$($b$)$ Evaluate the following by hand, showing all your working:

$((56{)}^{15}+35{)}^2$mod$29$

$($c$)$ The list $(x_i{)}_{1.\mathrm{.}6}=(P,A,C,$I,$N,G)$ is to be sorted using Selection sort. The

sorting is to be achieved by progressively modifying an index function $,$ rather

than by shuffling members of the list itself. So initially $(x_i{)}_{1.\mathrm{.}6}=(x_{(i)}{)}_{1.\mathrm{.}6}$ where

$(i)=$i for $i=1,$dots,$6,$ and when sorting is complete $$ is sufficiently changed so

that $(x_{(i)}{)}_{1\mathrm{.}66}$ is in alphabetical order. Complete the following so that it repre$-$

sents the final index function.

$([1,2,3,4,5,6])larr$ Write $in$ this line

$($d$)$ The list

$(7,1,3,4,6,8,5,5)$

is to be sorted into non$-$decreasing order using Merge sort $($for reference, a de$-$

scription of the algorithm is given on the next page$).$ A comparison operation is

performed when two elements in a list are compared to see which is bigger. How

many comparison operations will be performed during the sorting process?