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)

$(1 \cdot 1)^{10000}=(1+0 \cdot 1)^{10000}$
$={ }^{10000} C_0(1)^{10000}+{ }^{10000} C_1(1)^{9999}(0 \cdot 1)+\ldots .+$ Other terms
$=1 \times 1+10000 \times 0 \cdot 1+\ldots$ Other terms $\left(\because{ }^n C_0=1,{ }^n C_1=n\right)$
$=1+1000+$ Other terms
$=(1001+$ Other terms $)>1000 \Rightarrow(1 \cdot 1)^{10000}>1000$