Find the number of terms in the expansion of $(1 - 5 x)^{7} + (1 + 5 x)^{7}$ ____.

8

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6

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5

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4

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Solution

The correct option is C $4$
$S = {(1 - 5 x)}^{7} + {(1 + 5 x)}^{7}$
$L e t 5 x = k$
$The above binomial expansion changes to$
$S= {(1 - k)}^{7} + {(1 - k)}^{7}$
$= [1 - C_{1}^{7} k + C_{2}^{7} k^{2} - C_{3}^{7} k^{3} . . . . . . . . C_{7}^{7}] + [1 + C_{1}^{7} k + C_{2}^{7} k^{2} + C_{3}^{7} k^{3} . . . . . . . . C_{7}^{7}]$
$= 2 [[1 + C_{2}^{7} k^{2} + C_{4}^{7} k^{4} + C_{6}^{7} k^{6}]]$
$H ence total number of terms will be 4$

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