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

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

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

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

Basic Mathematics I

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