Explanation

(b) The modulation index is given as
$\beta = \frac{\mathrm{\Delta}f}{f_{m}}$
Where, $\mathrm{\Delta}f$ is frequency deviation, $f_{m}$ the highest modulating frequency.
Given, $\mathrm{\Delta}f = 10\ kHz = 10 \times 10^{3}\ Hz,$
$f_{m} = 2\ kHz = 2 \times 10^{3}\ Hz$
$\therefore\ \beta = \frac{{10 \times 10}^{3}}{{2 \times 10}^{3}} = 5$