B.Sc. (Computer Science) Sem 1 Discrete Mathematics Nov 2023 Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 All questions are compulsory
2. Q2 Mixing of sub questions is not allowed. 23 marks
3. Q3 Write in clear, legible, writing Attempt any four: (20)
   • A) If > Ris defined by f(x) = 2x + 3; the show that f is bijection and hence find
   • B) if f(x) = 2x g(x) = . find the composite of the function define by (fog)(x) and
   • C) tf and R={(1,1),(1,2),(2,1),(2,2),(2,3),(3,1).(3,3)} . find M(R) and [M(R)]?
   • D) let A={1,2,3) and R be a relation on A defined by xRy iff x < y. Find R and draw its graph and
   • E) solve the following homogenous recurrence relation let A={1,2,3,4,5} and R be a partial order relation defined as
4. Q2 Attempt any four: 20 marks
   • A) Onan English test, a student must write two essays. For the first essay , the student must select From topics A,B,and C. For the second essay, the student must select from topics 1,2,3 and 4. How many different ways can student select the two essay topics? (make tree diagram and salve by
   • B) Show that a party of 20 people, there are two people who have the same number of friends
   • C) An investigator interviewed 100 interviewers to determine their skills, expert in C language, expert in Oracle, expert in V.B. occurred is are 10 are in all three, 20 are skilled in C and
5. Q5 B. 30 are skilled in V.B. and Oracle, 25 are skilled in C and Oracle , 12 are skilled in C Only, are skilled in V.B. only and 8 are skilled in Oracle only. Then How many are skilled in many are unskilled? many are skilled in C but not in V.B, (iv)How many are skilled in V.B. and oracle but not C
   • D) Suppose that there are 9 faculty members in the mathematics and 11 in the computer science Department. How many ways are there to select a committee to develop a discrete mathematics Course at a school if the committee is to consist of three faculty members from the mathematics And four from the computer science Department?
   • E) Find the coefficient of x3y3z2 in (2x — 3y +
   • F)Each user on,a computer system has a password which is six to seven characters long where each characteys is an upper case letter or a digit. Each password must contain at least on digithow many possible password are there?
6. Q3 Attempt any four: 20 marks
   • A) Write the definition of tree. Draw all non-isomorphic trees Draw all pussible non-isoniorphic spanning trees of the following graph
   • C) Write the definition of binary all non-isomorphic binary trees of height 2
   • D) tind the adjacency matrix of following graph E} Define Euler path, cycie, Hamiltonian path and Hamiltonian graph
   • F) find the pre-order traversal of the given rooted tree T as shown in the figure
7. Q4 Attempt any five:
   • A) Find first six terms of the sequence defined by the following recurrence relation
   • B) Find characteristic equation and characteristic roots of recurrencs relation
   • i) ay + 12a,_2 = 0
   • C) how that there does not exist 7 lectures each of 30 minutes from 10 tp 1 pm
   • D) A of 30 have been trained as astronauts tc 26 the first mission to mars How many ways are there to select a crew of six ta go an this mission?
   • E) write the properties of tree
   • F) Define null graph, complete graph with example

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