Question

Assertion :The number of roots of the equation $x\sin x=1\forall x\in [-2\pi ,0)\cup (0,2\pi ]$ is $2$ Reason: Number of roots of the equation $y=f\left(x\right)=g\left(x\right)$ are the number of points where two curves meet each other.

• 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 D Assertion is incorrect but Reason is correct.

$x\sin x=1$
$\Rightarrow \sin x=\frac{1}{x}=y$
By graph both curves intersect at four points
$\therefore$ Number of solutions are 4.
$\therefore$ Assertion is false & Reason is correct.