First slide

Binomial theorem for positive integral Index

Question

$The coefficient of x^{50} in (1 + x)^{41} {(1 - x + x^{2})}^{40} is$

Moderate

A

0
B

1
C

2
D

3

Solution

$\begin{array}{rcl} Coefficient of x^{50} in {(1 + x)}^{41} {(1 - x + x^{2})}^{40} \\ = & Coefficient of x^{50} in (1 + x) {(1 + x^{3})}^{40} \end{array}$
$= coefficient of x^{50} in (1 + x) (1 +^{40} C_{1} x^{3} + ...... +^{40} C_{16} {(x^{3})}^{16} +^{40} C_{17} {(x^{3})}^{17} + .....) = 0$

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