The output characteristics of a transistor is shown in the figure....

From the formula of current gain, $\beta = {\left(\dfrac{{\Delta i}_{C}}{{\Delta i}_{B}}\right)}_{{V}_{CE} = 10}$

${\Delta i}_{C} = \left(4 . 5 - 3\right)mA$

$⇒ {\Delta i}_{C} = 1 . 5mA$

$⇒ {\Delta i}_{C} = 1 . 5 \times {10}^{- 3}A$

${\Delta i}_{B} = \left(30 - 20\right)\mu A$

$⇒ {\Delta i}_{B} = 10\mu A$

$⇒ {\Delta i}_{B} = 10 \times {10}^{- 6}A$

$⇒ {\Delta i}_{B} = {10}^{- 5}A$

$⇒ \beta = {\left(\dfrac{{\Delta i}_{C}}{{\Delta i}_{B}}\right)}_{{V}_{CE} = 10} = \left(\dfrac{1 . 5 \times {10}^{- 3}}{{10}^{- 5}}\right)$

$⇒ \beta = \left(1 . 5 \times {10}^{- 3} \times {10}^{5}\right)$

$⇒ \beta = 150$