All India Computer Science Engineering (CSE) Group

Which of the following is not a type of database?
  • a)
    Hierarchical
  • b)
    Network
  • c)
    Distributed
  • d)
    Decentralized
Correct answer is option 'D'. Can you explain this answer?

Gate Gurus answered  •  3 weeks ago
Different types are:
1) Centralized
2) Distributed
3) Relational
4) NoSQL
5) Cloud
6) Object-oriented
7) Hierarchical
8) Network

What is the largest integer m such that every simple connected graph with n vertices and n edges contains at least m different spanning trees?
  • a)
    1
  • b)
    2
  • c)
    3
  • d)
    n
Correct answer is option 'C'. Can you explain this answer?

Vibhor Goyal answered  •  4 weeks ago
A graph is connected iff all nodes can be traversed from each node. For a graph with n nodes, there will be n-1 minimum number of edges.
Given that there are n edges, that means a cycle is there in the graph.
The simplex graph with these conditions may be:

Now we can make a different spanning tree by removing one edge from the cycle, one at a time.
Minimum cycle length can be 3, So, there must be atleast 3 spanning trees in any such Graph.

Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?
  • a)
    1/8
  • b)
    1
  • c)
    7
  • d)
    8
Correct answer is option 'C'. Can you explain this answer?

Gate Gurus answered  •  4 weeks ago
A cycle of length 3 can be formed with 3 vertices. There can be total 8C3 ways to pick 3 vertices from 8. The probability that there is an edge between two vertices is 1/2. So expected number of unordered cycles of length 3 = (8C3)*(1/2)3 = 7

Let G be a weighted undirected graph and e be an edge with maximum weight in G. Suppose there is a minimum weight spanning tree in G containing the edge e. Which of the following statements is always TRUE?
  • a)
    There exists a cutset in G having all edges of maximum weight.
  • b)
    There exists a cycle in G having all edges of maximum weight
  • c)
    Edge e cannot be contained in a cycle.
  • d)
    All edges in G have the same weight
Correct answer is option 'A'. Can you explain this answer?

Gate Gurus answered  •  4 weeks ago
Background : Given a connected and undirected graph, a spanning tree of that graph is a subgraph that is a tree and connects all the vertices together.
  1. A spanning tree has exactly V – 1 edges.
  2. A single graph can have many different spanning trees. A minimum spanning tree (MST) or minimum weight spanning tree for a weighted, connected and undirected graph is a spanning tree with weight less than or equal to the weight of every other spanning tree. The weight of a spanning tree is the sum of weights given to each edge of the spanning tree.
  3. There can be more that one possible spanning trees of a graph. For example, the graph in this question has 6 possible spanning trees.
  4. MST has lightest edge of every cutset. Remember Prim’s algorithm which basically picks the lightest edge from every cutset.
Choices of this question :
a) There exists a cutset in G having all edges of maximum weight : This is correct. If there is a heaviest edge in MST, then there exist a cut with all edges with weight equal to heavies edge. See point 4 discussed in above background.

b) There exists a cycle in G having all edges of maximum weight : Not always TRUE. The cutset of heaviest edge may contain only one edge. In fact there may be overall one edge of heavies weight which is part of MST (Consider a graph with two components which are connected by only one edge and this edge is the heavies)
c) Edge e cannot be contained in a cycle. Not Always True. The curset may form cycle with other edges.
d) All edges in G have the same weight Not always True. As discussed in option b, there can be only one edge of heaviest weight.

Which kind of traversal order trie gives the lexicographical sorting of the set of the strings?
  • a)
    Preorder
  • b)
    Postorder
  • c)
    Level order
  • d)
    Inorder
Correct answer is option 'A'. Can you explain this answer?

Gate Gurus answered  •  4 weeks ago
To print the string in alphabetical order we have to first insert in the trie and then perform preorder traversal to print in alphabetical order.

Let G be a simple graph with 20 vertices and 8 components. If we delete a vertex in G, then number of components in G should lie between ____.
  • a)
    8 and 20
  • b)
    8 and 19
  • c)
    7 and 19
  • d)
    7 and 20
Correct answer is option 'C'. Can you explain this answer?

Gate Gurus answered  •  4 weeks ago
Case 1: If the vertex we are deleting from G is an isolated vertex, which is a component by itself, then number of components in G becomes 7.
Case 2: If G is a start Graph, then by deleting the cut vertex of G, we get 19 components.
Hence, number of components in G should lie between 7 and 19.

What is the maximum number of edges in an acyclic undirected graph with n vertices?
  • a)
    n-1
  • b)
    n
  • c)
    n + 1
  • d)
    2n-1
Correct answer is option 'A'. Can you explain this answer?

Gate Gurus answered  •  4 weeks ago
n * (n – 1) / 2 when cyclic. But acyclic graph with the maximum number of edges is actually a spanning tree and therefore, correct answer is n-1 edges.

Which of the following data structure is useful in traversing a given graph by breadth first search?
  • a)
    Stack
  • b)
    List
  • c)
    Queue
  • d)
    None of the above.
Correct answer is option 'C'. Can you explain this answer?

Machine Experts answered  •  4 weeks ago
BFS performs level-order traversal which can be fairly done using a queue. A queue uses FIFO ordering and the nodes that we enqueue first are explored first maintaining the order of traversal.
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