BPSC 48th to 52nd Exam Prelims 2008 Solved Paper

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Question : 34 of 150

Marks: +1, -0

The expression

4 /{^3 √{9}^3√ {3 }+1}

has the value –

$3^{1/3} + 1$
$3^{1/2} + 1$
$3^{1/3} – 1$
$3^{1/2} – 1$

Solution:

From the question

\;{4}/{√^{3}{9} × √^{3}{3+1}}

=\;{(√^{3}{3})^{3}+1}/{(√^{3}{3})^{2}-√^{3}{3}+1}

=\;{(√^{3}{3}+1)[(√^{3}{3})^{2}-√^{3}{3}+1]}/{(√^{3}{3})^{2}-√^{3}{3}+1}

=√^{3}{3}+1=(3)^{\;{1}/{2}}+1

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