MCQ
Statement $1$ : A function $f:R \to R$ is continuous at $x_0$ if and only if $\mathop {\lim }\limits_{x \to {x_0}} \,f\left( x \right)$ exists and $\mathop {\lim }\limits_{x \to {x_0}} \,f\left( x \right) = f\left( {{x_0}} \right)$

Statement $2$ :  A function $f : R \to R$ is discontinuous at $x_0$ if and only if, $\mathop {\lim }\limits_{x \to {x_0}} \,f\left( x \right)$ exists and $\mathop {\lim }\limits_{x \to {x_0}} \,f\left( x \right) \ne f\left( {{x_0}} \right)$

  • A
    Statement $1$ is true, Statement $2$ is true,Statement $2$ is not a correct explanation of Statement $1$ 
  • B
    Statement $1$ is false, Statement $2$ is true
  • C
    Statement $1$ is true, Statement $2$ is true,Statement $2$ is a correct explanation of Statement $1$ 
  • Statement $1$ is true, Statement $2$ is false

Answer

Correct option: D.
Statement $1$ is true, Statement $2$ is false
d
Statement $-1$ is true. It is the definition of continuity. Statement $-2$ is false

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