Q$.$ Programs A and B are analyzed and found to have worst$-$case running times no greater than $150($nlogn$)$ and n$2,$ respectively.

Which of the following statements does the analysis imply?

$($a$)$ Program A will run faster on average for sufficiently large n$.$

$($b$)$ Program B will run faster on average for small n$.$

$($c$)$ Program A is probably simpler to code than program B$.$

$($d$)$ There exists some input for which program B takes longer than program A$.$

$($e$)$ none of the above

$$

Q$.$ An algorithm takes $10$ seconds for an input size of $50.$

$$ If the algorithm is quadratic, approximately how long does it take to solve a problem of size $100?$

$($a$)10$ seconds

$($b$)20$ seconds

$($c$)40$ seconds

$($d$)100$ seconds

$($e$)$ none of the above

$$

Q$13.$ An algorithm takes $30$ seconds for an input of size $1000.$ If the algorithm is quadratic, how large a problem can be solved in two minutes?

$($a$)2000$

$($b$)4000$

$($c$)6000$

$($d$)60000$

$($e$)$ none of the above

Q$.$ An algorithm takes $6$ seconds to solve a problem of size $100$ and ten minutes to solve a problem of size $1000.$

What is the likely running time of the algorithm?

$($a$)$ constant

$($b$)$ linear

$($c$)$ quadratic

$($d$)$ cubic

$($e$)$ none of the above