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$CH_4$ cannot be obtained by

$\begin{array}{1 1}(a)\;\text{Kolbe's electrolysis}&(b)\;\text{Wurtz reaction}\\(c)\;\text{Corey-House synthesis}&(d)\;\text{All of these}\end{array}$

In Kolbe's electrolysis we get alkane corresponding to dimer of alkyl part of acid salt.
In Wurtz reaction and Corey-House synthesis we get R-R or R-R'.Thus $CH_4$ cannot be obtained by any one of above method
$CH_3COONa+NaOH \quad\underrightarrow{CaO}\quad CH_4+Na_2CO_3$
Hence (d) is the correct answer.