# Aptitude Question ID : 92997

The minimun value of $2\sin ^{2}\theta +3\cos ^{2}\theta$is :
[A]0
[B]2
[C]3
[D]1

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