Question

If p, q, n are three positive real numbers and p > q then which of the following is correct.

• A. ${\left[\frac{1}{p}\right]}^{\frac{1}{n}}<{\left[\frac{1}{q}\right]}^{\frac{1}{n}}$
• B. $p^{\frac{1}{n}}<q^{\frac{1}{n}}$
• C. $p^{\frac{-1}{n}}>q^{\frac{-1}{n}}$
• D. $p^n<q^n$

Answer 1

The correct option is A

${\left[\frac{1}{p}\right]}^{\frac{1}{n}}<{\left[\frac{1}{q}\right]}^{\frac{1}{n}}$

Given that, p > q

⇒ $\frac{1}{p}<\frac{1}{q}$ (using the property of inequality)
${\left[\frac{1}{p}\right]}^{\frac{1}{n}}<{\left[\frac{1}{q}\right]}^{\frac{1}{n}}$