Discrete Mathematics Online Test

1. A binary cycle space forms a ______ over the two element field.

2. _________ is used to implement the Boolean functions.

3. A single card is drawn from a standard deck of playing cards. What is the probability that the card is a face card provided that a queen is drawn from the deck of cards?

4. Determine the solution for the recurrence relation a_n = 6a_n-1−8a_n-2 provided initial conditions a₀=3 and a₁=5.

5. For any graph say G, Cayley graph is ______________

6. In signed representation 5 is represented in binary as 0101.

7. _______ characterizes the properties of distributive lattices.

8. Let A be a set of k (k>0) elements. Which is larger between the number of binary relations (say, N_r) on A and the number of functions (say, N_f) from A to A?

9. A ______ is a graph which has the same number of edges as its complement must have number of vertices congruent to 4m or 4m modulo 4(for integral values of number of edges).

10. G is a simple undirected graph and some vertices of G are of odd degree. Add a node n to G and make it adjacent to each odd degree vertex of G. The resultant graph is ______

11. What is the generating function for generating series 1, 2, 3, 4, 5,… ?

12. Which of the following two sets are disjoint?

13. The independent term of x is 80000 in the expansion of (3x+b/x)⁶, where b is a positive constant. What the value of b?

14. Determine all possibilities for the solution set of the homogeneous system of 5 equations in 3 unknowns and the rank of the system is 3.

15. What is the range of a function?

16. For some number x, Floor(x) <= x <= Ceil(x).

17. Which of the following case does not exist in complexity theory?

18. If X is an idempotent nonsingular matrix, then X must be ___________

19. If set A has 4 elements and B has 3 elements then set n(A X B) is?

20. A square matrix A = [a_ij ]_nxn, if a_ij = 0 for i > j then that matrix is known as _______

21. If n(A)=20 and n(B)=30 and n(A U B) = 40 then n(A ∩ B) is?

22. The contrapositive of p → q is the proposition of ____________

23. Intersection of subgroups is a ___________

24. The hexadecimal expansion of (177130)₁₀ is ___________

25. p ∨ q is logically equivalent to ________

26. State whether the given statement is true or false.

1, 1, 1, 1, 1........ is a GP series.

27. If a number is 2² x 3¹ x 5⁰ and b is 2¹ x 3¹ x 5¹ then lcm of a, b is?

28. Determine the number of essential prime implicants of the function f(a, b, c, d) = Σm(1, 3, 4, 8, 10, 13) + d(2, 5, 7, 12), where m denote the minterm and d denotes the don’t care condition.

29. Time complexity of the binary search algorithm is constant.

30. If f(x) = (x³ - 1) / (3x + 1) then f(x) is?

31. What is the number of vertices in an undirected connected graph with 39 edges, 7 vertices of degree 2, 2 vertices of degree 5 and remaining of degree 6?

32. A → (A ∨ q) is a __________

33. How many ways can 8 prizes be given away to 7 students, if each student is eligible for all the prizes?

34. A compound proposition that is neither a tautology nor a contradiction is called a ___________

35. A 6-sided die is biased. Now, the numbers one to four are equally likely to happen, but five and six is thrice as likely to land face up as each of the other numbers. If X is the number shown on the uppermost face, determine the expected value of X when 6 is shown on the uppermost face.

36. Amit must choose a seven-digit PIN number and each digit can be chosen from 0 to 9. How many different possible PIN numbers can Amit choose?

37. A bag contains 25 balls such as 10 balls are red, 7 are white and 8 are blue. What is the minimum number of balls that must be picked up from the bag blindfolded (without replacing any of it) to be assured of picking at least one ball of each colour?

38. In which cipher each letter of the plaintext is substituted by any other letter to form the cipher message?

39. What is the one's complement of the number 1010110?

40. A polygon with 12 sides can be triangulated into _______

41. Let X be a n-square matrix such that Y = X + 8I. Which of the following property will exist?

42. The tree elements are called __________

43. For any function fof ^-1(x) is equal to?

44. There are _________ numbers of Boolean functions of degree n.

45. The quotient when 19 is divided by 6 is?

46. Suppose a relation R = {(3, 3), (5, 5), (5, 3), (5, 5), (6, 6)} on S = {3, 5, 6}. Here R is known as _________

47. The greatest common divisor of 0 and 5 is ___________

48. In the given Geometric progression, '2²⁵' would be a term in it.

32, 256, 2048, 16384,.........,250.

49. “Match will be played only if it is not a humid day.” The negation of this statement is?

50. In which of the following problems recurrence relation holds?