For a transistor,if the emitter current $I_E = 25 \, mA$ and the base current $I_B = 1 \, mA$,what is the ratio of the collector current $I_C$ to the emitter current $I_E$?

For transistor action:
$(1)$ Base,emitter and collector regions should have similar size and doping concentrations.
$(2)$ The base region must be very thin and lightly doped.
$(3)$ The emitter-base junction is forward biased and base-collector junction is reverse biased.
$(4)$ Both the emitter-base junction as well as the base-collector junction are forward biased.
Which one of the following pairs of statements is correct?

In a properly biased transistor:

What is the voltage gain of a common-emitter amplifier with an input resistance of $3 \ \Omega$ and a load resistance of $24 \ \Omega$? (Given $\beta = 6$)

In the circuit shown in the figure,the input voltage $V_i$ is $20\, V$,$V_{BE} = 0$,and $V_{CE} = 0$. The values of $I_B$,$I_C$,and $\beta$ are given by:

In the given circuit,a transistor with a current gain $\beta = 100$ is used. To have $V_{CE} = 5 \text{ V}$ and $V_{BE} = 0$,what should be the value of the base resistance $R_b$?