MTH202- Discrete Mathematics FINALTERM EXAMINATION Fall 2009 (2)

FINALTERM EXAMINATION

Fall 2009

MTH202- Discrete Mathematics

Time: 120 min

Marks: 80

Gray Highlighted are correct answers…………

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

Let A = {a, b, c} and

R = {(a, c), (b, b), (c, a)} be a relation on A. Is R

► Transitive

► Reflexive

► Symmetric

► Transitive and Reflexive

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

Symmetric and antisymmetric are

► Negative of each other

► Both are same

► Not negative of each other

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

The statement p « q º q « p

describes

► Commutative Law:

► Implication Laws:

► Exportation Law:

► Equivalence:

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

The relation as a set of ordered pairs as shown in figure is

► {(a,b),(b,a),(b,d),(c,d)}

► {(a,b),(b,a),(a,c),(b,a),(c,c),(c,d)}

► {(a,b), (a,c), (b,a),(b,d), (c,c),(c,d)}

► {(a,b), (a,c), (b,a),(b,d),(c,d)}

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

The statement p ®q º (p Ù ~q) ®c

describes

► Commutative Law:

► Implication Laws:

► Exportation Law:

► Reductio ad absurdum

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

A circuit with one input and one output signal is called.

► NOT-gate (or inverter)

► OR- gate

► AND- gate

► None of these

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

If f(x)=2x+1, then fg(x)=

►

►

►

ee bhai aap f(x) main x ki jagah g(x) put karen then simplify it

like this

2(x^2 - 1) + 1 = 2x^2 -2 + 1 = 2x^2 - 1

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

Let g be the functions defined by

g(x)= 3x+2 then gog(x) =

►

► 6x+4

► 9x+8

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

How many integers from 1 through 1000 are neither multiple of 3 nor multiple of 5?

► 333

► 467

► 533

► 497

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

What is the smallest integer N such that

► 46

► 29

► 49

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

What is the probability of getting a number greater than 4 when a die is thrown?

►

►

►

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

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)

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

If a die is thrown then the probability that the dots on the top are prime numbers or odd numbers is

► 1

►

►

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

The probability of getting 2 heads in two successive tosses of a balanced coin is

►

►

►

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

The probability of getting a 5 when a die is thrown?

►

►

►

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

If a coin is tossed then what is the probability that the number is 5

►

► 0

► 1

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

If A and B are two sets then The set of all elements that belong to both A and B , is

► A È B

► A Ç B

► A--B

► None of these

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

What is the expectation of the number of heads when three fair coins are tossed?

► 1

► 1.34

► 2

► 1.5

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

If A, B and C are any three events, then

P(AÈBÈC) is equal to

► P(A) + P(B) + P(C)

► P(A) + P(B) + P(C)- P(AÇB) - P (A ÇC) - P(B ÇC) + P(A ÇB ÇC)

► P(A) + P(B) + P(C) - P(AÇB) - P (A ÇC) - P(B ÇC)

► P(A) + P(B) + P(C) + P(A ÇB ÇC)

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

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

► One to one function

► Conditional probability

► Random variable

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

The power set of a set A is the set of all subsets of A, denoted P(A).

► False

► True

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

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

► Simple walk

► Circuit

► Closed walk

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

If a graph has any vertex of degree 3 then

► It must have Euler circuit

► It must have Hamiltonian circuit

► It does not have Euler circuit

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

The square root of every prime number is irrational

► True

► False

► Depends on the prime number given

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

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

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

If r is a positive integer then gcd(r,0)=

► r

► 0

► 1

► None of these

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

Combinatorics is the mathematics of counting and arranging objects

► True

► False

► Cannot be determined

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

A circuit that consist of a single vertex is called

► Trivial

► Tree

► Empty

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

In the planar graph, the graph crossing number is

► 0

► 1

► 2

► 3

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

How many ways are there to select five players from a 10 member tennis team to make a trip to a match to another school?

► C(10,5)

► C(5,10)

► P(10,5)

► None of these

Question No: 31 ( Marks: 1 ) - Please choose one

The value of 0! Is

► 0

► 1

► Cannot be determined

Question No: 32 ( Marks: 1 ) - Please choose one

If the transpose of any square matrix and that matrix are same then matrix is called

► Additive Inverse

► Hermition Matrix

► Symmetric Matrix

Question No: 33 ( Marks: 1 ) - Please choose one

The value of is

► 0

► n(n-1)

►

► Cannot be determined

Question No: 34 ( Marks: 1 ) - Please choose one

If A and B are two disjoint 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: 35 ( Marks: 1 ) - Please choose one

Any two spanning trees for a graph

► 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: 36 ( Marks: 1 ) - Please choose one

When P(k) and P(k+1) are true for any positive integer k, then P(n) is not true for all +ve Integers.

► True

► False

Question No: 37 ( Marks: 1 ) - Please choose one

n² > n+3 for all integers n ³3.

► True

► False

Question No: 38 ( Marks: 1 ) - Please choose one

Quotient –Remainder Theorem states that for any positive integer d, there exist unique integer q and r such that _______________ and 0≤r

► n=d.q+ r

► n=d.r+ q

► n=q.r+ d

► None of these

Question No: 39 ( Marks: 1 ) - Please choose one

Euler formula for graphs is

► f = e-v

► f = e+v +2

► f = e-v-2

► f = e-v+2

Question No: 40 ( Marks: 1 ) - Please choose one

The degrees of {a, b, c, d, e} in the given graph is

► 2, 2, 3, 1, 1

► 2, 3, 1, 0, 1

► 0, 1, 2, 2, 0

► 2,3,1,2,0

Question No: 41 ( Marks: 2 )

Let then find

Question No: 42 ( Marks: 2 )

Write the contra positive of the following statements:

1. For all integers n, if n² is odd then n is odd.

2. If m and n are odd integers, then m+n is even integer.

Question No: 43 ( Marks: 2 )

How many distinguishable ways can the letter of the word HULLABALOO be arranged.

Question No: 44 ( Marks: 3 )

Find the variance s² of the distribution given in the following table.

xi	1	3	4	5
f(xi)	0.4	0.1	0.2	0.3

Question No: 45 ( Marks: 3 )

Prove that every integer is a rational number.

Question No: 46 ( Marks: 3 )

a. Evaluate P(5,2)

b. How many 5-permutations are there of a set of five objects?

Question No: 47 ( Marks: 5 )

Is it possible to have a simple graph with four vertices of degree 1, 1, 3, and 3.If no then give reason?(Justify your answer)

Question No: 48 ( Marks: 5 )

Find the GCD of 500008, 78 using Division Algorithm.

Question No: 49 ( Marks: 5 )

Find the M number of ways that ten chocolates can be divided among three children if the youngest child is to receive four chocolates and each of the others three chocolates.

Question No: 50 ( Marks: 10 )

In the graph below, determine whether the following walks are paths, simple paths, closed walks, circuits,

simple circuits, or are just walk?

i) v₀ e₁ v₁ e₁₀ v₅ e₉ v₂ e₂ v₁

ii) v₄ e₇ v₂ e₉ v₅ e₁₀ v₁ e₃ v₂ e₉ v₅

iii) v₂

iv) v₅ v₂ v₃ v₄ v₄v₅

v) v₂ v₃ v₄ v₅ v₂v₄ v₃ v₂