Basic Mathematics I

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1st Module Assessment

If det(A)= 0, then A is *_*

Singular

Transpose of a rectabgular matrix is a **__** matrix.

Select one:

a. uper traingular

b. square

c. rectangular

d. row

Question 2

In product of matrices “A × B”, being conformable confirms that______.

Select one:

a. None of these

b. No. of columns in B=No. of rows in A

c. Both of these

d. No. of columns in A=No. of rows in B

Question 3

** _** matrix has number of rows same as number of columns.

Select one:

a. square

b. rectangular

c. row

d. uper traingular

Question 4

Elements of the cartesian product of two sets (A x B) is of the type **__**

Select one:

a. 5-tuple

b. 3-tuple

c. 2-tuple

d. 4-tuple

Question 5

In a symmetric matric A transpose = ** _**.

Select one:

a. A

b. 3A

c. minus A

d. 2A

Question 6

Order of a row matrix can be of the form **__**.

Select one:

a. 1 x n

b. 2 x n

c. n x 1

d. n x 2

Question 7

De Morgan’s Law of intersection states that, complement of **of A and B is same as __** of “A complement” and “B complement”.

Select one:

a. union, difference

b. union, intersection

c. intersection, union

d. difference, intersection

Question 8

If in matrix “A”, element “a_11=3”, then in matrix “5A”, element “a_11=?”

Select one:

a. 9

b. 3

c. 15

d. 25

Question 9

In a skew-symmetric matric A transpose = ** _**.

Select one:

a. A

b. minus A

c. 3A

d. 2A

Question 10

A set is an unordered collection of ** _** objects.

Select one:

a. distinct

b. different

c. same

d. none of these

Which set amongst can be considered as a trivial subset of any set?

a. empty set phi

Question 11

Which set amongst can be considered as a trivial subset of any set?

Select one:

a. equal set

b. Singleton set

c. empty set phi

d. universal set

Question 12

Cardinality of the power set of the set A = {1,2,3}, will be **__**.

Select one:

a. 4

b. 8

c. 3

d. 6

Question 13

Set including “cat family animals that can fly”, can be an example of **__** set.

Select one:

a. null

b. all of these

c. void

d. empty

Question 14

Which amongst the following is/are features of row echelon form of a mtrix (A) ?

Select one:

a. all entries below a_11 should be zero

b. a_11 should be equal to 1

c. row containing all zeros placed at the bottom

d. all of these

Question 15

Determinant of 3 x 3 matrix having first row [ 1 2 5], second row [ 3 5 7] and third row [ 4 5 0] will be ** __**.

Select one:

a. 4

b. 2

c. -3

d. -4

Question 16

Universal Set (U) = {1,2,3,4,5,6,7,8,9}; Set A = {1,4,6} and Set B = {3,5,2}. Set A union (B complement)= ?

Select one:

a. B complement

b. A complement

c. U

d. A intersection (B complement)

Question 17

Order of the resultant matrix as you multiplyr matrix A of order (3×1) and matrix B of order (1×3), will be ** _**.

Select one:

a. (1×1)

b. (3×3)

c. (3×1)

d. (1×3)

30/30

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2nd Module Assessment

Question 1

Logical connective “Exclusive OR/XOR” corresponds to the concept of ** _** in the set theory.

Select one:

a. symmetric difference

b. Complement

c. Union

d. Intersection

Question 2

Sentence “C++ is the best language” is ** __**.

Select one:

a. proposition

b. Interrogatie sentence

c. Opinion

d. Imperative sentence

Question 3

Negation of the truth values represented by XOR, will be reflected by the connective **__**.

Select one:

a. XNOR

b. NAND

c. XOR

d. AND

Question 4

For an implication “p implies q”, if “~q” becomes hypothesis and “~p” becomes conclusion, then it is ** __** of the given implication “p implies q”.

Select one:

a. Biconditional 22

b. Inverse

c. Contrapositive

d. Converse

Question 5

Which amongst the following can not be propositions?

Select one:

a. All of these

b. Opinions

c. Interrogative sentences

d. Imperative sentences

Question 6

For an implication “p implies q”, if “q” becomes hypothesis and “p” becomes conclusion, then it is ** __** of the given implication “p implies q”.

Select one:

a. Contrapositive

b. Converse

c. Inverse

d. Biconditional

Question 7

If p is false and q is false then ~ p Λ ~q is

Select one:

a. FALSE

b. Absurd

c. Can’t Say

d. True

Question 8

Logical connective “conjunction/AND” corresponds to the concept of ** _** in the set theory.

Select one:

a. symmetric difference

b. Complement

c. Intersection

d. Union

Question 9

Logical operation “negation” corresponds to the concept of ** _** in the set theory.

Select one:

a. symmetric difference

b. Complement

c. Union

d. Intersection

Question 10

If p is true and q is false then ~(p Λ q) is

Select one:

a. True

b. FALSE

c. Can’t Say

d. Absurd

Question 11

If p = Roses are red and q = Violets are blue then the statement “if roses are red then voilets are blue” can be represented as ** _**.

Select one:

a. ~(p –> q)

b. q –> p

c. p –> q

d. None of these

Question 12

If p = Roses are red and q = Violets are blue then the statement “roses are not red and voilets are not blue” can be represented as ** _**.

Select one:

a. ~p V ~q

b. ~(p Λ q)

c. ~p Λ ~q

d. ~p Λ q

Question 13

If p = Roses are red and q = Violets are blue then the statement “it is not the case that roses are red or voilets are blue” can be represented as ** _**.

Select one:

a. ~p Λ ~q

b. ~p V q

c. ~p V ~q

d. p Λ ~q

Question 14

If p = Roses are red and q = Violets are blue then the statement “it is not the case that roses are red and voilets are blue” can be represented as ** _**.

Select one:

a. ~p V ~q

b. ~(p Λ ~q)

c. ~p Λ ~q

d. ~(p Λ q)

Question 15

~(p Λ q) is logically equivalen to **__**

Select one:

a. ~ p Λ q

b. ~ p Λ ~q

c. p Λ ~q

d. ~ p V ~q

Question 16

If p = Roses are red and q = Violets are blue then the statement “if roses are not red then violets are not blue” can be termed as ** _**.

Select one:

a. Biconditional

b. Converse

c. Contrapositive

d. Inverse

Question 17

If p = Roses are red and q = Violets are blue then the statement “if violets are not blue then roses are not red” can be termed as ** _**.

Select one:

a. Biconditional

b. Converse

c. Inverse

d. Contrapositive

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4th Module Assessment

Graph is made of

Both of these

Question 1

In an undirected graph, degree of a node is defined by ** _**.

Select one:

a. numebr of edges coming in

b. number of edges in the graph

c. numebr of edges going out

d. number of edges incident

Question 2

When there is a path between every pair of vertices, it is called **__**.

Select one:

a. Complete graph

b. Connected graph

c. Biconnected graph

d. Tree

Question 3** _** is subactegory of Directed graphs.

Select one:

a. Biconnected graph

b. DAG

c. Connected graph

d. Complete graph

Question 4

In a type of graph DAG, “A” refers to ** __**.

Select one:

a. additional

b. acyclic

c. accelerated

d. acquired

Question 5

In an undirected graph is (u,v) same as (v,u)?

Select one:

a. Yes

b. Absurd

c. Can’t Say

d. No

Question 6

A DAG with a restriction that a child can have only one parent is called ** __**.

Select one:

a. Connected graph

b. Biconnected graph

c. Tree

d. Complete graph

Question 7

In a directed graph is (u,v) same as (v,u)?

Select one:

a. No

b. Can’t Say

c. Absurd

d. Yes

Question 8

In a directed graph, indegree of the node is defined by ** _**.

Select one:

a. number of edges incident

b. number of edges coming in

c. number of edges going out

d. number of edges in the graph

Question 9

A node ‘v’ is said to be ** _** node of node ‘u’ if and only if there exists an edge between ‘u’ and ‘v’

Select one:

a. single

b. simple

c. multiple

d. adjacent

Question 10

In a directed graph, outdegree of the node is defined by ** _**.

Select one:

a. numebr of edges going out

b. numebr of edges coming in

c. number of edges incident

d. number of edges in the graph

A ** _** does not have more than one edge between any two vertices and no edge starts and ends at the same vertex.

Simple Graph

Question 11

Traversing a graph such that we do not repeat a vertex nor we repeat a edge but the starting and ending vertex must be same i.e. we can repeat starting and ending vertex only is called *_*

Select one:

a. all of these

b. Path

c. Cycle

d. Walk

Question 12

** __** allows edges connect a vertex to itself

Select one:

a. pseudograph

b. all of these

c. Multigraph

d. Simple Graph

Question 13

A complete graph has ** _** number of edges.

Select one:

a. n(n+1)/2

b. n(n-1)/2

c. 2n(n-1)/n

d. None of these

Question 14

** __** allows multiple edges between two vertices.

Select one:

a. pseudograph

b. Simple Graph

c. all of these

d. Multigraph

Question 15

The maximum number of edges in a bipartite graph on 12 vertices is ** __**?

Select one:

a. 24

b. 30

c. 36

d. 15

Question 16

A graph G has 8 edges. Find the number of vertices, if the degree of each vertex is 2.

Select one:

a. 8

b. 7

c. 6

d. 5

Question 17

A simple graph G has 24 edges and degree of each vertex is 4. Find the number of vertices.

Select one:

a. 13

b. 12

c. 10

d. 11

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Assignment 2

Case Study

Solve the system of linear equations by matrix inversion method, 3x+5y = 1 and 2x+y=3.

Question 1 : Matrix inversion method can be applied in the following case/es.

Select one:

a. when coefficient matrix is non singular

b. when coefficient matrix is square matrix

c. both of these

d. none of these

Question 2

Determinant os the coefficient matrix (A) is ** __**.

Select one:

a. -7

b. -1

c. 2

d. 0

Question 3

Coefficient matrix (A) is a______ matrix in this case.

Select one:

a. Symmetric

b. Skew-Symmetric

c. Singular

d. Non-Singular

Question 4

First row second column in the cofactor matrix of A is **__**.

Select one:

a. -2

b. -5

c. 1

d. 4

Question 5

First row first column entry in the inverse of the matrix A is **__**.

Select one:

a. -3/7

b. -4/7

c. -1/7

d. -6/7

15/15

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