Non Removable Discontinuities

Q. Which of the following is/are function(s)?

1. 
2. 
3. 
4. 

Q.

$f\left(x\right)=\left[x\right]$ is discontinuous at $x=1$ because

1. Value of function is not defined

2. Value of $f\left(x\right)$ is finite but not equal to the limit

3. Limit doesn't exist

4. Statement wrong, function is continuous

Q.

In which of the following cases is the function f(x) discontinuous at a?

1. $\underset{x\to a}{Lt}f\left(x\right)=\infty$

2. $\underset{x\to a^{-}}{Lt}f\left(x\right)\ne \underset{x\to a^{+}}{Lt}f\left(x\right)$

3. $f\left(a\right)\ne \underset{x\to a^{+}}{Lt}f\left(x\right)$

4. $\underset{x\to a}{Lt}f\left(x\right)=0$