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MTH202 Current Final Term Papers Fall 2011 ( 03 Feb to 16 Feb 2012 )
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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:
· Reductio ad absurdum
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
· Additive Inverse
· 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
=
4·
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
· Additive Inverse
· 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)
· Adjoint of Matrix
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
contradiction.(Page 198)
· 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
plz send on my id onlyyzain@gmail.com
mth202 solved papers
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