First slide

Binomial theorem for positive integral Index

Question

The coefficient of $x^{60} in (1 + x)^{51} {(1 - x + x^{2})}^{50}$ is

Moderate

A

$^{50} C_{20}$
B

$- (^{50} C_{20})$
C

$^{51} C_{20}$
D

$- (^{51} C_{20})$

Solution

The coefficient of $x^{60}$ in $(1 + x)^{51} {(1 - x + x^{2})}^{50}$
= the coefficient of $x^{60}$ in $(1 + x) {(1 - x^{3})}^{50}$
$=^{50} C_{20}$

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