Data Structure

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Question 1

In a binary max heap containing n numbers, the smallest element can be found in _________ time. NTA NET JUNE 2020

A	O(n)
B	O(log n)
C	O(1)
D	O(log log n)

Question 2

Which among the following statement(s) is (are) true? NTA NET JUNE 2020
A. A hash function takes a message of arbitrary length and generates a fixed length code.
B. A hash function takes a message of fixed length and generates a code of variable length.
C. A hash function may give same hash value for distinct message.
Choose the correct answer from the options given below:

A	(A) only
B	(B) and (C) only
C	(A) and (C) only
D	(B) only

Question 3

Let G be a directed graph whose vertex set is the set of numbers from 1 to 100. There is an edge from a vertex i to a vertex j if and only if either j=i+1 or j=3i. The minimum number of edges in a path in G from vertex 1 to vertex 100 is _____ NTA NET JUNE 2020

A	23
B	99
C	4
D	7

Question 4

What is the worst case running time of Insert and Extract Min in an implementation of a priority queue using an unsorted array? Assume that all insertions can be accomodated. NTA NET December 2019

A	θ(1), θ(n)
B	θ(n), θ(1)
C	θ(1), θ(1)
D	θ(n), θ(n)

Question 5

When using Dijkstra's algorithm to find the shortest path in a graph. Which of the following statement is not true? NTA NET December 2019

A	It can find shortest path within the same graph data structure.
B	Every time a new node is visited, we choose the node with smallest known distance / cost to visit first.
C	Shortest path always passes through least number of vertices.
D	The graph needs to have a non negative weight on every edge.

Question 6

The time complexity to multiply two polynomials of degree n using Fast Fourier transform method is NTA NET December 2019

A	θ(n lg n)
B	θ(n^2)
C	θ(n)
D	θ(lg n)

Question 7

Suppose that a connected planar graph has six vertices, each of degree four. Into how many regions is the plane divided by a planar representation of this graph? NTA NET JUNE 2019

A	6
B	8
C	12
D	20

Question 8

Which of the following is application of depth - first search? NTA NET JUNE 2019

A	Only topological sort
B	Only strongly connected components
C	Both topological sort and strongly connected components
D	Neither topological sort nor strongly connected components

Question 9

There are many sorting algorithms based on comparison The running time of heapsort algorithm is O(nlogn). Like P, but unlike Q, heapsort sorts in place where (P,Q) is equal to

A	Merge Sort, Quick Sort
B	Quick Sort, Insertion Sort
C	Insertion Sort, Quick Sort
D	Insertion Sort, Merge Sort

Question 10

Which data structure is used by the compiler for managing variables and their attributes? NTA NET JUNE 2019

A	Binary tree
B	Link list
C	Symbol table
D	Parse table

Question 11

Which of the following is best running time to sort n integers in the range 0 to n²-1? NTA NET JUNE 2019

A	O(logn)
B	O(n)
C	O(nlogn)
D	O(n^2)

Question 12

The solution of the recurrence relation CBSE NET JULY 2018 T(m) = T(3m/4) + 1 is :

A	θ(lg m)
B	θ(m)
C	θ(mlg m)
D	θ(lglg m)

Question 13

Consider the array A=<4,1,3,2,16,9,10,14,8,7>. After building heap from the array A, the depth of the heap and the right child of max - heap are ____ and ___________ respectively. ( Root is at level 0). CBSE NET JULY 2018

A	3, 14
B	3, 10
C	4, 14
D	4, 10

Question 14

A hash function h is defined h(key) = key mod 7, with linear probing, is used to insert the keys 44,45,79,55,91,18,63 into a table indexed from 0 to 6. What will be the location of key 18? CBSE NET JULY 2018

A	3
B	4
C	5
D	6

Question 15

Which of the following algorithms solves the single - source shortest paths? CBSE NET JULY 2018

A	Prim's Algorithm
B	Floyd - Warshall Algorithm
C	Johnson's Algorithm
D	Dijkstra's Algorithm

Question 15 Explanation:

Floyd - Warshall Algorithm - All Pair shortest path algorithm Dijikstra's Algorithm: Single Source Shortest path algorithm.

Question 16

A text is made up of the characters A, B, C, D, E each occurring with the probability 0.08, 0.40, 0.25, 0.15 and 0.12 respectively. The optimal coding technique will have the average length of: CBSE NET JULY 2018

A	2.4
B	1.87
C	3.0
D	2.15

Question 17

A binary search tree in which every non - leaf node has non - empty left and right subtrees is called a strictly binary tree. such a tree with 19 leaves: CBSE NET JULY 2018

A	Cannot have more than 37 nodes
B	has exactly 37 nodes
C	has exactly 35 nodes
D	cannot have more than 35 nodes

Question 18

Match the following with respect to algorithm paradigms: CBSE NET JULY 2018

List - I	List - II
A. The 8 - Queen's problem	(i) Dynamic programming
B. Single Source shortest paths	(ii) Divide and conquer
C. STRASSEN's Matrix multiplication	(iii) Greedy approach
D. Optimal binary search trees	(iv) Backtracking

A	A - iv, B - i, C - iii, D - ii
B	A - iv, B - iii, C - i, D - ii
C	A - iii, B - iv, C - ii, D - i
D	A - iv, B - iii, C - ii, D - i

Question 19

The maximum number of comparisons needed to sort 9 items using radix sort is (assume each item is 5 digit octal number): CBSE NET JULY 2018

A	45
B	72
C	360
D	450

Question 20

A 5 - ary tree is tree in which every internal node has exactly 5 children. The number of left nodes in such a tree with 8 internal nodes will be: CBSE NET JULY 2018

A	30
B	33
C	45
D	125

Question 21

Consider a Boolean function of 'n' variables. The order of an algorithm that determines whether the Boolean function produces a output 1 is: CBSE NET JULY 2018

A	Logarithmic
B	Linear
C	Quadratic
D	Exponential

Question 22

The solution of recurrence relation: NTA NET December 2018

T(n) = 2T(sqrt(n)) + lg(n)

A	O(lg(n))
B	O(n lg(n))
C	O(lg(n) lg(n))
D	O(lg(n) lg (lg(n)))

Question 23

The elements 42, 25, 30, 40, 22, 35, 26 are inserted one by one in the given order into a max - heap. The resultant max - heap is stored in an array implementation is NTA NET December 2018

A	<42, 40, 35, 25, 22, 30, 26>
B	<42, 35, 40, 22, 25, 30, 26>
C	<42, 40, 35, 25, 22, 26, 30>
D	<42, 35, 40, 22, 25, 26, 30>

Question 24

Consider two sequences X and Y: NTA NET December 2018

X = {0, 1, 2, 1, 3, 0, 1}

Y = {1, 3, 2, 0, 1, 0}

The length of the longest common subsequence between X and Y is

A	2
B	3
C	4
D	5

Question 25

Consider the following postfix expression with single digit operands: NTA NET December 2018

6 2 3 * / 4 2 * + 6 8 * -

The top two elements of the stack after the second * is evaluated, are:

A	8, 2
B	8, 1
C	6, 2
D	6, 3

Question 26

A binary search tree is constructed by inserting the following numbers in order: NTA NET December 2018

60, 25, 72, 15, 30, 68, 101, 13, 18, 47, 70, 34

The number of nodes is the left subtree is

A	5
B	6
C	7
D	3

Question 27

In a ternary tree, the number of internal nodes of degree 1,2 and 3 is 4, 3 and 3 respectively. The number of leaf nodes in the ternary tree is NTA NET December 2018

A	9
B	10
C	11
D	12

Question 28

Match List I with List II and choose the correct answer from the code given below: NTA NET December 2018

List - I (Graph ALgorithm)	List - II (Time complexity)
A. Dijkstra's Algorithm	(i) O(E lgE)
B. Kruskal's Algorithm	(ii) Θ(V³)
C. Floyd-Warshall algorithm	(iii) O(V²)
D. Topological sorting	(iv) Θ(V+E)

where V and E are the number of vertices and edges in graph respectively.

A	A - i, B - iii, C - ii, D - iv
B	A - iii, B - i, C - ii, D - iv
C	A - i, B - iii, C - iv, D - ii
D	A - iii, B - i, C - iv, D - ii

Question 29

In K-coloring of an undirected graph G = (V,E) is a function c:V → {0,1,2,....,K - 1} such that c(u) ≠ c(v) for every edge (u,v) ϵ E. Which of the following is not correct? NTA NET December 2018

A	G is bipartite
B	G is 2 - colorable
C	G has cycles of odd length
D	G has no cycles of odd length

Question 30

Consider a singly linked list. What is the worst case time complexity of the best - known algorithm to delete the node a, pointer to this node is q, from the list? NTA NET December 2018

A	O(n lg n)
B	O(n)
C	O(lg n)
D	O(1)

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