Question

The coefficient of `x^(53)` in the expansion
`sum_(m=0)^(100) ""^(100)C_(m)(x-3)^(100-m)2^(m)` is
A. `.^(100)C_(47)`
B. `.^(100)C_(53)`
C. `-.^(100)C_(53)`
D. `-.^(53)C_(100)`

Answer 1

Correct Answer - C
The given sigma is the expansion of
`[(x-3)+2]^(100)=(x-1)^(100)= (1-x)^(100)`
Therefore, `x^(53)`will occur in `T_(54)`.
Therefore, the coefficient is `-.^(100)C_(53)`.