CompSci alogrithm subject questions: $1)$Given a polynomial as follows,

$P(x)=a_0+a_1{x}^3+a_2{x}^7+a_3{x}^{11}+a_4{x}^{15}$

to evaluate it for arbitrary coefficients $\{a_0,a_1,a_2,a_3,a_4\}$ and some given value $x,$

the minimum number of multiplications that one needs is:

$($a$)5$

$($b$)6$

$($c$)7$

$($d$)8$ or more

$2)$Which of the following growth functions has the highest order of growth?

$($a$)n$

$($b$)logn$

$($c$)nlogn$

$($d$)n^2$

$3)$If a given array does not contain any adjacent inversion, then it does not contain

any global inversion.

$($a$)$ true

$($b$)$ false

$4)$Is it possible that one can find the solution for the problem: Finding both the

minimum and the maximum of an array with $n$ elements using an algorithm that

is in $(n)?$

$($a$)$ yes

$($b$)$ no

$5)$Given an $n-$element array with $n>7,$ it is possible to arrange these $n$ elements,

such that all of them are NOT in place. $($Assume that these elements are distinct.$)$

$($a$)$ true

$($b$)$ false

$6)$When we use the linear search on many different input arrays, sometimes we have

unordered arrays and sometimes we have ordered arrays. Which of the following

statements about the efficiency is correct?

$($a$)$ We will get better efficiency whenever we process the ordered arrays.

$($b$)$ We will get better efficiency whenever we process the unordered arrays.

$($c$)$ We will get the same efficiency no matter we process the ordered or unordered

arrays.

$7)$Which of the following growth functions has the lowest order of growth?

$($a$)\sqrt[100]{n}$

$($b$)logn$

$($c$)\frac{n^2+7n+1}{n-3}$

$($d$)n^{0\mathrm{.}000001}$