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# MTH202 Current Final Term Papers Fall 2011 ( 03 Feb to 16 Feb 2012 )

MTH202 Current Final Term Papers Fall 2011 ( 03 Feb to 16 Feb 2012 )

Current Final Term Fall 2011 Papers, Feb 2012 Final Term Papers, Final Term Fall 2011 Papers, Solved Papers, Solved Past Papers, Solved MCQs

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### Replies to This Discussion

yar koi tu apna paper upload kare ka kia patteren tha.

Please Share your Current Papers Questions/Pattern here to help each other. Thanks

Sir kindly upload the current paper of MTH202 paper. My mth202 paper on Date:7-02-212.
i prepare myself for current paper patern.

bhai mera mth202 ka paper 16 feb ko h....

MTH202 - Final Term Fall 2011 Current Paper

Three horses A, B and C are in a race, probability that A wins is twice the probability of that the horse B wins, and probability that B wins is twice the probability of that the C wins. What is the probability that either A or B wins.
given, set A={children of both sexes}, B={at most one boy}, if a family have two children then show that the sets are dependent events.
A connected planar graph has 30 edges and 20 faces, what is the number of vertices of the graph.
Find adjacency matrix of the graph. (given graph was example of the handout with four vertices at page 301 of hand out.)
The given graph is not planar. give reasons.... (bipartite graph k3,3 was given, at page 316 of handout)
find the sum of the infinite series 1, squareroot of 2, 2,....
(keep sharing your experience, even if you remember a single question, best of luck)

my today paper.

Attachments:

✿Bîã✿ plz mujhy send kar do app k pas jo mth202 k past papers hain

Final Term From Feb-2012 to July-2009
Latest Solved MCQ + subjective from Final term Papers
MTH202- Discrete Mathematics
Resource Person Hina
Question No: 1 If a set contains exactly m distinct elements where m denotes some non negative integer
then the set is.
· Finite (Page 40)
· Infinite
· None of these
Question No: 2 In a directed graph of a Irreflexive relation, there should be
· Loop on a one point
· No loop at any point (Page 89)
· No point connected
Question No: 4 How many functions are there from a set with three elements to a set with two elements?
· 6
· 8
· 12
nm = 23 = 8
Question No: 5 Let n and d be integers and d ≠ 0. Then n is divisible by d or d divides n
If and only if
· n= k.d for some integer k (Page 179)
· n=d
· n.d=1
none of these
Question No: 6 Let f and g be the functions defined by
f(x)= 2x+3 & g(x)= 3x+2 then composition of f and g is
· 6x+6
· 5x+5
· 6x+7
fog
=
f (3x + 2)
= 2 (3x + 2) + 3
= 6 x + 4 + 3
= 6 x + 7
Question No: 7 Let f is defined recursively by
F(0)=3
F(n+1)=2f(n)+2
Then f(2)=
· 8
· 10
· 18
· 21
f (1) = 2 f (0) + 2 = 2 (3) + 2 = 6 + 2 = 8
f (2) = 2 f (1) + 2 = 2 (8) + 2 = 16 + 2 = 18
Question No: 9 If a pair of dice is thrown then the probability of getting a
total of 5 or 11 is
1
· 18
1
· 9
·
1
6
Outcomes with sum of 5 = (1, 4) (2, 3), (3, 2) , (4,1)
Outcomes with sum of 11 = (5, 6), (6, 5)
Total outcomes for 5 &11 = 6
Total outcome for 2 dice = 6 × 6 = 36
Probabilit
y =
6
=
1
36 6
Question No: 10 If a die is rolled then what is the probability that the
number is greater than 4
· 1
3
3
· 4
1
· 2
Number greater than 4 = 5, 6
Probability =
2
=
1
6 3
Question No: 11 What is the expectation of the number of heads when three fair coins are tossed?
· 1
· 1.34
· 2
· 1.5 (Page 277)
Question No: 13 The Hamiltonian circuit for the following graph is
· abcdefgh
· abefgha
· abcdefgha (Page 297)
Question No: 14 Let n and d be integers and d ≠ 0. Then n is divisible by d or d divides n
If and only if
· n= k.d for some integer k (Page 179)
· n=d
· n.d=1
· none of these
Question No: 16 The sum of two irrational number must be an irrational number
· False (Page 197)
· True
Question No: 17 The square root of every prime number is irrational
· True
· False
· Depends on the prime number given
Question No: 18 he greatest common divisor of 27 and 72 is
· 27
· 9
· 1
None of these
S o l u t i o n :
1.Divide 72 by
27:
2.Divide 27 by
18:
3.Divide 18 by
9:
This gives 72 = 27 · 2 + 18
This gives 27 = 18 · 1 + 9
This gives 18 = 9 · 2 + 0
Hence greatest common divisor (72, 27) = 9.
Question No: 19 If T is a full binary tree and has 5 internal vertices then the total vertices of T
are
· 11
· 12
· 13
None of the these
2k + 1 = 2 (5) + 1 = 10 +1 = 11
Question No: 20 Suppose that a connected planar simple graph has 30 edges. If a plane
drawing of this graph has 20 faces,
how many vertices does the graph have?
· 12 (Page 318)
· 13
· 14
Question No: 21 How many different ways can three of the letters of the word BYTES be
chosen if the first letter must be
B ?
· P(4,2)
· P(2,4)
· C(4,2)
None of these
Question No: 22 The value of 0! Is
· 0
· 1 (Page 160)
· Cannot be determined
Question No: 23 An arrangement of objects with the consideration of order is called
· Permutation (Page 219)
· Combination
· Selection
· None of these
Question No: 25 Among 200 people, 150 either swim or jog or both. If 85 swim and 60 swim and
jog, how many jog?
· 125 (Page 241)
· 225
· 85
· 25
Question No: 26 If a graph is a tree then
· it has 2 spanning trees
· it has only 1 spanning tree (Page 329)
· it has 4 spanning trees
· it has 5 spanning trees
Question No: 27 Euler formula for graphs is
· f = e-v
· f = e+v +2
· f = e-v-2
· f = e-v+2 (Page 317)
Question No: 28 The given graph is
· Simple graph
· Complete graph
· Bipartite graph
· Both (i) and (ii)
· Both (i) and (iii)
Question No: 29 An integer n is odd if and only if n = 2k + 1 for some integer k.
· True (Page 187)
· False
· Depends on the value of k
Question No: 30 If P( A ∩ B) = P( A) P( B) then the events A and B are called
· Independent (Page 272)
· Dependent
· Exhaustive
FINALTERM Spring 2010
MTH202- Discrete Mathematics
Question No: 5
The part of definition which can be expressed in terms of smaller versions of itself is called
· Base
· Restriction
· Recursion (page 159)
· Conclusion
Question No: 6
é N ù = 9
ê 6 ú
What is the smallest integer N such that
· 46
· 29
· 49
N = 6 × (9 −1) + 1
= 6 × 8 + 1 =
49
Question No: 8 What is the probability that a hand of five cards contains four cards of one
kind?
· 0.0018
· 1
2
· 0.0024 (page 253)
Question No: 9 A rule that assigns a numerical value to each outcome in a sample space is
called
· One to one function
· Conditional probability
· Random variable (Page 274)
Question No: 10
A walk that starts and ends at the same vertex is called
· Simple walk
· Circuit
· Closed walk (Page 292)
Question No: 11 The Hamiltonian circuit for the following graph is
· abcdefgh
· abefgha
· abcdefgha (Page 297)
Question No: 14
The square root of every prime number is irrational
· True
· False
· Depends on the prime number given
Question No: 15 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) (Page 207)
· gcd(a,r)=gcd(b,r)
· gcd(a,q)=gcd(q,r)
Question No: 16 The greatest common divisor of 27 and 72 is
· 27
· 9
· 1
· None of these
Question No: 24 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 (Page 329)
· May or may not contain same number of edges
Question No: 25 When 3k is even, then 3k+3k+3k is an odd.
· True
· False
Question No: 26 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 (Page 201)
· 0<r<d
· 0≤d<r
· None of these
Question No: 27 The value of
xùú for x = -3.01 is
Ø -3.01
Ø -3
Ø -2
Ø -1.99
−3.01
−3.01
= −4 + 0.99
= −4 + 0.99
= −4
= −4 +1 = −3
Question No: 29 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 (Page 187)
Question No: 30 ( Marks: 1 ) - Please choose one
If P( A ∩ B) = P( A) P( B) then the events A and B are called
· Independent (Page 272)
· Dependent
· Exhaustive
FINALTERM EXAMINATION
Fall 2009
MTH202- Discrete Mathematics
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
Symmetric and antisymmetric are
· Negative of each other
· Both are same
· Not negative of each other (Page 90)
Question No: 3 The statement p N q N q N p describes
· Commutative Law:
· Implication Laws:
· Exportation Law:
· Equivalence:
Question No: 4 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 The statement p Uq U (p U ~q) Uc describes
· Commutative Law:
· Implication Laws:
· Exportation Law:
Question No: 6 A circuit with one input and one output signal is called.
· NOT-gate (or inverter) (Page 31)
· OR- gate
· AND- gate
· None of these
Question No: 7
g(x)=x 2 -1
If
f(x)=2x+
1,
then fg(x)=
· x2 -1
· 2x2 -1
o 2x3 -1
fg ( x
) =
f ( x2 −1)
f ( x2 −1) = 2 ( x2 −1) +1
= 2x2 − 2 +1
= 2x2 − 2
Question No: 8 Let g be the functions defined by g(x)= 3x+2 then gog(x) =
9 x2 + 4 ·
· 6x+4
· 9x+8
gg ( x ) = g (3x + 2)
g (3x + 2) = 3(3x + 2) + 2
= 9x + 6 + 2
= 9x + 8
Question No: 9 How many integers from 1 through 1000 are neither
multiple of 3 nor multiple of 5?
· 333
· 467
· 1
· 2
· 3
· 2
· 533 (Page 245)
· 497
Question No: 10
é N ù = 9
ê 6 ú
What is the smallest integer N such that
· 46
· 29
· 49
N = 6 × (9 −1) + 1
= 6 × 8 + 1 =
49
Question No: 11 What is the probability of getting a number greater than 4 when a die is thrown?
Ø
1
3
Number greater than 4 = 5, 6
Probability =
2
=
1
6 3
Question No: 12 If A and B are two disjoint
(mutually exclusive) events then P(AUB) =
· P(A) + P(B) + P(ANB)
· P(A) + P(B) + P(AUB)
· P(A) + P(B) - P(ANB)
· P(A) + P(B) - P(ANB)
· P(A) + P(B) Page (240)
Question No: 13
If a die is thrown then the probability that the dots on the top are prime numbers or odd numbers is
· 1
· 1
2
Ø
2
3
Prime number or odd number =1,3,5
Total outcomes =6
Probability = 3/6=1/2
Question No: 14
The probability of getting 2 heads in two successive tosses of a balanced coin is
1
Ø 4
Ø
1
22
Ø 3
Question No: 15 The probability of getting a 5 when a die is thrown?
Ø
1
6
5
Ø 6
1
Ø 3
Question No: 16 If a coin is tossed then what is the probability that the number is 5
1
Ø 2
Ø 0
Ø 1
Wrong Question
Question No: 17 If A and B are two sets then The set of all elements that belong to both A and B , is
► A N B
► A U B (Page 42)
► A--B
► None of these
Question No: 18 What is the expectation of the number of heads when three fair coins are tossed?
► 1
► 1.34
► 2
► 1.5 (Page 277)
Question No: 19 ( Marks: 1 ) - Please choose one
If A, B and C are any three events, then
P(ANBNC) is equal to
· P(A) + P(B) + P(C)
· P(A) + P(B) + P(C)- P(AUB) - P (A UC) - P(B UC) + P(A UB UC) (Page 264)
· P(A) + P(B) + P(C) - P(ANB) - P (A NC) - P(B NC)
· P(A) + P(B) + P(C) + P(A NB NC)
Question No: 20 A rule that assigns a numerical value to each outcome in a sample space is called
· One to one function
· Conditional probability
· Random variable (Page 274)
Question No: 21 The power set of a set A is the set of all subsets of A, denoted P(A).
· False
· True (Page 68)
Question No: 22 A walk that starts and ends at the same vertex is called
· Simple walk
· Circuit
· Closed walk (Page 292)
Question No: 23 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 The square root of every prime number is irrational
· True
· False
· Depends on the prime number given
Question No: 25 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 (Page 202)
· False
· None of these
Question No: 26 If r is a positive integer then gcd(r,0)=
· r
· 0
· 1
· None of these
Question No: 27 Combinatorics is the mathematics of counting and arranging objects
· True (Page 209)
· False
· Cannot be determined
Question No: 28 A circuit that consist of a single vertex is called
· Trivial (Page 322)
· Tree
· Empty
Question No: 29 In the planar graph, the graph crossing number is
· 0 (Page 314)
· 1
· 2
· 3
Question No: 30 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 The value of 0! Is
· 0
· 1
· Cannot be determined
Question No: 32 If the transpose of any square matrix and that matrix are same then matrix is called
· Hermition Matrix
· Symmetric Matrix (Page 299)
Question No: 34 If A and B are two disjoint sets then which of the following must be true
· n(AUB) = n(A) + n(B) (Page 257)
· n(ANB) = n(A) + n(B) - n(ANB)
· n(ANB)= ø
· None of these
Question No: 35 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 (Page 329)
· May or may not contain same number of edges
Question No: 36 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 (Lecture 23)
Question No: 37 > n+3 for all integers n U3.
· True
· False
Question No: 38 Quotient –Remainder Theorem states that for any positive integer d, there exist
unique integer q and r such that and 0≤r<d.
· n=d.q+ r (Page 201)
· n=d.r+ q
· n=q.r+ d
· None of these
Question No: 39 Euler formula for graphs is
· f = e-v
· f = e+v +2
· f = e-v-2
· f = e-v+2 (Page 317)
Question No: 40 The degrees of {a, b, c, d, e} in the given graph is
a b
e
d c
· 2, 2, 3, 1, 1
· 2, 3, 1, 0, 1
· 0, 1, 2, 2, 0
· 2,3,1,2,0 Correct answer on Paper 307
FINALTERM
EXAMINATION Spring
2009
MTH202- Discrete Mathematics (Session
- 2)
Question No: 1 The negation of “Today is Friday” is
· Today is Saturday
· Today is not Friday
· Today is Thursday
Question No: 2 An arrangement of rows and columns that specifies the truth value of a compound
proposition for all possible truth values of its constituent propositions is called
· Truth Table (Page 6)
· Venn diagram
· False Table
· None of these
Question No: 4 Contra positive of given statement “If it is raining, I will take an umbrella” is
· I will not take an umbrella if it is not raining.
· I will take an umbrella if it is raining.
· It is not raining or I will take an umbrella.
· None of these.
Question No: 5 Let A= {1, 2, 3, 4} and R = {(1, 1), (2, 2), (3, 3),(4,4)} then
· R is symmetric.
· R is anti symmetric.
· R is transitive.
· R is reflexive.
· All given options are true
Question No: 6 A binary relation R is called Partial order relation if
It is Reflexive and transitive
It is symmetric and transitive
It is reflexive, symmetric and transitive
It is reflexive, anti symmetric and transitive
Question No: 7 How many functions are there from a set with three elements to a set with two elements?
Ø 6
Ø 8
Ø 12
nm = 23 = 8
Question No: 8 1,10,102 ,103 ,104 ,105 ,106 ,107 ,................
is
· Arithmetic series
· Geometric series
· Arithmetic sequence
· Geometric sequence
Question No: 9 x
for x = -2.01 is
· -2.01
· -3
· -2 (Page 249)
· -1.99
Question No: 10 If A and B are two disjoint (mutually exclusive) events then P(AÈB) =
Ø P(A) + P(B) + P(AÇB)
Ø P(A) + P(B) +
P(AUB) Ø P(A) + P(B) -
P(AÇB) Ø P(A) + P(B) -
P(AÇB) Ø P(A) + P(B)
Question No: 11 If a die is thrown then the probability that the dots on the top are prime numbers or odd numbers is
Ø
1
Ø
1
2
2
Ø 3
Question No: 12 If P( A ∩ B) = P( A) P( B) then the events A and B are called
· Independent (Page 272)
· Dependent
· Exhaustive
Question No: 13 A rule that assigns a numerical value to each outcome in a sample space is called
· One to one function
· Conditional probability
· Random variable (Page 274)
Question No: 14 The expectation of x is equal to
Ø Sum of all terms
Ø Sum of all terms divided by number of terms
Ø å xf (x) (Page 277)
Question No: 15 The degree sequence {a, b, c, d, e} of the given graph is
a b
e
d c
· 2, 2, 3, 1, 1
· 2, 3, 1, 0, 1 (Page 307)
· 0, 1, 2, 2, 0
· 2,3,1,2,0
Question No: 16 Which of the following graph is not possible?
· Graph with four vertices of degrees 1, 2, 3 and 4. (Page 287)
· Graph with four vertices of degrees 1, 2, 3 and 5.
· Graph with three vertices of degrees 1, 2 and 3.
· Graph with three vertices of degrees 1, 2 and 5.
Question No: 17 The graph given below
· Has Euler circuit
· Has Hamiltonian circuit
· Does not have Hamiltonian circuit (Page 297)
Question No: 18 Let n and d be integers and d ¹ 0. Then n is divisible by d or d divides n
If and only if
· n= k.d for some integer k (Page 179)
· n=d
· n.d=1
· none of these
Question No: 20 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 = 1. (Page 187)
· r = 1 or s = 0.
· r = 2 or s = 3.
· None of these
Question No: 21 The method of loop invariants is used to prove correctness of a loop with respect to certain pre and postconditions.
· True (Page 203)
· False
· None of these
Question No: 22 The greatest common divisor of 27 and 72 is
· 27
· 9
· 1
· None of these
S o l u t i o n :
1.Divide 72 by
27:
2.Divide 27 by
18:
3.Divide 18 by
9:
This gives 72 = 27 · 2 + 18
This gives 27 = 18 · 1 + 9
This gives 18 = 9 · 2 + 0
Hence greatest common divisor (72, 27) = 9.
Question No: 23 If a tree has 8 vertices then it has
·
6
e
dges
·
7
e
dges
·
9
e
dges
Question No: 24 Complete graph is planar if
·
n
=

n
>4
· n ≤ 4 (Page 315)
Question No: 25 The given graph is
Ø
· Simple graph
· Complete graph
· Bipartite graph
· Both (i) and (ii)
Both (i) and (iii)
Question No: 26 The value of 0! Is
· 0
· 1 (Page 160)
· Cannot be determined
Question No: 27 Two matrices are said to confirmable for multiplication if
· Both have same order
· Number of columns of 1st matrix is equal to number of rows in 2nd matrix (Page 300)
· Number of rows of 1st matrix is equal to number of columns in 2nd matrix
Question No: 28 The value of (-2)! Is
· 0
· 1
· Cannot be determined (Page 217)
Question No: 30 The number of k-combinations that can be chosen from a set of n elements can be
written as
· nCk (Page 225)
kCn
· nPk
· kPk
Question No: 31 If the order does not matter and repetition is allowed then total number of
ways for selecting k sample from n. is
· nk
· C(n+k-1,k) (Page 229)
· P(n,k)
· C(n,k)
Question No: 32 If the order matters and repetition is not allowed then total number of ways
for selecting k sample from n. is
· nk
· C(n+k-1,k)
· P(n,k)
· C(n,k) (Page 225)
Question No: 33 To find the number of unordered partitions, we have to count the ordered
partitions and then divide it by suitable number to erase the order in partitions
· True (Page 233)
· False
· None of these
Question No: 34 A tree diagram is a useful tool to list all the logical possibilities of a sequence
of events where each event can occur in a finite number of ways.
· True (Page 237)
· False
Question No: 36 What is the output state of an OR gate if the inputs are 0 and 1?
· 0
· 1
· 2
· 3
Question No: 39 ( Marks: 1 ) - Please choose one
n! >2n for all integers n ³4.
· True
· False
Question No: 40 +, −, ×, ÷
are
· Geometric expressions
· Arithmetic expressions
· Harmonic expressions
FINALTERM
EXAMINATION Fall
2009
MTH202- Discrete
Mathematics
Question No: 1 The negation of “Today is Friday” is
· Today is Saturday
· Today is not Friday
· Today is Thursday
Question No: 2 In method of proof by contradiction, we suppose the statement to be proved is
false.
· True (Page 193)
· False
Question No: 3 Whether the relation R on the set of all integers is reflexive, symmetric, anti
symmetric, or transitive,
where (x, y)∈R if and only if xy ≥1
· Anti symmetric
· Transitive
· Symmetric
· Both Symmetric and transitive
h tt p : // ww w . m at hs . uq . ed u .a u /c o u r s e s /M A T H 10 6 1 / w k b o o k s o l s /c h a p 10 / S 10_5_3 s o l
u t i o n . h tm Question No: 4 The inverse of given relation R = {(1,1),(1,2),(1,4),(3,4),
(4,1)} is
· {(1,1),(2,1),(4,1),(2,3)}
· {(1,1),(1,2),(4,1),( 4,3),(1,4)}
· {(1,1),(2,1),(4,1),(4,3),(1,4)}
Question No: 5 A circuit with one input and one output signal is called.
· NOT-gate (or inverter) (Page 31)
· OR- gate
· AND- gate
· None of these
Question No: 6 A sequence in which common difference of two consecutive terms is same is
called
· geometric mean
· harmonic sequence
· geometric sequence
· arithmetic progression (Page 146)
Question No: 8 How many integers from 1 through 100 must you pick in order to be sure of
getting one that is divisible b 5?
· 21
· 41
· 81 (Page 241)
· 56
Question No: 9 What is the probability that a randomly chosen positive two-digit number is a
multiple of 6?
· 0.5213
· 0.167 (Page 254)
· 0.123
Question No: 10 If a pair of dice is thrown then the probability of getting a total of 5 or 11 is

1
18

1
9

1
6
Outcomes with sum of 5 = (1, 4) (2, 3), (3, 2) , (4,1)
Outcomes with sum of 11 = (5, 6), (6, 5)
Total outcomes for 5 &11 = 6
Total outcome for 2 dice = 6 × 6 = 36
Probabilit
y =
6
=
1
36 6
Question No: 11
If a die is rolled then what is the probability that the number is greater than
4

1
3

3
4

1
2
Number greater than 4 = 5, 6
Probability =
2
=
1
6 3
Question No: 12
If a coin is tossed then what is the probability that the number is 5

1
2
· 0
· 1
Wrong Question
Question No: 13 If A and B are two sets then The set of all elements that
belong to both A and B , is
· A ∪ B
· A ∩ B (Page 42)
· A--B
· None of these
Question No: 14 If A and B are two sets then The set of all elements that belong to A but not B , is
· A ∪ B
· A ∩ B
· None of these
· A—B
Question No: 15
If A, B and C are any three events, then P(A∪B∪C) is equal to
· P(A) + P(B) + P(C)
· P(A) + P(B) + P(C)- P(AUB) - P (A UC) - P(B UC) + P(A UB UC) (Page 264)
· P(A) + P(B) + P(C) - P(A∩B) - P (A ∩C) - P(B ∩C)
· P(A) + P(B) + P(C) + P(A ∩B ∩C)
Question No: 16 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: 17 The contradiction proof of a statement pq involves
· Considering p and then try to reach q
· Considering ~q and then try to reach ~p
· Considering p and ~q and try to reach contradiction (Not sure)
· None of these
Question No: 18 How many ways are there to select a first prize winner a second prize winner, and a
third prize winner from 100 different people who have entered in a contest.
· None of these
· P(100,3)
· P(100,97)
· P(97,3)
Question No: 19 A vertex of degree 3 is called a
· Terminal vertex
· Internal vertex (Page 323)
Question No: 20 Suppose that a connected planar simple graph has 30 edges. If a plane drawing of
this graph has 20 faces, how many vertices does the graph have?
· 12 (Page 318)
· 13
· 14
Question No: 21 How many different ways can three of the letters of the word BYTES be chosen if the
first letter must be B ?
· P(4,2)
· P(2,4)
· C(4,2)
· None of these
Question No: 22 For the given pair of graphs whether it is
· Isomorphic
· Not isomorphic
Question No: 23 On the set of graphs the graph isomorphism is
· Isomorphic Invariant (Page 307)
· Equivalence relation
· Reflexive relation
Question No: 24 A matrix in which number of rows and columns are equal is called
· Rectangular Matrix
· Square Matrix (Page 289)
· Scalar Matrix
Question No: 25 If the transpose of any square matrix and that matrix are same then matrix is called
· Hermition Matrix
· Symmetric Matrix (Page 299)
Question No: 26 The number of k-combinations that can be chosen from a set of n elements can be
written as
· nCk (Page 225)
· kCn
· nPk
· kPk
Question No: 27 The value of C(n, 0) =
· 1 (Page 226)
· 0
· n
· None of these
Question No: 28 If the order does not matter and repetition is not allowed then total number of ways
for selecting k sample from n. is
· P(n,k)
· C(n,k)
· nk
· C(n+k-1,k) (Page 225)
Question No: 29 If A and B are two disjoint sets then which of the following must be true
· n(A∪B) = n(A) + n(B) (Page 257)
·
n(A

B) = n(A) + n(B) - n(A∩B)
·
n(A∪B)= ø
· None of these
Question No: 30 Among 200 people, 150 either swim or jog or both. If 85 swim and 60 swim and jog,
how many jog?
· 125 (Page 241)
· 225
· 85
· 25
Question No: 31 If two sets are disjoint, then P∩Q is
· ∅
· P
· Q
·
P

Q
Question No: 32 Every connected tree
· does not have spanning tree
· may or may not have spanning tree
· has a spanning tree (Page 329)
Question No: 33 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 (Lecture 23)
· False
Question No: 34 When 3k is even, then 3k+3k+3k is an odd.
· True
· False
Question No: 35 5n -1 is divisible by 4 for all positive integer values of n.
· True
· False
Question No: 36 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 (Page 201)
· 0<r<d
· 0≤d<r
· None of these
Question No: 37 The given graph is
· Simple graph
· Complete graph
· Bipartite graph
· Both (i) and (ii)
· Both (i) and (iii)
Question No: 38 An integer n is even if and only if n = 2k for some integer k.
· True (Page 187)
· False
· Depends on the value of k
Question No: 39 The word "algorithm" refers to a step-by-step method for performing some action.
· True (Page 201)
· False
· None of these
Question No: 40 The adjacency matrix for the given graph is
0 1 1 0 0
1 0 0 1 0
► 1 0 0 1 1
0 0 1 0 1
1 0 0 1 0
0 1 1 0 1
1 0 0 0 0
► 1 0 0 1 1
0 0 1 0 1
1 0 1 1 0
0 1 0 0 1
1 0 0 0 0
► 1 0 0 1 0
0 0 1 0 1
0 0 1 1 0
► None of these
FINALTERM EXAMINATION Fall
2008
MTH202- Discrete Mathematics (Session - 3)
Question No: 1 When 5k is even, then 5k+5k+5k is odd.
· True
· False
Question No: 2 An arrangement of objects without the consideration of order is called
· Combination
· Selection
· None of these
· Permutation
Question No: 3 In the following graph
v1 v4 How many simple paths are there from to
· 2
· 3
· 4
Question No: 4 Changing rows of matrix into columns is called
· Symmetric Matrix
· Transpose of Matrix (Page 229)
Question No: 5 The list of the degrees of the vertices of graph in non increasing order is called
· Isomorphic Invariant
· Degree Sequence (Page 307)
· Order of Graph
Question No: 6 A vertex of degree greater than 1 in a tree is called a
· Branch vertex (Page 323)
· Terminal vertex
· Ancestor
Question No: 7 The word "algorithm" refers to a step-by-step method for performing some action
· True (Page 201)
· False
· None of these
Question No: 8 The sum of two irrational number must be an irrational number
· True
· False (Page 197)
Question No: 9 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 = 1. (Page 187)
· r = 1 or s = 0.
· r = 2 or s = 3.
· None of these
Question No: 10 An integer n is even if, and only if, n = 2k for some integer k.
· True (Page 187)
· False
· Depends on the value of k
Question No: 11 For any two sets A and B, A – (A – B) =
Ø A Ç B Ø
A È B Ø A –
B
Ø None of these
Question No: 12 A walk that starts and ends at the same vertex is called
· Simple walk
· Circuit
· Closed walk (Page 292)
Question No: 14 Two distinct edges with the same set of end points are called
· Isolated
· Incident
· Parallel (Page 284)
Question No: 15
The probability of getting 2 heads in two successive tosses of a balanced coin is
1
Ø 4
Ø
1
22
Ø 3
· 2
· 3
· 2
Question No: 16 What is the probability of getting a number greater than 4 when a die is thrown?
1
· 1
3
Number greater than 4 = 5, 6
Probability =
2
=
1
6 3
Question No: 17 If two relations are reflexive then their composition is
· Antisymmetric
· Reflexive
· Irreflexive
· Symmetric
Question No: 19 Select the correct one
· A proof by contradiction is based on the fact that a statement can be true and false at the same
time.
· A proof by contraposition is based on the logical equivalence between a statement and its
· The method of loop invariants is used to prove correctness of a loop without any conditions.
· None of the given choices
Question No: 20 According to Demorgan’s law
ØØ
Correct
Ø
Ø

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