Question

Let $a=1\cdot 2\cdot 3\cdot 4\cdot 5$. Then

• A. $5^5\ge a$
• B. $3^5\ge 5!$
• C. $5^5\ge 6a$
• D. None of these

Answer 1

Answer: (A), (B)

Since $A.M.>G.M.$
$\Rightarrow \frac{1+2+3+4+5}{5}\ge \sqrt[5]{1\cdot 2\cdot 3\cdot 4\cdot 5}$
$\Rightarrow 3\ge \sqrt[5]{a}$
$\Rightarrow 3^5\ge a=5!$
Also, $5^5\ge 1\cdot 2\cdot 3\cdot 4\cdot 5=a$.