FINALTERM EXAMINATION
Fall 2009
MTH202- Discrete Mathematics
Time: 120 min
Marks: 80
If A and B are two disjoint (mutually exclusive) events then
P(AÈB) =
► P(A) + P(B) + P(AÇB)
► P(A) + P(B) + P(AUB)
► P(A) + P(B) - P(AÇB)
► P(A) + P(B) - P(AÇB)
► P(A) + P(B)
If p=It is red,
q=It is hot
Then, It is not red but hot is denoted by 
► True
► False
If (
) = A, then (
) = B
► True
► False
► Cannot be determined
How many integers from 1 through 1000 are neither multiple of 3 nor multiple of 5?
► 333
► 467
► 533
► 497
The value of 
for -2.01 is
► -3
► 1
► -2
If
p = Nadia is hard working ,
q = Nadia is good in mathematics
"Nadia is hard working and good in mathematics" is denoted by
► 
► 
► 
► 
A die is thrown twice. What is the probability that the sum of the number of dots shown is 3 or 11?
► 
► 
► 
If A and B are independent events then 
► P (B)
► P (A)
► 
What is the expectation of the number of heads when three fair coins are tossed?
► 1
► 1.34
► 2
► 1.5
Every relation is
► function
► may or may not function
► bijective mapping
► Cartesian product set
The statement p « q º (p ®q)Ù(q ®p)
describes
► Commutative Law
► Implication Laws
► Exportation Law
► Equivalence
Given
► 
► 
► Zero
► 
The square root of every prime number is irrational
► True
► False
► Depends on the prime number given
A predicate is a sentence that contains a finite number of variables and becomes a statement when specific values are substituted for the variables
► True
► False
► None of these
If r is a positive integer then gcd(r,0)=
► r
► 0
► 1
► None of these
Associative law of union for three sets is
► 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
Values of X and Y, if the following order pairs are equal.
(4X-1, 4Y+5)= (3,5)
will be
► (x,y) = (3,5)
► (x,y) = (1.5,2.5)
► (x,y) = (1,0)
► None of these
The expectation of x is equal to
► Sum of all terms
► Sum of all terms divided by number of terms
► 
A line segment joining pair of vertices is called
►
► Edge
► Node
The indirect proof of a statement pàq involves
► Considering ~q and then try to reach ~p
► Considering p and ~q and try to reach contradiction
► Both 2 and 3 above
► Considering p and then try to reach q
The greatest common divisor of 5 and 10 is
► 5
► 0
► 1
► None of these
Suppose that there are eight runners in a race first will get gold medal the second will get siver and third will get bronze. How many different ways are there to award these medals if all possible outcomes of race can occur and there is no tie.
► P(8,3)
► P(100,97)
► P(97,3)
► None of these
The value of 0! Is
► 0
► 1
► Cannot be determined
Which of the following graphs are tree?
► a, b, c
► b, c, d
► c, d, e
► a , c, e
A sub graph of a graph G that contains every vertex of G and is a tree is called
► Trivial tree
► empty tree
► Spanning tree
In the planar graph, the graph crossing number is
► 0
► 1
► 2
► 3
A matrix in which number of rows and columns are equal is called
► Rectangular Matrix
► Square Matrix
► Scalar Matrix
Changing rows of matrix into columns is called
► Symmetric Matrix
► Transpose of Matrix
► Adjoint of Matrix
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
When 3k is even, then 3k+3k+3k is an odd.
► True
► False
When 5k is even, then 5k+5k+5k is odd.
► True
► False
5n -1 is divisible by 4 for all positive integer values of n.
► True
► False
If r is a positive integer then gcd(r, 5) =
► r
► 5
► 0
► None of these
The product of the positive integers from 1 to n is called
► Multiplication
► n factorial
► Geometric sequence
The expectation m for the following table is
| xi | 1 | 3 |
| f(xi) | 0.4 | 0.1 |
► 0.5
► 3.4
► 0.3
► 0.7
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
► None of these
The given graph is
► Simple graph
► Complete graph
► Bipartite graph
► Both (i) and (ii)
► Both (i) and (iii)
is called proposition or statement.
► True
► False
An integer n is odd if and only if n = 2k + 1 for some integer k.
► True
► False
► Depends on the value of k
An integer n is called a perfect square if and only if n = k2 for some integer k.
► True
► False
► Depends on the value of k
( Marks: 2 )
Find the degree sequence of the following graph
( Marks: 2 )
Let A and B be events with
( Marks: 3 )
Find the greatest common divisor of the following pair of integer:
72,63
( Marks: 2 )
Find all non isomorphic simple connected graphs with three vertices.
( Marks: 3 )
How many 3-digit numbers can be formed by using each one of the digits 2,3,5,7,9 only once?
( Marks: 3 )
How many permutations of the letter of the word
( Marks: 5 )
A die is weighted so that the outcomes produce the following probability distribution:
| Outcome | 1 | 2 | 3 | 4 | 5 | 6 |
| Probability | 0.1 | 0.3 | 0.2 | 0.1 | 0.1 | 0.2 |
Consider the event
A= {even number} then find the following
(a) P(A)
(b) P (Ac)
( Marks: 5 )
Determine whether the given graphs have an Euler circuit? If it does, find such a circuit, if it does not, give an argument to show why no such circuit exists.
( Marks: 5 )
By using Mathematical induction prove that for all positive integers n
.
( Marks: 10 )
Prove by mathematical induction that 
is divisible by 4 for all
.
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