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7.Binomial Theorem
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જો ${\left( {\frac{3}{{{{\left( {84} \right)}^{\frac{1}{3}}}}} + \sqrt 3 \ln \,x} \right)^9},\,x > 0$ માં પ્રથમ $7^{th}$ પદ $729$ હોય તો $x$ ની શકય કિમત મેળવો
A
$e^2$
B
$e$
C
$\frac {e}{2}$
D
$2e$
Solution
$\mathrm{T}_{7}=^{9} \mathrm{C}_{6}\left(\frac{3}{(84)^{1 / 3}}\right)^{3}(\sqrt{3} \ln \mathrm{x})^{6}=729$
$\Rightarrow(\ln \mathrm{x})^{6}=1$
$\Rightarrow \ln \mathrm{x}=\pm 1$
$\Rightarrow \mathrm{x}=\mathrm{e}, 1 / \mathrm{e}$
Standard 11
Mathematics
