please please please answer all the questions correctly: no need for explanation, just answer all of them directly.

Given a polynomial as follows,

$P(x)=a_0+a_1{x}^3+a_2{x}^6+a_3{x}^9+a_4{x}^{12},$

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

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 ondered 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.

Which of the following growth functions has the highest order of growth?

$($a$)n$

$($b$)logn$

$($c$)nlogn$

$($d$)n^2$

If a given array does not contain any adjacent inversion, then it does not contain any global inversion.

$($a$)$ true $($b$)$ false

Is it possible that one can find the solution for the problem: Finding the minimum of an array with $n$ elements with an algorithm that is in $(n)?$

$($a$)$ yes

$($b$)$ no

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

Given an $n-$element array with $n>1,$ 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

Which of the following growth functions has the lowest order of growth?

$($a$)\sqrt[\phantom{2}]{n^3+3n^2+5}$

$($b$)2^n$

$($c$)\frac{n}{logn}$

$($d$)n+logn$

Which of the following growth functions has the lowest order of growth?

$($a$)logn$

$($b$)\frac{n^2+5n+8}{n+2}$

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

$($d$)\sqrt[\phantom{2}]{n}logn$

Which of the following functions increases faster in the long run?

$($a$){1\mathrm{.}0000001}^n$

$($b$)n^{98765430}$

Let $n={10}^{{10}^{10}}.$ Which of the following expressions is larger?

$($a$)lo{g}_{10}n$

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

Given an $n-$element array with $n>1,$ it is possible to arrange these $n$ elements,

such that only two of the elements are in place. $($Assume that these elements are

distinct.$)$

$($a$)$ true

$($b$)$ false