To solve this problem, we need to analyze the given transistor circuit.$\\$Given:$\\ V_i = 20 \,$V$, \, V_{BE} = 0, \, V_{CE} = 0 \\$The transistor is in saturation, so $V_{CE} = 0. \\$Let's calculate the base current $I_B: \\$The voltage across $R_B$ is $V_i - V_{BE} = 20 \,$V.$\\ I_B = \frac{V_i - V_{BE}}{R_B} = \frac{20 \, V}{500 \, k \Omega} \\ I_B = \frac{20}{500 \times 10^3} \\ I_B = 40 \, \mu A \\$Next, calculate the collector current $I_C: \\$Since the transistor is in saturation, $V_{CE} = 0. \\$The voltage across $R_C$ is $20 \,$V$. \\ I_C = \frac{20 \, V}{4 \, k \Omega} \\ I_C = \frac{20}{4 \times 10^3} \\ I_C = 5 \, mA \newline$Finally, calculate $\beta: \\ \beta = \frac{I_C}{I_B} = \frac{5 \, mA}{40 \, \mu A} \\ \beta = \frac{5 \times 10^{-3}}{40 \times 10^{-6}} \\ \beta = 125 \\$Therefore, the values are $I_B = 40 \, \mu$A$, \, I_C = 5 \,$mA$, \, \beta = 125. \\$This corresponds to Option 4.