$1-$ Evaluate the voltages at all nodes and the currents through all branches in the circuit of the following circuit. Assume $=100.$

$2-$ Solve the problem in the question#$1$ for the case of a voltage ot $-vv$ teeding the bases. What voltage appears at the emitters?

$3-$ Solve the problem in the question#$1$ with the voltage feeding the bases changed to $+10$ V $.$ Assume that ${}_{\text{m}\text{i}\text{n}}=30,$ and find $V_E,V_B,I_{C_1},$ and $I_{C_2}.$

$4-$ For the circuit in the following figure, find $V_B$ and $V_F$ for $v_{\text{I}}=0V,+2V,-2\mathrm{.}5$ V $,$ and $-5$ V $.$ The BJTs have $=50.$

$5-$ In the circuit shown in the following figure, the transistor has $=50.$ Find the values of $V_B,V_E,$ and $V_C,$ and verify that the transistor is operating in the active mode. What is the largest value that $R_C$ can have while the transistor remains in the active mode?