First slide

Binomial theorem for positive integral Index

Question

$Unit digit of 7^{886} is$

Moderate

A

1
B

3
C

7
D

9

Solution

$7^{886} = {(7^{2})}^{443}$
$\begin{array}{l} = (50 - 1)^{443} \\ = 50^{443} - 443 C_{1} (50)^{442} + \dots . {}^{443}C_{442} (50) - 1 \\ = 10 m + 9 w h e r e m i s s o m e i n t e g e r (\sin c e, a d d - 9 a n d 9) \end{array}$
$\Rightarrow$ Last digit of $7^{886}$ is 9

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