Parsing

Consider the following grammar along with translation rules.
\begin{aligned} &S \rightarrow S_1 \# T & & \{S._{val}=S_{1.val}*T._{val} \} \\ &S \rightarrow T & & \{S._{val}=T._{val} \} \\ &T \rightarrow T_1 \% R & & \{T._{val}=T_{1.val} \div R._{val} \} \\ &T \rightarrow R & & \{T._{val}=R._{val} \} \\ &R \rightarrow id & & \{R._{val}=id._{val} \} \\ \end{aligned}
Here \# and \% are operators and id is a token that represents an integer and id_{.val} represents the corresponding integer value. The set of non-terminals is \{S,T,R,P \} and a subscripted non-terminal indicates an instance of the non-terminal.
Using this translation scheme, the computed value of S_{.val} for root of the parse tree for the expression 20 \# 10 \% 5 \# 8 \% 2 \% 2 is

Consider the augmented grammar with \{+, *, (, ), id \} as the set of terminals.
\begin{aligned}&S' \rightarrow S \\ &S \rightarrow S+R|R \\ &R \rightarrow R*P|P \\ &P \rightarrow (S)|id \end{aligned}
If I_0 is the set of two LR(0) items \{ [S' \rightarrow S.], [S \rightarrow S.+R] \}, then goto(closure(I_0 ),+) contains exactly ______ items.

Which one of the following statements is TRUE?

Consider the following augmented grammar with \{ \#, @, <, >, a, b, c \} as the set of terminals.

\begin{array}{l} S' \rightarrow S \\ S \rightarrow S \# cS \\ S \rightarrow SS \\ S \rightarrow S @ \\ S \rightarrow < S > \\ S \rightarrow a \\ S \rightarrow b \\ S \rightarrow c \end{array}

Let I_0 = \text{CLOSURE}(\{S' \rightarrow \bullet S\}). The number of items in the set \text{GOTO(GOTO}(I_0 \lt ), \lt ) is ___________

Consider the following C code segment:

a = b + c;
e = a + 1;
d = b + c;
f = d + 1;
g = e + f;

In a compiler, this code segment is represented internally as a directed acyclic graph (DAG). The number of nodes in the DAG is _____________