Previous Year Very Short Questions of DS (B-TECH information technology 3rd)

Discrete structures

Previous year question paper with solutions for Discrete structures

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  1. Write characteristic equation of the recurrence relation.
  2. Define index and indexed sets.
  3. Define Objective functions with example.
  4. Define asymmetric relation with example.
  5. If a set A has n elements, how many relation are there from A to A?
  6. Define symmetric relation with example.
  7. Define normal subgroup.
  8. Write elementary properties of a ring.
  9. Discuss Boolean ring.
  10. What is difference between a graph and a tree?
  11. If number of diagonals in a polygon is 44, find the number of sides in a polygon.
  12. How many distinct four digit integers can one make from digits 1, 3, 3, 7, 8, 8.
  13. Define Lattice with an example.
  14. Define Existential quantifier and universal quantifier.
  15. Define Semi-group.
  16. Show that we can have A  B = A  C without B = C.
  17. Define ring with example..
  18. Find the multiplication table for G = {1, 2, 3, 4, 5, 6} under multiplication modulo 7.
  19. Define transitive relation.
  20. Define cyclic group.
  21. If H is a subgroup of the group G, among the right cosets of H in G, prove that there is only one subgroup, viz. H
  22. Let f : X X;X = {0,1,2,3,4,5,6} defined by f (x) = 4x mod 5. Write the function f as a set of ordered pairs.
  23. Give an example of Hamiltonian graph.
  24. Define semigroup.
  25. Find the number of distinct permutations that can be formed from all the letters of the word ‘MATHEMATICS’.
  26. Show that the set of 2 × 2 non-singular matrices with rational entries is a group with respect to matrix multiplication.
  27. Let D70 = {1, 2, 5, 7, 10, 14, 35, 70} and define m n, if m divides n. Show that (D70, ) is a Boolean Algebra.
  28. Define chromatic number.
  29. What is the difference between a graph and a tree?
  30. If P(n, r) = 0, then what is the value of r?