31. The number of different binary trees with 6 nodes is .............
(A) 6 (B) 42
(C) 132 (D) 256
32. Let A[1...n] be an array of n distinct numbers. If i<j and A[i]>A[j], then the pair (i,j) is called an inversion of A. What is the expected number of inversions in any permutation on n elements?
(A) θ(n) (B) θ(lg n)
(C) θ(nlg n) (D) θ(n2)
33. Which one of the following array represents a binary max-heap?
(A) [26, 13, 17, 14, 11, 9, 15]
(B) [26, 15, 14, 17, 11, 9, 13]
(C) [26, 15, 17, 14, 11, 9, 13]
(D) [26, 15, 13, 14, 11, 9, 17]
34. Match the following:
(a) Huffman codes (i) O(n2)
(b) Optimal polygon triangulation (ii) θ(n3)
(c) Activity selection problem (iii) O(nlgn)
(d) Quicksort (iv) θ(n)
(a) (b) (c) (d)
(A) (i) (ii) (iv) (iii)
(B) (i) (iv) (ii) (iii)
(C) (iii) (ii) (iv) (i)
(D) (iii) (iv) (ii) (i)
35. Suppose that we have numbers between 1 and 1000 in a binary search tree and want to search for the number 364. Which of the following sequences could not be the sequence of nodes examined?
(A) 925, 221, 912, 245, 899, 259, 363, 364
(B) 3, 400, 388, 220, 267, 383, 382, 279, 364
(C) 926, 203, 912, 241, 913, 246, 364
(D) 3, 253, 402, 399, 331, 345, 398, 364
36. A triangulation of a polygon is a set of T chords that divide the polygon into disjoint triangles. Every triangulation of n-vertex convex polygon has ................ chords and divides the polygon into ............... triangles.
(A) n-2, n-1 (B) n-3, n-2
(C) n-1, n (D) n-2, n-2
37. Implicit return type of a class constructor is:
(A) not of class type itself (B) class type itself
(B) a destructor of class type (D) a destructor not of class type
38. It is possible to define a class within a class termed as nested class. There are ............ types of nested classes.
(A) 2 (B) 3
(C) 4 (D) 5
39. Which of the following statements is correct?
(A) Aggregation is a strong type of association between two classes with full ownership.
(B) Aggregation is a strong type of association between two classes with partial ownership.
(C) Aggregation is a weak type of association between two classes with partial ownership.
(D) Aggregation is a weak type of association between two classes with full ownership.
40. Which of the following statements is correct?
(A) Every class containing abstract method must not be declared abstract.
(B) Abstract class cannot be directly initiated with ‘new’ operator.
(C) Abstract class cannot be initiated.
(D) Abstract class contains definition of implementation.