If d/dx{x^n - a1x^n-1 + a2x^n-2 + ....+(-1)^n an} e^x = x^n e^x Then the value of ar , 0 < r ≤ n, is equal to

Question

If \(\{\frac{d}{dx}{x^n-a_1x^{n-1}+a_2x^{n-2}+..+(-1)^na_n}\}\)

e^x = xⁿe^x,

Then the value of ar , 0 < r ≤ n, is equal to

A. \(\frac{n!}{r!}\)

B. \(\frac{(n-r)!}{r!}\)

C. \(\frac{n!}{(n-r)!}\)

D. none of these

Answer 1

Correct Answer is (C) \(\frac{n!}{(n-r)!}\) 

Given:

 \(\{\frac{d}{dx}{x^n-a_1x^{n-1}+a_2x^{n-2}+..+(-1)^na_n}\}\)

e^x = xⁿe^x