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

Question

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

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

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - B
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`