MTH202 Final Term Solved Paper For Success

FINALTERM  EXAMINATION

Spring 2010

MTH202- Discrete Mathematics (Session - 1)

Time: 90 min

Marks: 60

  www.allvupastpapers.blogspot.com     

Question No: 1    ( Marks: 1 )    - Please choose one

 Whether the relation R on the set of all integers is reflexive, symmetric, antisymmetric, or transitive, where  if and only if

       ► Antisymmetric

       ► Transitive

                       *► Symmetric

       ► Both Symmetric and transitive

   

Question No: 2    ( Marks: 1 )    - Please choose one

 For a binary relation R defined on a set A , if for all  then R is

                        * ► Antisymmetric

       ► Symmetric

       ► Irreflexive

   

Question No: 3    ( Marks: 1 )    - Please choose one

 If ( ) = A, then ( ) = B

       ► True

                           * ► False

       ► Cannot be determined

By : Adeel Abbas

   

Question No: 4    ( Marks: 1 )    - Please choose one

 Let

  www.allvupastpapers.blogspot.com     

 

►-6

          -*►2

►8

   

Question No: 5    ( Marks: 1 )    - Please choose one

 The part of definition which can be expressed in terms of smaller versions of itself is called

       ► Base

       ► Restriction

                                    *► Recursion

       ► Conclusion

   

Question No: 6    ( Marks: 1 )    - Please choose one

 What is the smallest integer N such that  

                                    * ► 46

       ► 29

       ► 49

   

Question No: 7    ( Marks: 1 )    - Please choose one

 In probability distribution random variable f satisfies the conditions

       ►

      www.allvupastpapers.blogspot.com     

                                    * ►

       ►

       ►

   

Question No: 8    ( Marks: 1 )    - Please choose one

 What is the probability that a hand of five cards contains four cards of one kind?

       ► 0.0018

       ►

                                    *► 0.0024

   

Question No: 9    ( Marks: 1 )    - Please choose one

      A rule that assigns a numerical value to each outcome in a sample space is called

By : Adeel Abbas

       ► One to one function

       ► Conditional probability

                                 *  ► Random variable

   

Question No: 10    ( Marks: 1 )    - Please choose one

 A walk that starts and ends at the same vertex is called

       ► Simple walk

       ► Circuit

                            *► Closed walk      

   

Question No: 11    ( Marks: 1 )    - Please choose one

 The Hamiltonian circuit for the following graph is

  www.allvupastpapers.blogspot.com     

         

       ► abcdefgh

       ► abefgha

                                    *► abcdefgha

   

Question No: 12    ( Marks: 1 )    - Please choose one

 Distributive law of union over intersection for three sets

       ► A È (B È C) = (A È B) È C

       ► A Ç (B Ç C) = (A Ç B) Ç C

                                    *► A È (B Ç C) = (A È B) Ç  (A È B)

       ► None of these

   

Question No: 13    ( Marks: 1 )    - Please choose one

 The indirect proof of a statement pàq involves

►Considering ~q and then try to reach ~p

  www.allvupastpapers.blogspot.com     

►Considering p and ~q and try to reach contradiction

                              *►Both 2 and 3 above

►Considering p and then try to reach q

    By : Adeel Abbas

Question No: 14    ( Marks: 1 )    - Please choose one

 The square root of every prime number is irrational

       ► True

                            *► False

       ► Depends on the prime number given

   

Question No: 15    ( Marks: 1 )    - Please choose one

 If a and b are any positive integers with b≠0 and q and r are non negative integers such that  a= b.q+r then

                                    *► gcd(a,b)=gcd(b,r)

  www.allvupastpapers.blogspot.com     

       ► gcd(a,r)=gcd(b,r)

       ► gcd(a,q)=gcd(q,r)

   

Question No: 16    ( Marks: 1 )    - Please choose one

 The greatest common divisor of 27 and 72 is

       ► 27

       ► 9

                                    *► 1

       ► None of these

   

Question No: 17    ( Marks: 1 )    - Please choose one

 In how many ways can a set of five letters be selected from the English Alphabets?

                                          *► C(26,5)

       ► C(5,26)

       ► C(12,3)

       ► None of these

  www.allvupastpapers.blogspot.com     

   

Question No: 18    ( Marks: 1 )    - Please choose one

 A vertex of degree greater than 1 in a tree is called a

       ► Branch vertex

                                    *► Terminal vertex

       ► Ancestor

   

Question No: 19    ( Marks: 1 )    - Please choose one

 For the given pair of graphs whether it is By : Adeel Abbas

                        

     www.allvupastpapers.blogspot.com     

                                            

       

       ► Isomorphic

                                    *► Not isomorphic

   

Question No: 20    ( Marks: 1 )    - Please choose one

 The value of (-2)! Is

       ► 0

       ► 1

                        * ► Cannot be determined

      www.allvupastpapers.blogspot.com     

Question No: 21    ( Marks: 1 )    - Please choose one

 In the following graph

            

                             

How many simple paths are there from   to 

       ► 2

                       *► 3

       ► 4

   

Question No: 22    ( Marks: 1 )    - Please choose one

 The value of   is

       ► 0

                           *► n(n-1)

       ►

       ► Cannot be determined

    www.allvupastpapers.blogspot.com     

 

Question No: 23    ( Marks: 1 )    - Please choose one

 If A and B are finite (overlapping) sets, then which of the following must be true

       ► n(AÈB) = n(A) + n(B)

                    * ► n(AÈB) = n(A) + n(B) - n(AÇB)

       ► n(AÈB)= ø

       ► None of these

   

Question No: 24    ( Marks: 1 )    - Please choose one

 Any two spanning trees for a graph By : Adeel Abbas

       ► Does not contain same number of edges

                        *► Have the same degree of corresponding edges

       ► contain same number of edges

       ► May or may not contain same number of edges

   

Question No: 25    ( Marks: 1 )    - Please choose one

 When 3^k is even, then 3^k+3^k+3^k is an odd.

       ► True

                         *► False

     www.allvupastpapers.blogspot.com     

Question No: 26    ( Marks: 1 )    - Please choose one

 Quotient –Remainder Theorem states that for any positive integer d, there exist unique integer q and r such that n=d.q+ r and _______________.

                                    *  ► 0≤r<d

       ► 0<r<d

       ► 0≤d<r

       ► None of these

   

Question No: 27    ( Marks: 1 )    - Please choose one

 The value of  for  x = -3.01 is

             *► -3.01

       ► -3

       ► -2

       ► -1.99

   

Question No: 28    ( Marks: 1 )    - Please choose one

 If p= A Pentium 4 computer,

    q= attached with ups.

 Then  "no Pentium 4 computer is attached with ups" is denoted by

       ► ~ (pÙq)

       ► ~ pÚq

       ► ~ pÙq

    www.allvupastpapers.blogspot.com     

                                    *► None of these

   

Question No: 29    ( Marks: 1 )    - Please choose one

 An integer n is prime if and only if n > 1 and for all positive integers r and s, if

    n = r·s, then

►r = 1 or s = 2.

►r = 1 or s = 0.

►r = 2 or s = 3.

►None of these

   

Question No: 30    ( Marks: 1 )    - Please choose one

 If  then the events A and B are called

  www.allvupastpapers.blogspot.com     

                                    *►Independent

►Dependent

►Exhaustive

   

Question No: 31    ( Marks: 2 )

 Let A and B be the events. Rewrite the following event using set notation

                     “Only A occurs”

   

Question No: 32    ( Marks: 2 )

   Suppose that a connected planar simple graph has 15 edges. If a plane drawing of this graph has 7 faces, how many vertices does this graph have?

By : Adeel Abbas

Answer:

Given,

Edges = v =15

Faces = f = 7

Vertices = v =?

According toEuler Formula, we know that,

            f= e – v +2

Putting values, we get

            7 = 15 – v + 2

            7 = 17 – v

Simplifying

            v =1 7-7 =10

  www.allvupastpapers.blogspot.com     

Question No: 33    ( Marks: 2 )

 How many ordered selections of two elements can be made from the set {0,1,2,3}?

   

Answer

  The order selection of two elements from 4 is as

P(4,2) =  4!/(4-2)!

            =  (4.3.2.1)/2!

            = 12

  www.allvupastpapers.blogspot.com     

Question No: 34    ( Marks: 3 )

 Consider the following events for a family with children:

A={children of both sexes}, B={at most one boy}.Show that A and B are dependent events if a family has only two children.

   

Question No: 35    ( Marks: 3 )

 Determine the chromatic number of the given graph by inspection.

                              www.allvupastpapers.blogspot.com     

   

Question No: 36    ( Marks: 3 )

 A cafeteria offers a choice of two soups, five sandwiches, three desserts and three drinks. How many different lunches, each consisting of a soup, a sandwiche, a dessert and a drink are possible? By : Adeel Abbas

   

Question No: 37    ( Marks: 5 )

 A box contains 15 items,4 of which are defective and 11 are good. Two items are selected. What is probability that the first is good and the second defective?

 Answer

  

Question No: 38    ( Marks: 5 )

 Draw a binary tree with height 3 and having seven terminal vertices.

   

Question No: 39    ( Marks: 5 )

 Find n if

      P(n,2) = 72

  www.allvupastpapers.blogspot.com     

By ADEEL ABBAS, Bhakkar. AdeelAbbasbk@gmail.com