Question

If the coefficients of `(r-5)^(t h)` and `(2r-1)^(t h)` terms in the expansion of `(1+x)^(34)` are equal, find `rdot`

Answer 1

Correct Answer - `r = 14`
The coefficient of `(r-5)` th and `(2r-1)` the terms of the expansion `(1+x)^(34)` are `.^(34)C_(r-6)` and `.^(34)C_(2r-2)`, respectively.
Since they are equal so `.^(34)C_(r-6) = .^(34)C_(2r-2)`
Therefore, either `r - 6 = 2r-2` or `r - 6 = 34 - (2r-2)`
[Using the fact that if `.^(n)C_(r) = .^(n)C_(p)`, then either `r = p` or `r = n - p` ]
So, we get `r = - 4` or `r = 14`. r being a natural number, `r = - 4` is not possible.
So `r = 14`.