on every point of the set
Consider the following statements :
Statement 1 : \(\lim\limits_{x\rightarrow1}\frac{ax^2+bx+c}{cx^2+bx+a}\) is 1 (where a + b + c ≠ 0)
Statement 2 : \(\lim\limits_{x\rightarrow-2}\frac{\frac{1}{x}+\frac{1}{2}}{x+2}\) is \(\frac{1}{4}\)

If f(x) = \(\left\{ \begin{aligned}     & \frac{1-\cos Kx}{x\sin x} ,\ \ \text{if x}\neq0 \\     &\ \ \ \ \ \  \ \frac{1}{2}\ \ \ \ \ \ \ \ \  ,\ \ \  \text{if x=0} \end{aligned} \right.\) is continuous at x = 0, then the value of K is

The right hand and left hand limit of the function
f(x) = \(\left\{ \begin{aligned}     & \frac{e^{1/x}-1}{e^{1/x}+1}\ \ ,\ \ \text{if x}\ne0   \\     & \ \ \ \ \ \ 0 \ \ \ \ \ \ \ \ ,\ \ \text{if x = 0}    \end{aligned} \right.\) are respectively