Q$1.$ Find the topological sorting problem for the given graph A and B using DFS Method.

$(2$ Mark $)$

Q$2.$ Apply Merge sort and Quick to sort the list, I,N$,$D$,$O$,$N$,$E$,$S$,$I,A in alphabetical order.

$(2$ Mark $)$

Q$3.$ Explain Master Theorem $.$Using Master Theorem solved the following recurrence.

$(2$ Mark$)$

relation

i$)T(n)=6T(2\frac{n}{19})+n^2$

j$)T(n)=24T(3\frac{n}{72})+n^2$

Q$4.$ Write the Recursive algorithm for Quick Sort.Consruct the recurrence relation for

recursive algorithm and solve using backward Subtution.

$(2$ Mark$)$

Q$5.$ Solve the following equations using Gaussian Elimination Method:

$(2$ Mark$)$

$-5x_1-3x_2+6x_3=10$

$7x_1+6x_2-7x_3=-23$

$2x_1-4x_2-3x_3=-20$