$[25$ marks$]$

Multiple Choice Questions:

$f(n)=3nlogn+2n^2+4log{n}^2.f(n)$ is $O(g(n)).$ Choose the most correct value for $g(n).$

a$)n^2$

b$)n$

c$)$ nlogn

d$)log{n}^2$

$f(n)=5n^3+6n^2-7n+8.f(n)$ is $(g(n)).$ Choose the most correct value for $g(n).$

a$)n^3$

b$)8$

c$)1$

d$)5n^3$

$f(n)=9n^2+10n^{\frac{1}{2}}-11logn+12.f(n)$ is $(g(n)).$ Choose the most correct value for $g(n).$

a$)n^2$

$b{n}^{\frac{1}{2}}$

c$)$ nlogn

d$)1$

Running times of some algorithms to perform a task are given below. Which one of the following algorithms will you choose when input size $\text{'}n\text{'}$ is very large?

a$)O(n^2)$

b$)$ nlogn$)$

c$)O(2^n)$

d$)O(n^3)$

Space complexity of some algorithms to perform a task are given below. Which one of the following algorithms will you choose when input size $\text{'}n\text{'}$ is very large?

a$)O(logn)$

b$)O(nlogn)$

c$)O(2^n)$

d$)O(n)$

To calculate four way set disjointness the following code can be used def disjoint$4($A$,$ B$,$ C$,$ D$)$:

for $a$ in $A$ :

for $b$ in $B$ :

for $c$ in $C$ :

for $d$ in $D$ :

if $a==b=c==d$ :

return False

return True

What will be the running time of the algorithm?

a$)O(log{n}^4)$

b$)O(n^4)$

c$)O(4n)$

d$)O(4+n)$

Which one of the following is an example of geometric progression?

a$)1,2,3,4$dots

b$)2,4,6,7$dots

c$)4,8,12,16$dots

d$)1,3,9,27$dots