Question

Last two digits of $21^{100}$ are

• A. 00
• B. 01
• C. 11
• D. 21

Answer 1

Answer: (B)

$(21{)}^{100}=(1+20{)}^{100}$
$=1+{}^{100}{C}_1\cdot 20+{}^{100}{C}_2\cdot 20^2+\cdots +{}^{100}{C}_{100}\cdot 20^{100}$
Hence, last two digit are $01$ .