Consider two distinct positive numbers \( m, n \) with \( m > n \). Let \[ x = n^{\log_n m}, \quad y = m^{\log_m n}. \] The relation between \( x \) and \( y \) is -
If \[ \log_{p^{1/2}} y \times \log_{y^{1/2}} p = 16, \] then find the value of the given expression.
If 0.01 mol of $\mathrm{P_4O_{10}}$ is removed from 0.1 mol, then the remaining molecules of $\mathrm{P_4O_{10}}$ will be:
An element has two isotopes having atomic masses 10 and 15 u, respectively. If the percent abundance of lighter isotopes is 80%, then the average atomic mass of the element is: