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UPSC NDA 2 2022 Mathematics Solved Paper

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Consider the following for the next three (03) items that follow:

Let

A=\begin{pmatrix} 0 & \sin^2 \theta & \cos^2 \theta \\ \cos^2 \theta & 0 & \sin^2 \theta \\ \sin^2 \theta & \cos^2 \theta & 0 \end{pmatrix}

and

A=P+Q

where

P

is symmetric matrix and

Q

is skew-symmetric matrix.

[NDA II 2022]

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Question : 39 of 120

Marks: +1, -0

What is the minimum value of determinant of

A

$\;\frac{1}{4}$
$\;\frac{1}{2}$
$\;\frac{3}{4}$
1

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