Let [.] denote the greatest integer function. Assertion (A) : $\lim _{x \rightarrow \infty} \frac{[x]}{x}=1$ Reason $(R)$ : $f(x)=x-1, g(x)=[x], h(x)=x$ and $\lim _{x \rightarrow \infty} \frac{f[x]}{x}=\lim _{x \rightarrow \infty} \frac{h(x)}{x}=1$

• Correct answer
  A

  A is true, $\mathrm{R}$ is true: $\mathrm{R}$ is correct explanation of $\mathrm{A}$
• B

  A, R are true; R is not the correct explanation of $A$
• C

  $\mathrm{A}$ is true, $\mathrm{R}$ is false
• D

  A is false, R is true

Hence, the correct answer is option: 'A'.