Question

Assertion :$f\left(x\right)=\sin x+\left[x\right]$ is discontinuous at $x=0$ because Reason: If $g\left(x\right)$ is continuous and $h\left(x\right)$ is discontinuous at $x=a$, then $g\left(x\right)+h\left(x\right)$ will necessarily be discontinuous at $x=a$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

At $x=0$, $\sin x$ is continuous but $\left[x\right]$ is not continuous.
Hence $f\left(x\right)=\sin x+\left[x\right]$ is discontinuous at $x=0$
Thus both statement are correct and Assertion is followed by Reason.