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If the coefficients of the r^t^h and (r+1)^t^h terms in the expansion of (3+7 x)^{29} are equal, then r is equal to 

Option: 1

20


Option: 2

21


Option: 3

22


Option: 4

23


Answers (1)

best_answer

\begin{aligned} & \mathrm{T}_{\mathrm{r}-1+1}={ }^{29} \mathrm{C}_{\mathrm{r}-1}(3)^{29-\mathrm{r}+1}(7 \mathrm{x})^{\mathrm{r}-1} \\ & ={ }^{29} \mathrm{C}_{\mathrm{r}-1} 3^{30-\mathrm{r}}(7 \mathrm{x})^{\mathrm{r}-1}----(1) \\ & \mathrm{~T}_{\mathrm{r}+1}={ }^{29} \mathrm{C}_{\mathrm{r}} 3^{29-\mathrm{r}}(7 \mathrm{x})^{\mathrm{r}}---(2) \end{aligned}

Comparing coefficient of x from (i) and (ii) 
\begin{aligned} & \frac{3}{29-r+1}=\frac{7}{r} \\ & \mathrm{r}=21 . \end{aligned}

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