Question

Which among the following is /are true?
I. $(1.1{)}^{10000}>100$
II. $(1.1{)}^{10000}<100$
III. $(1.1{)}^{10000}>1000$
IV. $(1.1{)}^{10000}<1000$

• A. I and IV are true
• B. II and IV are true
• C. I and III are true
• D. Only IV is true

Answer 1

Answer: (C)

$(1\cdot 1{)}^{10000}=(1+0\cdot 1{)}^{10000}$
$={}^{10000}{C}_0(1{)}^{10000}+{}^{10000}{C}_1(1{)}^{9999}(0\cdot 1)+\dots .+$ Other terms
$=1\times 1+10000\times 0\cdot 1+\dots$ Other terms $\left(\because {}^n{C}_0=1,{}^n{C}_1=n\right)$
$=1+1000+$ Other terms
$=(1001+$ Other terms $)>1000\Rightarrow (1\cdot 1{)}^{10000}>1000$