Question

Assertion (A): $f\left(x\right)=\frac{\sin \left\{\right[x\left]\pi \right\}}{1+x^2}$ is continuous on $R$ (where $\left[x\right]$ denotes greatest integer function of $x$).
Reason (R): Every constant function is continuous on $R$

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true and R is not the correct explanation of A
• C. A is true but R is false
• D. R is true but A is false

Answer 1

The correct option is A Both A and R are true and R is the correct explanation of A

$f\left(x\right)=\frac{\sin \left\{\left[2\right]\pi \right\}}{1+x^2}$

$\left[x\right]$ will always give us an integer

and we know that $\sin \left(n\pi \right)=0,nϵI$

$\Rightarrow f\left(x\right)=\frac{0}{1+x^2}=0$

$\Rightarrow f\left(x\right)$ is a constant function.

$\Rightarrow f\left(x\right)$ is continuous on R.