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UPSC NDA II 2025 Mathematics Paper

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Question Numbers: 21-22

For the following two (02) items:

Let

\alpha

and

\beta

be the roots of the quadratic equation

(x^{2} + (\log_{0.5}(\alpha^{2}))x + (\log_{0.5}(\alpha^{2}))^{4} = 0.

where

a^{2} \neq 1

and

\log_{0.5}(\alpha^{2}) > 0

Further,

\beta^{2} = \alpha (\log_{\alpha^{2}}(0.5))

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Question : 21 of 120

Marks: +1, -0

What is ẞ equal to?

$\log_{a^{2}}(0.5)$
$\log_{0.5}(a^{2})$
$2(\log_{a^{2}}(0.5))$
$2\log_{0.5}(a^{2})$

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