Determine the value of $x$ in the expression of ${(2 + x)}^{5}$ , if the second term in the expansion is $240$

(24)^{\frac{1}{4}}

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6

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3

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None of the above

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Solution

The correct option is C $3$
The general term of $(a + x)^{n}$ is $^{n} C_{r} a^{(n - r)} x^{r}$

Here, $n = 5$
we will get second term if we put $r = 1$

The second term will be $^{5} C_{1} (2^{(5 - 1)}) x$
$= 5 (2^{4}) x$

$5 (2^{4}) x = 240$ ...... given
Therefore
$5 (16) x = 240$
$80 (x) = 240$
$x = 3$

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