Question

If $a={\left(100\right)}^{1/100}$ and $b={\left(101\right)}^{1/101}$ then

• A. $a=b$
• B. $a>b$
• C. $a<b$
• D. none of these

Answer 1

Answer: (B)

$a>b$

Consider the function $x^{1/x}$

$f^{\prime }\left(x\right)=\frac{(1-\ln x)}{x^2}.x^{1/x}$

$f\left(x\right)$ is monotonic strictly decreasing for $x>e$. Thus $f\left(101\right)<f\left(100\right)$

$\therefore b<a$