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# Week 11 - Graded Assignment - 11 > **Course:** Jan 2026 - Mathematics I > Week 11 - Graded Assignment - 11 > **Last Submitted:** You have last submitted on: 2026-04-29, 12:03 IST --- ## Introduction USE THE FOLLOWING INFORMATION FOR QUESTIONS \[5-6\]: Shreya needs to perform 10 tasks namely {$A,B,C,D,.....J$}. Som...

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Week 11 - Graded Assignment - 11

Course: Jan 2026 - Mathematics I

Week 11 - Graded Assignment - 11

Last Submitted: You have last submitted on: 2026-04-29, 12:03 IST

Introduction

USE THE FOLLOWING INFORMATION FOR QUESTIONS [5-6]: Shreya needs to perform 10 tasks namely {

A,B,C,D,.....J

}. Some tasks needs to be performed after performing a particular task. In the below table, column 1 shows the tasks and column 2 shows the sets of tasks that can be performed only after performing the particular task.

(Use the following information for questions 10 & 11)

(Use the following information for questions 12 & 13)

(Use the following information for questions 14 & 15)

Question 1

An undirected graph G has 38 vertices and the degree of each vertex is at least 7. What is the minimum number of edges that the graph G can have?

Your Answer: 133

Status: Yes, the answer is correct. Score: Score: 1

Feedback/Explanation: (Type: Numeric) 133.0

Accepted Answers:

(Type: Numeric) 133.0

Question 2

If G is a connected undirected graph such that every vertex has degree at most 4 , and the shortest path between any two vertices has length at most 2, then what is the maximum number of vertices in G? (Hint: Try to draw the BFS tree starting with any vertex)

Your Answer: 17

Status: Yes, the answer is correct. Score: Score: 1

Feedback/Explanation: (Type: Numeric) 17

Accepted Answers:

(Type: Numeric) 17

Question 3

Suppose

A

is the adjacency matrix of a connected undirected graph

G

. If

A^2 = \begin{bmatrix} 1 & 1 & 1 & 0 & 1 & 1 \\ 1 & 1 & 1 & 1 & 0 & 1 \\ 1 & 1 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 1 & 1 \\ 1 & 0 & 1 & 1 & 1 & 1 \\ 1 & 1 & 0 & 1 & 1 & 1 \\ \end{bmatrix}

and the shortest path between any two vertices has length at most 2, then which of the following may represent the graph

G

Feedback/Explanation:

Accepted Answers:

Question 4

Suppose

G

is a graph with 6 vertices {

0,1,2,3,4,5

} and the adjacency matrix of the graph

G

A = \begin{bmatrix} 0 & 0 & 1 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ \end{bmatrix}

. Which of the following statements is True?

The graph $G$ is a directed acyclic graph.
From vertex 4, every other vertex is reachable.
The longest path in the graph $G$ has length 4, in terms of number of edges.
The longest path in the graph is $4 \longrightarrow 0 \longrightarrow 2 \longrightarrow 3$

Feedback/Explanation: The graph

G

is a directed acyclic graph.

From vertex 4, every other vertex is reachable.

The longest path in the graph is

4 \longrightarrow 0 \longrightarrow 2 \longrightarrow 3

Accepted Answers:

The graph

G

is a directed acyclic graph.

From vertex 4, every other vertex is reachable.

The longest path in the graph is

4 \longrightarrow 0 \longrightarrow 2 \longrightarrow 3

Question 5

Which of the following sequences may represent the possible order in which Shreya can perform the tasks?

$A,C,B,D,E,I,F,H,G,J$
$A,D,C,B,E,I,F,H,G,J$
$C,A,D,E,B,I,F,G,H,J$
$D,C,A,B,E,I,F,H,G,J$

Feedback/Explanation:

A,C,B,D,E,I,F,H,G,J

A,D,C,B,E,I,F,H,G,J

D,C,A,B,E,I,F,H,G,J

Accepted Answers:

A,C,B,D,E,I,F,H,G,J

A,D,C,B,E,I,F,H,G,J

D,C,A,B,E,I,F,H,G,J

Question 6

If each task takes 5 minutes to complete and she performs all the independent tasks simultaneously, then the time(in minutes) taken by Shreya to complete all the tasks is

Your Answer: 25

Feedback/Explanation: (Type: Numeric) 30

Accepted Answers:

(Type: Numeric) 30

Question 7

An undirected weighted graph

G

is shown below. Find the set of all positive integer values of

x

such that if we use Dijkstra’s algorithm, there will be a unique shortest path from vertex

a

to vertex

j

that contains the edge

(b, e)

$\{x | x \in \mathbb{Z},0 < x < 8\}$
$\{x | x \in \mathbb{Z},0 < x < 7\}$
$\{x | x \in \mathbb{Z},0 < x < 6\}$
$\{x | x \in \mathbb{Z},0 < x < 9\}$

Status: Yes, the answer is correct. Score: Score: 1

Feedback/Explanation:

\{x | x \in \mathbb{Z},0 < x < 7\}

Accepted Answers:

\{x | x \in \mathbb{Z},0 < x < 7\}

Question 8

A directed graph

G

is shown below. Suppose we are trying to perform an algorithm to find the shortest path from vertex

v_0

v_4

. Which of the following statements is (are) correct?

Dijkstra’s algorithm can be used to find the shortest path from $v_0$ to $v_4$ .
Bellman-Ford algorithm can be used to find the shortest path from $v_0$ to $v_4$ because there are negative weighted edges.
The weight of the shortest path from $v_0$ to $v_4$ is $1$ .
Bellman-Ford algorithm cannot be used to find the shortest path from $v_0$ to $v_4$ because there is a negative cycle in the given graph.

Feedback/Explanation: Bellman-Ford algorithm cannot be used to find the shortest path from

v_0

v_4

because there is a negative cycle in the given graph.

Accepted Answers:

Bellman-Ford algorithm cannot be used to find the shortest path from

v_0

v_4

because there is a negative cycle in the given graph.

Question 9

Which of the following statements is (are) INCORRECT?

In an undirected graph $G$ , if all edges have different positive weights, then the minimum cost spanning tree of graph $G$ is unique.
If there is a cycle of weight $0$ in a directed graph $G$ , then we cannot find the shortest path using Bellman-Ford algorithm.
Suppose an acyclic undirected graph $G$ with $n$ vertices has $n − 1$ edges. Then the graph is connected.
In a graph $G$ , every edge with the minimum weight will be in the minimum cost spanning tree.

Status: Yes, the answer is correct. Score: Score: 1

Feedback/Explanation: If there is a cycle of weight

0

in a directed graph

G

, then we cannot find the shortest path using Bellman-Ford algorithm.

In a graph

G

, every edge with the minimum weight will be in the minimum cost spanning tree.

Accepted Answers:

If there is a cycle of weight

0

in a directed graph

G

, then we cannot find the shortest path using Bellman-Ford algorithm.

In a graph

G

, every edge with the minimum weight will be in the minimum cost spanning tree.

Question 10

An employee of that company wanted to travel from the city

C_2

to the city

C_5

. If he travelled by the cheapest route possible, then the total fare (in thousands of rupees) he paid for flight journey was

Your Answer: 15

Status: Yes, the answer is correct. Score: Score: 1

Feedback/Explanation: (Type: Numeric) 15

Accepted Answers:

(Type: Numeric) 15

Question 11

If an inspection team member wanted to inspect all the branches of the company starting from

C_2

and ending at

C_5

, visiting each branch exactly once, then which of the following routes should he choose in order to pay minimum fare for flight journey?

$C_2 \longrightarrow C_3 \longrightarrow C_1 \longrightarrow C_0 \longrightarrow C_4 \longrightarrow C_5$
$C_2 \longrightarrow C_1 \longrightarrow C_3 \longrightarrow C_4 \longrightarrow C_0 \longrightarrow C_5$
$C_2 \longrightarrow C_3 \longrightarrow C_1 \longrightarrow C_4 \longrightarrow C_0 \longrightarrow C_5$
Such a route is not possible.

Feedback/Explanation:

C_2 \longrightarrow C_1 \longrightarrow C_3 \longrightarrow C_4 \longrightarrow C_0 \longrightarrow C_5

Accepted Answers:

C_2 \longrightarrow C_1 \longrightarrow C_3 \longrightarrow C_4 \longrightarrow C_0 \longrightarrow C_5

Question 12

What is the total maintenance cost (in hundreds of rupees) of the optimum subset of links?

Your Answer: 31

Feedback/Explanation: (Type: Numeric) 15

Accepted Answers:

(Type: Numeric) 15

Question 13

Find the number of different ways of choosing an optimum subset of links for the given graph.

Your Answer: 2

Feedback/Explanation: (Type: Numeric) 4

Accepted Answers:

(Type: Numeric) 4

Question 14

Suppose we perform Prim’s algorithm on the graph

G

starting from vertex

A

to find an MCST. Then the order in which the vertices are added is

$A, C, F, G, B, D, E$
$A, B, D, E, G, C, F$
$A, B, G, C, F, D, E$
$A, C, F, G, E, D, B$

Feedback/Explanation:

A, B, G, C, F, D, E

Accepted Answers:

A, B, G, C, F, D, E

Question 15

Suppose we perform Kruskal’s algorithm on the graph

G

starting from vertex

C

to find an MCST. Which of the following edges are not added to the minimum cost spanning tree?

$(A, E)$
$(B, D)$
$(G, F)$
$(A, G)$

Feedback/Explanation:

(A, E)

(G, F)

Accepted Answers:

(A, E)

(G, F)

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Week 11 - Graded Assignment - 11

Introduction

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

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