3. Past Questions

Question 1

Which among $2^{1/2}$, $3^{1/3}$, $4^{1/4}$, $6^{1/6}$, $12^{1/12}$ is the largest?
[CAT 2006]

		$2^{1/2}$
		$3^{1/3}$
		$4^{1/4}$
		$6^{1/6}$
		$12^{1/12}$

Question 2

$p$ and $q$ are positive numbers such that $p^{q} = q^{p}$ and $q = 9p$. The value of $p$ is
[XAT 2013]

		$\sqrt{9}$
		$\sqrt[6]{9}$
		$\sqrt[9]{9}$
		$\sqrt[8]{9}$
		$\sqrt[3]{9}$

Question 3

The simplest value of the expression $\left( \dfrac{4^{p + \frac{1}{4}} \times \sqrt{2 \times 2^{p}}}{2 \times \sqrt{2^{-p}}} \right)^{\frac{1}{p}}$ is:
[IIFT 2015]

		$4$
		$8$
		$4^p$
		$8^p$