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.

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