Maths (bridge course)
Previous year question paper with solutions for Maths (bridge course) Dec-2018
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Question paper 1
SECTION-A
- Write briefly:
- Let
Answer:
(b) Let =
find the number of elements of a.Answer:
No of elements of A=3.
(c) Define an ant is ymmertic relation by giving suitable example .
Answer:
Antisymmetric Relation :A binary relation on a set x is antisymmetric
If there is no fair of distinct elts of X each of which is related by R to the other ,
Or equivalent ly,
If
For example ;
Is anti cymmetric on the set
(d)
and let R be a relation from A to B Defined by 
Determine the domain and range f R.Answer:
and Range of
(e) Write down the truth table of :
Answer:
p
q
T
T
F
F
F
T
F
F
T
T
F
T
T
F
T
F
F
T
T
T
(f) Write down the contrapositive of the conditional preposition;
Answer:
Contrapositive of
is
(g) Define a multi graph.
Answer:
Multi Graph: A graph which has multiple edges i.
is known as multi Graph .(h) Define a simple path and cycle in a graph.
Answer:
Simple path : An open walk in which every vertex is distinct is know as simple path
Cycle : A closed walk in which no vertex ( except the initial and terminal vertex) appears more than once.
(i) Determine whether the sequence
is solution of recurrence relationAnswer:
? 
not true
is not a solution.(j) Find the values of a,b,c,d from the equation:
Answer:
SECTION-B
2. IF A and B are any two sets, then prove that
Answer:
3. Prove the following by the principle of mathematical induction
Answer:
Basic we prove the result for n=1.
Assumption : We assume the result is true for n=k.
4. (a) Define the following graphs by taking suitable examples .
- Eulerian graph.
Answer:
A graph which contains either Euler path or Euler
Circuit is called Eulerian Graph.
ii. Hamiltonian graph
Answer:
A Graph Which contains either Hamiltonian circuit a Hamiltonian graph
(b) find the minimum n of colors required to paint the following graph
Answer:
5. Find the inverse of the following matric
Answer:
let
Co- factor matriy=
6. (a) Consider the following three relations on the set
Determine whether or not each of the above relations on A is:
(i) Reflexive (ii) symmetric; (iii) transitive;
Answer:
(a)
i. the only T is reflexive
ii.
.
S is not sym .
(iii)
(b) Verify that the proposition
is a contradiction. Answer:
P
Q
p∧q
p∨q
∼(p∨q)
(p∧q)∧∼(p∨q)
T
T
T
T
F
F
T
F
F
T
F
F
F
T
F
T
F
F
F
F
F
F
T
F
7. (a) Determine which of the following are Eulerian or Hamilton or both?
Answer:
This graph contains vertices of add degree.
∴
Graph is not evler graph Hamiltonian circuit 
(b) In a group of 50 person 14 drink tea but not coffee and 30 drink tea fond:
(i) How many drink tea and coffee both? (ii) How manu drink coffee but not tea ?
Answer:
The graph is Euler Graph
In this graph, neither Hamiltonian circuit exists nor the Hamiltonian path
Graph is not Hamiltonian Graph.