Suppose A = {a, b, c, d} and B = {p, q, r, s} are two sets. Consider the following relations on A \times B. - R_1 = {(a, p), (c, r), (d, q)} - R_2 = {(a, s), (b, s), (c, p), (d, r)} - R_3 = {(a, p), (b, r), (b, s), (d, q)} - R_4 = {(a, r), (b, p), (c, q), (d, s)} Which of the following statements are correct?

(D) R4 is a bijective function.

(A) R2,R3, and R4 are functions.

(C) R2 is an injective function.

Figure from the original question paper

(A) Option figure from the original question paper

(C) Option figure from the original question paper

(B) Option figure from the original question paper

(D) Option figure from the original question paper

Maths 1 End Term PYQ Jan 2024: 28 Apr 2024 (Set QDF1)

Question 1

+4 marksOne correct option

The DFS (Depth First Search) tree of a graph starting with vertex A is shown below. Choose the option which might be the original graph.

A
B
C
D

Show answer

Correct answer

B

Question 1 on its own page

Question 2

+4 marksOne or more correct options

Which of the following are valid topological orderings of the given DAG ?

Select all that apply.

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

Show answer

Correct answers

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

Question 2 on its own page

Question 3

+4 marksOne or more correct options

Suppose $A = \{a, b, c, d\}$ and $B = \{p, q, r, s\}$ are two sets. Consider the following relations on $A \times B$ .

$R_1 = \{(a, p), (c, r), (d, q)\}$
$R_2 = \{(a, s), (b, s), (c, p), (d, r)\}$
$R_3 = \{(a, p), (b, r), (b, s), (d, q)\}$
$R_4 = \{(a, r), (b, p), (c, q), (d, s)\}$

Which of the following statements are correct?

Select all that apply.

A
R2,R3, and R4 are functions.
B
R2 and R4 are functions.
C
R2 is an injective function.
D
R4 is a bijective function.

Show answer

Correct answers

B
R2 and R4 are functions.
D
R4 is a bijective function.

Question 3 on its own pageAlso asked in End Term 28 Apr 2024

Question 4

+4 marksOne or more correct options

Select all that apply.

A
B
C
D

Show answer

Correct answers

A
C

Question 4 on its own page

Question 5

+3 marksNumerical answer

What is the minimum number of colours required to colour the graph given below?

Show answer

Correct answer: 4

Question 5 on its own page

Question 6

+3 marksNumerical answer

Show answer

Correct answer: 1

Question 6 on its own page

Question 7

+2 marksNumerical answer

A person is climbing stairs and he stops at a point P on the stairs after reaching two third of the total distance of stairs. The stairs forms an isosceles triangle with the floor and wall. Assume the origin (0, 0) at the intersection of the wall and floor and the stairsis to the right of the wall. Based on the above data, answer the given subquestions.

Find the angle between the stairs and the wall (in degrees).

Show answer

Correct answer: 45

Question 7 on its own page

Question 8

+1 markNumerical answer

A person is climbing stairs and he stops at a point P on the stairs after reaching two third of the total distance of stairs. The stairs forms an isosceles triangle with the floor and wall. Assume the origin (0, 0) at the intersection of the wall and floor and the stairsis to the right of the wall. Based on the above data, answer the given subquestions.

Show answer

Correct answer: 2

Question 8 on its own page

Question 9

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 11

Question 9 on its own page

Question 10

+1 markNumerical answer

Based on the above data, answer the given subquestions.

**Note:**Enter your answer correctly to two decimal places.

Show answer

Correct answer: 0.125 (accepted within ±0.005)

Question 10 on its own page

Question 11

+2 marksNumerical answer

Consider an undirected graph G with 12 vertices, where the degree of each vertex is at least 2 and at most 5.
Based on the above data, answer the given subquestions.

Determine the minimum number of edges the graph G can have.

Show answer

Correct answer: 12

Question 11 on its own page

Question 12

+2 marksNumerical answer

Consider an undirected graph G with 12 vertices, where the degree of each vertex is at least 2 and at most 5.
Based on the above data, answer the given subquestions.

Determine the maximum number of edges the graph G can have.

Show answer

Correct answer: 30

Question 12 on its own page

Question 13

+1 markOne correct option

Based on the above data, answer the given subquestions.

A
TRUE
B
FALSE

Show answer

Correct answer

A
TRUE

Question 13 on its own page

Question 14

+1 markOne correct option

Based on the above data, answer the given subquestions.

A
TRUE
B
FALSE

Show answer

Correct answer

B
FALSE

Question 14 on its own page

Question 15

+1 markOne correct option

Based on the above data, answer the given subquestions.

A
TRUE
B
FALSE

Show answer

Correct answer

A
TRUE

Question 15 on its own page

Question 16

+1 markOne correct option

Based on the above data, answer the given subquestions.

A
TRUE
B
FALSE

Show answer

Correct answer

B
FALSE

Question 16 on its own page

Question 17

+1 markNumerical answer

Answer the given sub-questions.

Show answer

Correct answer: 4

Question 17 on its own page

Question 18

+1 markOne correct option

Answer the given sub-questions.

A
TRUE
B
FALSE

Show answer

Correct answer

B
FALSE

Question 18 on its own page

Question 19

+1 markOne correct option

Answer the given sub-questions.

A
TRUE
B
FALSE

Show answer

Correct answer

B
FALSE

Question 19 on its own page

Question 20

+1 markNumerical answer

Answer the given sub-questions.

Show answer

Correct answer: 2

Question 20 on its own page

Question 21

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 1

Question 21 on its own page

Question 22

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 14

Question 22 on its own page

Question 23

+3 marksOne or more correct options

Consider the following adjacency matrix

$\begin{array}{cc} & \begin{array}{ccccc} A & B & C & D & E \end{array} \\ \begin{array}{c} A \\ B \\ C \\ D \\ E \end{array} & \begin{pmatrix} 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 1 & 0 \end{pmatrix} \end{array}$

which represents graph $G$ which has 5 vertices $A, B, C, D$ and $E$ .

Based on the above data, answer the given subquestions.

Which of the following is true about the graph G?

Select all that apply.

A
The vertices A,B,D and E are reachable from vertex C.
B
The longest path in the graph G starts with vertex C and ends with vertex E.
C
The graph G is a directed acyclic graph.
D
The longest path in the graph G has length 3, in terms of number of edges.

Show answer

Correct answers

A
The vertices A,B,D and E are reachable from vertex C.
C
The graph G is a directed acyclic graph.
D
The longest path in the graph G has length 3, in terms of number of edges.

Question 23 on its own page

Question 24

+3 marksOne or more correct options

Consider the following adjacency matrix

$\begin{array}{cc} & \begin{array}{ccccc} A & B & C & D & E \end{array} \\ \begin{array}{c} A \\ B \\ C \\ D \\ E \end{array} & \begin{pmatrix} 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 1 & 0 \end{pmatrix} \end{array}$

which represents graph $G$ which has 5 vertices $A, B, C, D$ and $E$ .

Based on the above data, answer the given subquestions.

Which of the following graph(s) is represented by the given adjacency matrix?

Select all that apply.

A
B
C
D

Show answer

Correct answers

A
D

Question 24 on its own page