The smallest positive root of the equation ta | vedclass

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(C) The given equation is $	an x - x = 0$, which implies $	an x = x$.To find the roots, we look for the points of intersection of the curves $y =

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$\left(\pi, \frac{3\pi}{2}\right)$

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(C) The given equation is $	an x - x = 0$, which implies $	an x = x$.To find the roots, we look for the points of intersection of the curves $y = 	an x$ and $y = x$.At $x = 0$, both curves intersect at the origin, but we are looking for the smallest positive root.For $x \in \left(0, \frac{\pi}{2}ight)$, $	an x > x$, so there is no intersection in this interval.For $x \in \left(\frac{\pi}{2}, \piight)$, $	an x$ is negative while $x$ is positive, so there is no intersection.For $x \in \left(\pi, \frac{3\pi}{2}ight)$, the curve $y = 	an x$ starts from $-\infty$ at $x = \pi^+$ and increases to $+\infty$ at $x = \frac{3\pi}{2}^-$. Since the line $y = x$ is positive in this interval, the curve $y = 	an x$ must intersect the line $y = x$ at exactly one point.Thus, the smallest positive root lies in the interval $\left(\pi, \frac{3\pi}{2}ight)$.

Column-$I$ (Common Name)	Column-$II$ (Taxonomic category- Family)
$A$. Man	$I$. Poaceae
$B$. Datura	$II$. Anacardiaceae
$C$. Mango	$III$. Solanaceae
$D$. Wheat	$IV$. Hominidae

The smallest positive root of the equation $\tan x - x = 0$ lies in

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