a, b and c are true

only c is true

b and c are true

a and d are true

$\tan^{-1}\left[\left(\frac{\gamma^2-1}{\gamma}\right)\left(\frac{\sigma_x\sigma_y}{\sigma_x^2+\sigma_y^2}\right)\right]$

$\tan^{-1}\left[\left(\frac{\gamma}{\gamma^2-1}\right)\left(\frac{\sigma_x\sigma_y}{\sigma_x^2+\sigma_y^2}\right)\right]$

$\tan^{-1}\left[\left(\frac{\gamma}{1-\gamma^2}\right)\left(\frac{\sigma_x\sigma_y}{\sigma_x^2+\sigma_y^2}\right)\right]$

$\tan^{-1}\left[\left(\frac{1-\gamma^2}{\gamma}\right)\left(\frac{\sigma_x\sigma_y}{\sigma_x^2+\sigma_y^2}\right)\right]$

Bowley's index number

Fisher's index number

Edge-Worth's index number

Paasche's index number