Show that the language

$L=\{a^n{b}^k{c}^n$:$n0,kn\}$

is not regular.

Show that the language

$L=\{a^n{b}^k{c}^n{d}^k$:$n0,k>n\}$

is not regular.

Show that the language

$L=\{w$:$n_a(w)=n_b(w)\}$

is not regular. Is $L^{*}$ regular?