Question $1(1$ point$)$ What is the configuration after that?

$aax{q}_{2}bb$

$a{q}_2$axbb

$aax{q}_{1}bb$

$a{q}_1$axbb

$aa{q}_{1}bbb$ Question $2(1$ point$)$

Consider the following TM$.$

On input $00011122,$ the TM is reaches configuration $\frac{A}{O}OB11q_{2}22$ after $6$ steps. What is the next configuration? On input $00011122,$ the TM is reaches configuration A$00$B$11922$ after $6$ steps.

What is the next configuration?

$A00B11C{q}_{3}2$

$A00B11C{q}_{2}2$

$A00B11q_{2}22$

$A00B1q_{3}C_2$

$A00B1q_{2}C_2$Question $3(1$ point$)$

True or False: The string $00011122$ is accepted by the TM in problem $2.$

True

False

Question $4(1$ point$)$

What is the language of the TM shown in problem $2?$ Select all that apply.

$\{win{0}^{+}{1}^{+}{2}^{+}|n_0(w)=n_1(w)=n_2(w)\}$

$\{win{0}^{*}{1}^{*}{2}^{*}|n_0(w)=n_1(w)=n_2(w)\}$

$0^n{1}^n{2}^n,n0$

$\{win{0}^{+}{1}^{*}{2}^{*}|n_0(w)=n_1(w)=n_2(w)\}$

$0^n{1}^n{2}^n,n>0$

Consider the TM shown below

After the $3$rd step of computing the string aaabbb, configuration will be

$aa{q}_{1}bbb$

What is the configuration after that?