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

Q$2.$ Apply Merge sort and Quick to sort the list, $K,A,Y,M,J,B,O,A,R,D$ in alphabetical

order.

$(2$ Mark $)$

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

$(2$ Mark$)$

relation

g$)T(n)=9T(3\frac{n}{9})+n^2$

h$)T(n)=4T(\frac{4}{16})+1$

Q$4.$ Write the Recursive algorithm for Binary search $.$Consruct the recurrence relation for

recursive algorithm and solve using bachward Subtution.

Q$5.$ Evaluate the polynomial $f(x)=100x^5-30x^4-2x^3+3x^2+8x-10,$ for $x=-5,$ using Horner

Rule.

$(2$ Mark$)$

could you provide the answer of each question step by step