If n € N, n > 1, then value of E=a−nC1(a−1)+nC2(a−2)+…....+(−1)n(a−n)nCn is

A
$α$
B
0
C
$α^{2}$
D
2ⁿ

Solution:

Given equation can be rewritten as

$E = a [^{n} C_{0} -^{n} C_{1} +^{n} C_{2} - \dots + (- 1)^{n n} C_{n}]$ $+ [^{n} C_{1} - (2) (^{n} C_{2}) + (3) (^{n} C_{3}) - \dots + (- 1)^{n} (n) (^{n} C_{n})]$

$\Rightarrow E = 0 + 0 = 0$ $[by properties]$

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