B.Sc. (Computer Science) Sem 3 Discrete Mathematics 2015-16 ATKT Question Paper - Mumbai University | munotes
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Questions asked in this paper
g.P. Sem
Q.1 Attempt any four:
a) State the - exclusion principle How many positive integers not exe
divisible by 3, 5 or 79 find how
b) State the sum and Product rule. How many bit string there of leng
many of them ends with two bits 00?
State the Binomial theorem, Use it to prove:
/ = 2", for non negative integer n
(ii)
2"= 3", for non negative integer
d = 2 for non-negaul
) State the Vandermonde’s identify. Use it to prove
e) State and prove identity
f) Define the term Grammer. Explain the types of Grammer
g) Define the term:
(i) Turning Machine
(ii) Finite state automata
(iii) Types of languages
h) Consider following FSA. Find states, input letters, initial state, accepting state,
Also write it’s state table
4 Attempt any three: 152
a) Solve the recurrence relation a7 = + 2n
b) Write a note on Tower of Hanoi
(ii) Linked list representation using vertex and edge file
d) State the extended pigeonhole principle. Show that if seven colours are used to paint 60
bicycles atleast 9 bicycles will be of the same colour
e) A family of 4 brothers and 3 sisters are to be seated for photograph in one row. In how many
ways can they selected if:
(i) all sisters are sit together
(ii) no two sisters sit together
f) (i) Define a tree on 5 vertices with a suitable example
(ii) Perform inorder search on the following tree using inorder search algorithm
Q.1 Attempt any four:
a) State the - exclusion principle How many positive integers not exe
divisible by 3, 5 or 79 find how
b) State the sum and Product rule. How many bit string there of leng
many of them ends with two bits 00?
State the Binomial theorem, Use it to prove:
/ = 2", for non negative integer n
(ii)
2"= 3", for non negative integer
d = 2 for non-negaul
) State the Vandermonde’s identify. Use it to prove
e) State and prove identity
f) Define the term Grammer. Explain the types of Grammer
g) Define the term:
(i) Turning Machine
(ii) Finite state automata
(iii) Types of languages
h) Consider following FSA. Find states, input letters, initial state, accepting state,
Also write it’s state table
4 Attempt any three: 152
a) Solve the recurrence relation a7 = + 2n
b) Write a note on Tower of Hanoi
(ii) Linked list representation using vertex and edge file
d) State the extended pigeonhole principle. Show that if seven colours are used to paint 60
bicycles atleast 9 bicycles will be of the same colour
e) A family of 4 brothers and 3 sisters are to be seated for photograph in one row. In how many
ways can they selected if:
(i) all sisters are sit together
(ii) no two sisters sit together
f) (i) Define a tree on 5 vertices with a suitable example
(ii) Perform inorder search on the following tree using inorder search algorithm
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