For a common emitter configuration,if $\alpha$ and $\beta$ have their usual meanings,the incorrect relationship between $\alpha$ and $\beta$ is:

When the transistor is used as an amplifier,

For a transistor in the active region:
$(a)$ Base,emitter,and collector regions should have similar size and doping concentrations.
$(b)$ The base region must be very thin and lightly doped.
$(c)$ The emitter-base junction is forward-biased and the base-collector junction is reverse-biased.
$(d)$ Both the emitter-base junction and the base-collector junction are forward-biased.
Which one of the following pairs of statements is correct?

The base current is $100 \mu A$ and the collector current is $3 \text{ mA}$. $A$ change of $20 \mu A$ in the base current results in a change of $0.5 \text{ mA}$ in the collector current. The value of $\beta_{ac}$ is:

In a transistor circuit,the collector current is changed by $8.9 \ mA$,if the emitter current is changed by $9.0 \ mA$. The value of current amplification factor,$\beta$ is

In a transistor,a change of $8.0\, mA$ in the emitter current produces a change of $7.8\, mA$ in the collector current. What change in the base current is necessary to produce the same change in the collector current? (in $\mu A$)