IGNOU MCA MCS-33 Solved Assignment 2011

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s

Hint: s

Shortest path is = abdf

Question 3. a)A palindrome is a word that reads the same whether read from right to left or from the left to right, the word ROTOR, for example. Let be the number of words of length n, not necessarily meaningful, which are palindromes. We consider a single letter as a palindrome.

i)What are and? ii)Set up a recurrence for . iii)Check that

Is the solution to the recurrence? (10 Marks)

b) Show that a tree has at least 2 vertices of degree 1. (5 Marks)

Case 2: v!= ui, for any i v f u0,u1,.un a path of length (n+1)

There for T is not the longest path a contradiction.

There for our assumption d(u0) > 1 is wrong There fore d(u0) = 1 Hence we have more vertex of degree 1 So, T has at least two vertex of degree 1.

c)

Raghu goes to a grocery shop and purchases grocery for Rs. 23. He has 3 five rupee coins, 4 two rupee coins and 6 one rupee coins. In how many ways can he pay the shop keeper? Find a solution using generating functions. (5 Marks)

Hint:

there are three 5 Rs coin = 15 Rs. 4 two rupee coins = 8 Rs. 6 one rupee coins = 6 Rs. Total 11 coins and worth Rs. 29.00

The general function is [ x10 + x15 ] ( x2 + x4 + x6 + x8 )( x + x2 + x3 + x4 + x5 + x6)the coefficient of x23 in the above equation will give the solution

X10 .x8 . x5. = x23 X 15 .x8 = x23 X15 .x4 . x4 = x23 X15 .x2 .x6 = x23 X15 .x6. x2 = x23 There for ther are five way to pay Rs. 23