Skip to content
EndsemDec 20252019 patternSE Comp

Discrete Mathematics (DM) SPPU Endsem Question Paper Dec 2025

All 8 questions from this SPPU endsem paper, as printed. Read them here or open the PDF.

Open the PDFMost repeated DM questions
Subject code
210241
Pattern
2019 pattern
Exam
Endsem
Session
Dec 2025
Max. marks
70
Time
2½ Hours
Semester
III
Paper code
[6582]-40

Printed for: S.E. (Computer Engg./Artificial Intelligence and Data Science)

Instructions to the candidates

  1. Solve Q1 or Q2, Q3 or Q4, Q5 or Q6, Q7 or Q8.
  2. Neat diagrams must be drawn wherever necessary.
  3. Assume suitable data if necessary.

Questions

  1. Q1

    1. a)

      A committee including 3 boys and 4 girls is to be formed from a group of 10 boys and 12 girls. How many different committees can be formed from the group?

      [6]
    2. b)

      This part has equations that don’t show as text. Open the PDF to read it.

      [6]
    3. c)

      How many 4-letter words with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’, if repetition of letters is not allowed?

      [6]

  2. Q2

    1. a)

      From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

      Also asked:May 2025 ·May 2024

      [6]
    2. b)

      This part has equations that don’t show as text. Open the PDF to read it.

      [6]
    3. c)

      A box contains 4 red, 3 white and 2 blue balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colours? 2

      [6]

  3. Q3

    1. a)

      Show that the following graphs are isomorphic.

      Also asked:May 2024

      [7]
    2. b)

      List and explain the necessary and sufficient conditions for Hamiltonian and eulerian path with suitable exmples.

      Also asked:May 2024

      [5]
    3. c)

      Explain the terms adjacency matrix and incidence matrix.

      [5]

  4. Q4

    1. a)

      Use dijkstras algorithm to find the shortest path between A and Z in figure.

      [7]
    2. b)

      Show that in a connected planar graph with 6 vertices and 12 edges, each of the regions is bounded by 3 edges.

      [5]
    3. c)

      This part has equations that don’t show as text. Open the PDF to read it.

      [5]

  5. Q5

    1. a)

      Define following terms. i) Level of a tree ii) Height of a tree iii) Fundamental circuit 3

      Also asked:May 2024

      [6]
    2. b)

      Use labeling procedure to find a maximum flow in the transport network given in the following figure. Determine the corresponding minimum cut.

      [6]
    3. c)

      Construct Minimal spanning tree for the following graphs using prims algorithm.

      Also asked:May 2024

      [6]

  6. Q6

    1. a)

      Define following terms i) Forest ii) Fundamental cutsets iii) Game tree

      Also asked:May 2024

      [6]
    2. b)

      Construct Minimal spanning tree for the following graphs using kruskals algorithm.

      Also asked:May 2024

      [6]
    3. c)

      Construct an optimal tree for 8,9,10,11,13,15,22 using Huffman coding. 4

      Also asked:May 2024

      [6]

  7. Q7

    1. a)

      Define : i) Semi-group ii) Field iii) Monoid

      [6]
    2. b)

      This part has equations that don’t show as text. Open the PDF to read it.

      [6]
    3. c)

      This part has equations that don’t show as text. Open the PDF to read it.

      [5]

  8. Q8

    1. a)

      Define : i) Ring ii) Ring Homorphism iii) Integral domain

      Also asked:May 2025

      [6]
    2. b)

      This part has equations that don’t show as text. Open the PDF to read it.

      [6]
    3. c)

      This part has equations that don’t show as text. Open the PDF to read it.

      [5]