If the coefficients of rth and `(r+1)t h` terms in the expansion of `(3+7x)^(29)` are equal, then `r` equals a. 15 b. 21 c. 14 d. none of these

Options

A. 15
B. 21
C. 14
D. none of these

Answer

B

Explanation

We have `T_(r+1)=.^(29)C_(r)3^(29-r)(7x)^(r)=(.^(29)C_(r)xx3^(29-r)xx7^(r))x^(r)`

Coefficient of `(r+1)^(th)` term is `.^(29)C_(r) xx 3^(29-r)xx7^(r )`
and coefficient of `r^(th)` term is `.^(29)C_(r-1)xx3^(30-r) xx 7^(r-1)`
From given condition
`.^(29)C_(r) xx 3^(29-r) xx 7^(r) = .^(29)C_(r-1) xx 3^(30-r) xx 7^(r-1)`
`rArr (.^(29)C_(r))/(.^(29)C_(r-1)) = 3/7`
`rArr (30-r)/(r ) = 3/7` or `r = 21`