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Binomial Expression

If the coeffi...

Question

If the coefficient of $7^{t h}$ and $13^{t h}$ term in the expansion of $(1 + x)^{n}$ are equal, then $n =$

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Solution

The correct option is C 18
${(x + a)}^{n} = x^{n} + C_{1}^{n} x^{n - 1} a + . . . + C_{r}^{n} x^{n - r} a^{r} + . . . a^{n} S i n c e t h e (r + 1) t h t e r m i s C_{r}^{n} x^{n - r} a^{r} . H e n c e t h e c o e f f i c e n t o f 7 t h t e r m i s C_{6}^{n} a n d 13 t h t e r m i s C_{12}^{n} C_{6}^{n} = C_{12}^{n} ⟹ n = 18 H e n c e o p t i o n (C)$

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