Binomial Theorem And Its Simple Applications Question 205
Question: If $ 7^{9}+9^{7} $ is divided by 64 then the remainder is
Options:
A) 0
B) 1
C) 2
D) 63
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] We have $ 7^{9}+9^{7}={{(8-1)}^{9}}+{{(8+1)}^{7}}={{(1+8)}^{7}}-{{(1-8)}^{9}} $
$ =[1+{{,}^{7}}C_18+{{,}^{7}}C_28^{2}+…+{{,}^{7}}C_7,8^{7}] $
$ -[1-{{,}^{9}}C_18+{{,}^{9}}C_28^{2}-….-{{,}^{9}}C_98^{9}] $
$ ={{,}^{7}}C_18+{{,}^{9}}C_18+[{{,}^{7}}C_2+{{,}^{7}}C_3.8+…-{{,}^{9}}C_2+, $
$ ^{9}C_3.8-…]8^{2} $
$ =8(7+9)+64,k=8.16+64,k=64,q. $
Where $ q=k+2 $
Thus, $ 7^{9}+9^{7} $ is divisible by 64.
BETA
