Binomial Theorem And Its Simple Applications Question 139
Question: In the polynomial $ (x-1)(x-2)(x-3)………….(x-100), $ the coefficient of $ x^{99} $ is
[AMU 2002]
Options:
A) 5050
B) - 5050
C) 100
D) 99
Show Answer
Answer:
Correct Answer: B
Solution:
- $ (x-1)(x-2)(x-3)….(x-100) $
Number of terms = 100;
Coefficient of x99 = $ (x-1)(x-2)(x-3)…(x-100) $ = $ (-1-2-3-……-100) $ =
$ -(1+2+…..+100) $ = $ -\frac{100\times 101}{2} $ = - 5050.
BETA
