please solve all subtasks. dont provide partial solutions

Task $2.$

a$)$ Find grammars that generate languages on $x=\{0,1\}$ :

$(1.)$ STRINGS CONSISTING ONLY OF UMITS

$(2.)$ STUINGS STARTING WITH O AND EMDIMG WITH $1.$

NOTCE THAT YOU ARE NOT ASEED TO FIMD RIGHT LINEAR GRAMMERS.I

b$)$ DEtermine weather the WORD $0101$ belongs to one of the rollowing Regulars expressions, the LAMGUAGE they denote:

$(1.){01}^{**}{1}^{**}$

$(2.)01**1$

$(3.)O(11{)}^{**}(01{)}^{**}$

$(4.)0(10{)}^{**}{1}^{**}$

$(5.)0**10(0+1)$

$(6.)0^{**}(10+11{)}^{**}$

c$)$ fimd the finite automatom that recognizes the words of the markg language by the regular expression $(0+11{)}^{**}$

d$)$ FIND A FIMITE aUtomatom THAT RECOGMIEES THE wORDS OF THE LAMGUAGE $L=\{a(bb{)}^{h}a|h0\}.$ ALSO FIMD A RIGITT limear grammar titat generates that language as well as regular expression that denotes that layguage.

e$)$ FIND THE RIGIT$-$LIMEAR grammar that generates the language marked by the regular expression $0^{**}(1(0+1){)}^{**}$ FIND THE uLtimate automaton that RECOgmizes the wURDS of the LANGUAGE, MARKED bY tite previous REgULAR EXPRESSION. $($INSTRUCTION: WITEN WE ARE LOOKING FOR R$16147$ LINEAR GRAMMAR FOR WORDS OF THE FORM UV$,$ IN PUNCIPCE, We caN have productions $S|vT|,T$ OR $sT,Tv.$

PODUCTIONS FOR $u^{**}$ ARE OBTANED AS $SS||,$ AND ${}^{+}$AS $SS||..)..$ for tasks that require definition wrote definition and solve tasks. tnx