The ratio of the coefficient of terms $x^{n - r} a^{r}$ and $x^{r} a^{n - r}$ in the binomial expansion of $(x + a)^{n}$ will be

x : a

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n : r

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x : n

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none of these

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Solution

The correct option is D none of these
${(x + a)}^{n} = x^{n} + C_{1}^{n} x^{n - 1} a + . . . + C_{r}^{n} x^{n - r} a^{r} + . . . a^{n} S i n c e t h e (r + 1) t h t e r m i s C_{r}^{n} x^{n - r} a^{r} . R a t i o o f c o e f f i c e n t s i s \frac{C_{r}^{n}}{C_{n - r}^{n}} w h i c h i s e q u a l t o 1. H e n c e o p t i o n (D)$

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