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Plasmid DNA $(0.5 \: \mu g)$ containing an ampicillin resistance marker was added to $200 \: \mu l$ of competent cells. The transformed competent cells were diluted $10,000$ times, out of which, $50 \: \mu l$ was plated on agar plates containing ampicillin. A total of $35$ colonies were obtained. The transformation efficiency is _______$\times 10^6 \: \text{ cfu} \cdot \mu g^{-1}$
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