The expression $^{n} C_{0} + 4^{n} C_{1} + 4^{2}^{n} C_{2} + . . . . . . . . . . + 4^{n}^{n} C_{n}$ , equals

2^{2 n}

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2^{3 n}

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5^{n}

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None of these

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Solution

The correct option is C $5^{n}$
We know that
$\begin{matrix} ^{n} C_{0} + 4^{n} C_{1} + {4^{2}}^{n} C_{2} + . . . . . . . + 4^{n}^{n} C_{n} {(1 + x)}^{n} =^{n} C_{0} +^{n} C_{1} x +^{n} C_{2} x^{2} + . . . . . +^{n} C_{n} P u t t i n g x = 4 5^{n} =^{n} C_{0} + 4^{n} C_{1} + {4^{2}}^{n} C_{2} + . . . . . . . + 4^{n}^{n} C_{n} H e n c e, o p t i o n C i s t h e c o r r e c t a n s w e r . \end{matrix}$

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