Question

Assertion :Let $f\left(x\right)=[3+4\sin x]$ where [x] denotes the greatest integer function. The number of discontinuities of $f\left(x\right)$ in $[\pi ,2\pi ]$ is 6. Reason: The range of $f$ is {-1, 0,1,2, 3}

• 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. Both Assertion and Reason are incorrect

Answer 1

The correct option is D Both Assertion and Reason are incorrect

$f\left(x\right)$ will be discontinuous at the points where
$\sin x=\frac{1}{4},\frac{2}{4},\frac{3}{4},\frac{4}{4}$
as $-1\le \sin x\le 1$
Range of $[3+4\sin x]$ is $[-1,7]$