2
$latex 2\sin ^{2}\theta +3\cos ^{2}\theta$
$latex => 2\sin ^{2}\theta +2\cos ^{2}\theta +\cos ^{2}\theta$
$latex => 2\left ( \sin ^{2}\theta +\cos ^{2}\theta \right ) + \cos ^{2}\theta$
$latex => 2 + \cos ^{2}\theta$
Minimum value of $latex \cos\theta = -1$
But $latex \cos ^{2}\theta \geq 0, where \theta = 90\textdegree$
$latex [\cos 0\textdegree = 1, \cos 90\textdegree = 0]$
Hence required minimum value = 2 + 0 = 0
Option [B] is the right answer.