BSc IT Sem I 2023 2024 2024 COMPUTATIONAL LOGIC AND DISCRETE STRUCTURE Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 Attempt (Any Three) of the following 15 marks
   • a) Evaluate Transitive Closure cells with the help of Warshall’s Algorithm if
   • b) Prove by Mathematical Induction 12 + 23 + 33 + — — =
   • c) Find number of integers between 1 and 2100 that are divisible
   • d) Evaluate of RandS , Outdegree of RandS , Digraph of RandS if
   • e) Define — 1) Poset 2) Partially ordered Relation , Draw the Hasse’s Digraph With the help of matrix
   • f) Check whether the given equation is an equivalance relation if a= b(mod m), ifm divides a — b
2. Q2 Attempt (Any Three) of the following 15 marks
   • a) Let — by f(x) = prove that it is a bijective function also evaluate the formula for inverse function
   • b) Let f,g and h are the function from R to R defined as f(x) = 2x3 g(x) = 4x? ,h(x) = 4 Find a) ((gof)oh)(1) ((fof}og)(2) ) Define — 1) Logarithmic function 2) Exponential function 3) Ceiling function 4) Flooring function
   • 5) Chebyshev’s Inequality
   • d) Two cards are drawn froma pack of cards Find the probability that 1) Both are hearts
   • 2 ) One is heart and the other is a spade
   • e) Find Mean and Variance for the following probability cistribution j vcD g | F Y.Bsc ( IT) SEM | CLDS HRS 75 MARKS
   • f) For the following probability distribution Attempt (Any Three) of the following (15)
   • a) From 4 professor and 8 students a committee of 3 is to be formed .In how many ways this can be done if the committee contains
   • 1) Exactly one professor 2) at most one professor 3) at least 2 professor
   • b) Find the number of distinct permutation of the letters of the word QUALIFICATION
   • c) 20 Different books are to be arranged ona shelf . Find the number of ways in which this can be done if two specified books are 1) Always together 2) Never together
   • d) i)State and prove Pigeonhole Principle ii) There are 38 different time periods during which classes at a university can be scheduled If there are 677 diffferent classes many rooms will be needed
   • e) many solutions does the equation xty+z = 14 have where are non negative integers ,2) In how many ways can 15 balloons be distributed at a Birthday party
   • f) Evaluate first seven term of = + with ag = 1,01 =
3. Q4 Attempt (Any Three ) of the following 15 marks
   • a) Define the bipartite graph and check whether following graphs ave bipartite graphs
   • b) algorithm to the graph given below and find the shortest path from a to VCD F Y Bsc ( IT) SEM! CLDS 23 HRS 75 MARKS
   • c) For the given graph find- a) Adjacency matrix b) Adjacency List c) Verify handshaking theorem
   • d) Determine whether, the given graph is Eulerian, Semi-Eulerian or Neither Justify Define the Hamiltonian graph ,path ,circuit Check whether the following graph is
   • f) Explain the following terms. a) Breath first search b) Alpha-Beta pruning
4. Q5 Attempt any 3 15 marks
   • a) From the given tree Identify following Right subtree ,Parent child of tree , level of tree (A) By Huffman’s coding compression technique find the Huffman’s tree
   • c) Draw the unique binary tree for given in order and post order traversal
   • d) Find the minimal spanning tree of the given weighted tree using Prim’s Algorithm
   • e) Define- i) Poset and Lattice ii) Draw the diagram of the poset
   • f) Define the following terms Upper Bound 2) Lower Bound 3) Least upper bound 4) Greatest lower bound 5) Minimal and maximal element

Read from the scan above, so a character or two may differ. The scan is the original.