A transistor is used in common-emitter mode in an amplifier...

First, use the formula of current gain in terms of change in base current, and collector current,

$\beta = \dfrac{\Delta{I}_{c}}{\Delta{I}_{B}}$

given,

${V}_{BE} = 10 \times {10}^{- 3}V, ∆ {i}_{b} = 10 \times {10}^{- 6}A$,

$∆ {i}_{c} = 1 . 5 \times {10}^{- 3}A$ and ${R}_{L} = 5 \times {10}^{3}Ω$

So the formula of voltage gain,

${\beta}_{V} = \dfrac{∆ {V}_{CE}}{∆ {V}_{BE}} = \dfrac{∆ {i}_{c} \times {R}_{L}}{∆ {V}_{BE}}$

$⇒ {\beta}_{V} = \dfrac{1 . 5 \times {10}^{- 3} \times 5000}{10 \times {10}^{- 3}} = 750$