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JNTU ONLINE EXAMINATIONS [Mid 2 - Mathematical Foundation of Computer Science]
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1. How many ways can we get a sum of 8 when two in distinguishable dice are rolled? 1. 9 2. 10 3. 11 4. 12 2. In a railway compartment 6 seats are vacant on a bench. In how many ways can 3 passebn\ngers can sit on their? 1. 120 2. 110 3. 100 4. 90 3. A person has to arrange 5 books on a shelf. In how many ways can he do so? 1. 100 2. 110 3. 115 4. 120 4. How many different 8-bit strings are there that begin and end with one? 1. 58 2. 60 3. 62 4. 64 5. In how many ways can be draw a king or a queen from ordinary deck of playing cards? 1. 4 2. 6 3. 8 4. 10 6. How many ways can we get a sum of 7 when two distinguishable dice are rolled? 1. 4 2. 5 3. 6 4. 7 7. How many ways can we draw a club or a diamond from a pack of cards? 1. 24 2. 26 3. 30 4. 32 8. In how many ways can be drawn an ace or a king from an arbitrary deck of playing cards? 1. 4 2. 5
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3. 6 4. 7 How many possible out comes are there when we roll a pair of dice, one red and one green? 1. 36 2. 38 3. 40 4. 42 In how many different ways one can answer all the questions of a true-false test consisting of 4 questions? 1. 14 2. 16 3. 18 4. 20 How many ways 16-bit strings are there containing exactly five 0's? 1. 4367 2. 4366 3. 4369 4. 4368 From 10 programmers in how many ways can 5 be selected when a particular programmer included every time? 1. 126 2. 128 3. 122 4. 124 Determine the value of n if nC4=nC3.
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1. 4 2. 5 3. 6 4. 7 14. Determine the value of n if nCn-2=10. 1. 4 2. 5 3. 6 4. 7 15. The number of combinations of n things taken all at a time is 1. 0 2. 1! 3. 2! 4. 3! 16. (n+1)!/n! is 1. n!
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2. n 3. n+1 4. (n+1)! How many words of 3 distinct letters can formed from the letters of the word LAND? 1. 20 2. 24 3. 28 4. 32 There are 4 black, 3 green, 5red balls. In how many ways can they be arranged in a row? 1. 27720 2. 27770 3. 27790 4. 27710 In how many ways can one choose two cards in succession from a deck of 52 cards, such that the first chosen card is not replaced? 1. 52 X 50 2. 52 X 52 3. % X 50 4. 52 X 51 In how many ways can a party of persons arrange themselves around a circular table? 1. 6! 2. 8! 3. 8! 4. 9! Find the number of 4-combinations of 5-objects with unlimited repetitions. 1. 70 2. 60 3. 50 4. 40 In how many ways can a cricket eleven be selected out of 14 players when the captain is always to be included? 1. C(12,10) 2. C(13,10) 3. C(14,10) 4. C(15,10) Find the number of 3-combinations of 5-objects with unlimited repetitions. 1. 25 2. 35 3. 45 4. 55 In how many can a person invite one or more of his seven friends to a party? 1. 125
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2. 126 3. 127 4. 128 Find the number of binary numbers with five one s and three zero s. 1. 53 2. 54 3. 55 4. 56 How many 7 digit numbers can be formed using digits 1,7,2,7,6,7,6? 1. 420 2. 422 3. 424 4. 444 How many 4-digits numbers can be formed by using the digits 2,4,6,8 when repetition of digits is allowed? 1. 250 2. 254 3. 256 4. 260 How many 2-digits even numbers can be formed by using the digits 1,3,4,6,8 when repetition of digits is allowed? 1. 9 2. 15 3. 18 4. 21 Find the number of subsets of A={2,2,2,3,3,5,11}. 1. 42 2. 46 3. 47 4. 48 5. How many different possible outcomes are possible by tossing 6 similar coins? 1. 7 2. 6 3. 5 4. 4 The product of r consecutive integers is divisible by 1. r! 2. r 3. 2r 4. r3 Find the 10th term independent of x in the expansion of (2x2-1/x)12. 1. 1780/x2 2. 1760/x2
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3. 1770/x2 4. 1790/x2 Find the 10th term independent of x in the expansion of (2x2+1/x)12. 1. 7910 2. 7930 3. 7920 4. 7940 Find the term containing a4 in the expansion of (a-2/a)8. 1. 112 2. 111 3. 110 4. 113 Find the term independent of x in the expansion of (x2+1/x)12. 1. 494 2. 495 3. 496 4. 497 Find the number of terms in the expansion of (2x+3y-5z)8. 1. 43 2. 44 3. 45 4. 46 In the expansion of (a2-1/a3)n the fifth term is 10a-4. Find the value of n. 1. 6 2. 7 3. 8 4. 9 Find the number of terms in the expansion of (x1+x2+x3+x4+x5)10. 1. 1010 2. 1011 3. 1110 4. 1001 Out of 1200 students at a college, 582 took A, ^@& took B, %$# took C, 217 took A and B, 307 took A and C, 250 took both C and A, 222 took all 3 courses. How many took none of the three? 1. 0 2. 1 3. 2 4. 3 Among the first 500 positive integers, determine the integers which are not divisible by 2, nor by 3, nor by 5. 1. 181 2. 182
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3. 183 4. 184 Associative law is 1. A U B = B U A 2. A = A 3. (A U B) U C = A U (B U C) 4. B = B AΠΦ= 1. Φ 2. A 3. A' 4. 2A AΠA= 1. Φ 2. A 3. A' 4. 2A 40 computer programmers interviewed for a job. 25 knew JAVA, 28 knew ORACLE, and 7 knew neither language. How many knew both languages? 1. 18 2. 20 3. 22 4. 24 AUΦ= 1. Φ 2. A 3. A' 4. 2A AUA= 1. Φ 2. A 3. A' 4. 2A AUB= 1. A Π B 2. A U A 3. B U A 4. B U B Commutative law is 1. A U B = B U A 2. A = A 3. (A U B) U C = A U (B U C) 4. B = B
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49. The coefficient of X25 in (+X3+X8)10 is 1. 10!/2!3!4! 2. 10!/3!2!4! 3. 10!/4!3!56! 4. 10!/5!3!4! 50. Find a generating function for ar=the number of non-negative integral solutions to e1
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+e2+&.+en=r where 0<=ei. 1. (1+X+X2+----+XK+----.)n 2. (1+X-X2+----+XK+----)n 3. (1-X-X2+----.+XK+----.)n 4. (1-X+X2+----+XK+----.)n 51. The coefficient of X9 in (+X3+X8)10 is 1. C(9,3) 2. C(10,4) 3. C(10,3) 4. C(11,4) 52. Recurrence relation is also called as 1. Difference equation 2. reverse equation 3. forward equation 4. backward equation 53. The recurrence relation an=an-1+5, with a1=2, the sequence is
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1. 6, 11,16----2. 7,12,17---3. 8,13,18---4. 9,14,19----54. The recurrence relation an=an-1+an-2, with a1=a2=1, the sequence is
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1. 1,2,3,5,8 2. 2,3,5,8,13 3. 1,1,2,3,5,8,13 4. 2,5,8,13 55. The recurrence relation an=an-1+5, with a=6, the sequence is 1. 6, 11,16---2. 7,12,17---3. 8,13,18---4. 9,14,19---56. Find a generating function for ar=the number of non-negative integral solutions to e1 +e2+&.+en=r where 0<=ei<=1. 1. (1-X)n 2. (1+X)n 3. Xn
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4. (X-1)n Find the coefficient of X10 in 1/(1-X)5. 1. C(14,10) 2. C(10,10) 3. C(11,11) 4. C(13,11) Find the coefficient of X10 in (1+X+X2+X3+&.)2 1. 10 2. 11 3. 12 4. 13 Find the coefficient of X10 in 1/(1-X3. 1. (10)(11)/2 2. (12)(10)/2 3. (12)(11)/2 4. (10)(10)/2 Find a generating function for ar=the number of ways of distributing similar balls into n
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numbered bones where each box is non empty. 1. (X2+X3+----)n 2. (X+X2+X3+----)n 3. (1+X3+X4+---)n 4. (X+X5+X6+----)n 61. Find a generating function for ar=the number of ways the sum r can be obtained when 2 distinguishable dice are tossed. 1. (X+X2+X3+X4+X5+ X6)2 2. (X2+X3+X4+X5+ X6)2 3. (X+X2+X4+X5+ X6)2 4. (X+X2+X3+X5+ X6)2 62. Find a generating function for ar=the number of ways the sum r can be obtained when 2 distinguishable dice are tossed and the first shows an even number and second shows an odd number. 1. (X2+X4+X6)(X+X3+ X5) 2. (X2+X4)(X+X3- X5) 3. (X2+X4-X6)(X+ X5) 4. (X2+X6)(X+X3+ X5) 63. Generating function of 1 is 1. 1/(1+X) 2. 1/(1-X) 3. 1/(1-2X) 4. 1/(1-3X) 64. Generating function of an is
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1. 1/(1-X) 2. 1/(1+X) 3. 1/(1-aX) 4. 1/(1+aX) 65. Generating function of C(k,n ) is 1. (1+X)k 2. (1+3X)k 3. (1+2X)k 4. (1-X)k 66. find the particular solution of the difference equation ar+2-2ar+1+ar=3r+5. (1/3)r3+r2 (1/2)r3+r2 (1/4)r3+r2 (1/5)r3+r2 the recurrence relation ar-ar-1-6ar-2=-30, a0=20, a1=-5.
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1. 2. 3. 4. 67. solve
1. ar=11.2r+3.5r
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3. ar=1.2r+4.3r+5 4. ar=11.(-2)r+4.3r+5
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68. find the particular solution of the difference equation ar-1-5ar+1+6ar=5r.
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1. (1/6)5r 2. (1/5)5r 3. (1/6)6r 4. (1/6)4r 69. Find the particular solution of the difference equation ar-1-5ar+1+6ar=5r 1. (1/6)5r 2. (1/5)5r 3. (1/6)6r 4. (1/6)4r 70. Generating function of (n+3)(n+2)(n) is 1. 6/(1-X)2 2. 6X/(1-X)4 3. 6/(1-X)4 4. 6/(1-3X)3 71. Solve an =an-1+n, where a0=2. 1. an=n(n+1)/2+2 2. an=n(n+1)/2-2
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3. an=n(n-1)/2+2 4. an=n(n+1)/3+2 72. Solve an =an-1+2n+1, where a0=1. 1. 2. 3. 4. 73. Solve
an=(n-1)2 an=(n+1)2 an=(2n+1)2 an=(n+2)2 an =an-1+3n2+3n+1, where a0=1.
1. an=(n-1)2 2. an=(n+1)3 3. an=(2n+1)3
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74. Generating function of n+1 is 1. 1/(1-X)2 2. 1/(1+X)2 3. 1/(1-2X)2 4. 1/(1-3X)2 75. Generating function of n is 1. 1/(1-X)2 2. X/(1-X)2 3. X/(1-2X)2 4. 1/(1-3X)2 76. Generating function of (n+2)(n+1) is 1. 1/(1-X)2 2. X/(1-X)2 3. 2/(1-X)2 4. 1/(1-3X)2 77. Generating function of n(n+1) is 1. 1/(1-X)2 2. X/(1-X)2 3. 2/(1-X)2 4. 2X/(1-X)2 78. Generating function of (n+3)(n+2)(n+1) is 1. 6/(1-X)2 2. 6X/(1-X)4 3. 6/(1-X)4 4. 6/(1-3X)3 79. Find the coefficient of X14 in (1+X+X2+&&.+X8)10.
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4. an=(n+2)3
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2. an=2an-1+2an-2
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1. C(24,14)-10C(14,5) 2. C(23,14)-C(14,5) 3. C(23,14)+10C(14,5) 4. C(23,14)-10C(14,5) Find the coefficient of X12 in (1-X)20. 1. C(20,10) 2. C(20,11) 3. C(20,12) 4. C(20,9) Find the coefficient of X10 in 1/(1+X)3. 1. C(14,10) 2. C(10,10) 3. C(11,11) 4. C(13,11) Find the coefficient of X10 in (X3+X4+&..)2. 1. 4 2. 5 3. 6 4. 7 Find the coefficient of X14 in (1+X+X2+X3)10. 1. C(23,9)+C(10,1)C(19,10)+C(10,2)C(15,6)-C(10,3)C(11,2) 2. C(23,9)-C(10,1)C(19,10)+C(10,2)C(15,6)-C(10,3)C(11,2) 3. C(23,9)-C(10,1)C(19,10)-C(10,2)C(15,6)-C(10,3)C(11,2) 4. C(23,9)-C(10,1)C(19,10)+C(10,2)C(15,6)+C(10,3)C(11,2) Find a recurrence relation for the number of ways to arrange flags on a flagpole n feet tall using 4 types of flags: red flags 2 feet high, or white, blue, and yellow flags each 1 foot high. 1. an =an-1+an-2 3. an=3an-1+an-2 4. an=an-1-an-2
85. Find a recurrence relation for the number of ways to make a pile of a chips using garnet, gold, red, white, and blue chips such that no two gold chips are together. 1. an =an-1+an-2 2. an=2an-1+2an-2 3. an=an-1+2an-2 4. an=4an-1+4an-2 86. Find a recurrence relation for the number of n-digit ternary sequences that have an even number of 0's.
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1. an =an-1+3n-1 2. an=2an-1+2an-2 3. an=an-1+2an-2 4. an=an-1-an-2 87. Suppose a coin is flipped until 2 heads appear and then the experiment stops. Find a recurrence relation for the number of experiments that end on the nth flip or sooner. 1. an =an-1+an-2 2. an=2an-1+(n-1) 3. an=an-1+(2n-1) 4. an=an-1-an-2
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88. Find the coefficient of X10 in 1/(1-X)5. 1. C(14,10) 2. C(10,10) 3. C(11,11) 4. C(13,11) 89. A regular graph of degree _____ has no lines. 1. 0 2. 1 3. 2 4. 3 90. Suppose G is a non-directed graph with 12 edges. If G has 6 vertices each of degree 3 and the rest have degree less than 3, what is the minimum number of vertices G can have? 1. 6 2. 9 3. 12 4. 15 91. The maximum degree of any vertex in a simple graph with n vertices is 1. n 2. n+1 3. n-1 4. n+2 92. What is the largest number of vertices in a graph with 35 edges if all vertices are degree atleast 3. 1. 9 2. 11 3. 8 4. 10 93. A graph G has 21 edges, 3 vertices of degree 4 and other vertices of degree 3. Find the number of vertices in G.
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1. 10 2. 11 3. 12 4. 13 The maximum number of edges in a simple graph with n vertices is 1. n(n-1)/2 2. (n-1)/2 3. n(n+1)/2 4. n(n-1) A graph which allows more than one edge to join a pair of vertices is called 1. Simple graph 2. multigraph 3. null graph 4. weighted graph A graph G with no self loops is called a 1. Simple graph 2. multigraph 3. null graph 4. weighted graph A graph having loops but no multiple edges called a 1. Simple graph 2. multigraph 3. pseudo graph 4. weighted graph A simple graph G, in which every pair of distinct vertices are adjacent is called 1. Simple graph 2. multigraph 3. null graph 4. complete graph Which data structure is used to implement DFS? 1. Stack 2. queue 3. list 4. heap A binary tree T has n leaves. The number of nodes of degree 2 in T is 1. n-1 2. n 3. n+1 4. 2n The process of accessing data stored in a tape is similar to manipulating data on a 1. stack 2. list 3. queue
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4. heap 102. Find the order of vertices of G are processed using a DFS algorithm beginning at vertex A. 1. ABEFDGCH 2. ABFEDGHC 3. ABEFGDHC 4. ABEFDGHC 103. Find the order of vertices of G are processed using a DFS algorithm beginning at vertex A.
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1. ABEFDGCH 2. ABFEDGHC 3. ABEFCGHD 4. ABEFDGHC DFS stands for 1. Depth First Search 2. Deep First Search 3. Dangling First Search 4. Dig First Search Which data structure is used to implement DFS? 1. Stack 2. queue 3. list 4. heap Pre-order is nothing but 1. Depth First Order 2. Breadth First order 3. Topological order 4. Linear order The vertices visit order in DFS is (starting point is at 1)
1. 12485367 2. 12485637 3. 12845637 4. 12458637 108. Which is used to find the connected component of graph? 1. BFS 2. DFS 3. Simple Graph 4. Tree 109. Suppose G is a non-directed graph with 12 edges. If G has 6 vertices each of degree 3 and the rest have degree less than 3, what is the minimum number of vertices G can
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have? 1. 6 2. 9 3. 12 4. 15 The process of accessing data stored in a tape is similar to manipulating data on a 1. stack 2. list 3. queue 4. heap While traversing a graph by breadth first search beginning at a start vertex A, 1. We process all neighbors of A and then all the neighbors of A and so on 2. We process each vertex N along a path P which begins at A; then a neighbor of a neighbor A and so on. 3. We process vertices randomly till all are visited. 4. We process vertices by alphabet A graph G has 21 edges, 3 vertices of degree 4 and other vertices of degree 3. Find the number of vertices in G. 1. 10 2. 11 3. 12 4. 13 A regular graph of degree _____ has no lines. 1. 0 2. 1 3. 2 4. 3 The vertices visit order in BFS is (starting point is at 1)
1. 12485367 2. 12485637 3. 12845637 4. 12345678 115. BFS stands for 1. Best First Search 2. Bid First Search 3. Breadth First Search 4. Bi First Search 116. Which data structure is used to implement DFS? 1. Stack 2. queue 3. list 4. heap
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117. Find the order of vertices of G are processed using a BFS algorithm beginning at vertex A. 1. ABEFDGCH 2. ABCDEFGH 3. ABEFGDHC 4. ABEFDGHC 118. Find the order of vertices of G are processed using a BFS algorithm beginning at vertex A.
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1. ABEFDGCH 2. ABFEDGHC 3. ABEFCGHD 4. ADCBFEGH What is the largest number of vertices in a graph with 35 edges if all vertices are degree atleast 3. 1. 9 2. 11 3. 8 4. 10 A graph G has 21 edges, 3 vertices of degree 4 and other vertices of degree 3. Find the number of vertices in G. 1. 10 2. 11 3. 12 4. 13 A graph having loops but no multiple edges called a 1. Simple graph 2. multigraph 3. pseudo graph 4. weighted graph A simple graph G, in which every pair of distinct vertices are adjacent is called 1. Simple graph 2. multigraph 3. null graph 4. complete graph The maximum degree of any vertex in a simple graph with n vertices is 1. n 2. n+1 3. n-1 4. n+2 How many possible out comes are there when we roll a pair of dice, one red and one
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green? 1. 36 2. 38 3. 40 4. 42 In how many different ways one can answer all the questions of a true-false test consisting of 4 questions? 1. 14 2. 16 3. 18 4. 20 A person has to arrange 5 books on a shelf. In how many ways can he do so? 1. 100 2. 110 3. 115 4. 120 How many different 8-bit strings are there that begin and end with one? 1. 58 2. 60 3. 62 4. 64 The value of n!/(n-1)! Is 1. n 2. n! 3. n*n 4. (n-1)! If G is a simple connected planar graph with |E|>1, then there is a vertex v of G such that, deg(v) 1. ^lt; 5 2. <=5 3. >5 4. >=5 Count the number of regions in the following graph
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1. 5 2. 7 3. 9 4. 11 131. Eular's rule is 1. v+e+r=2 2. v-e+r=2 3. v-e-r=2 4. v+e-r=2
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132. A planar graph has only ___ infinite region(s). 1. one 2. two 3. three 4. four 133. A plane connected graph in which each region has degree equal to or greater than 3 and each vertex has degree equal to or greater than 3 is called a ___ graph. 1. critical planar 2. polyhedral 3. homeomorphic 4. isomorphic 134. A graph G is said to be ___ if G is non planar but any subgraph obtained by removing by vertex of G is planar. 1. critical planar 2. polyhedral 3. homeomorphic 4. isomorphic 135. If a connected planar graph G has e edges and r regions, then 1. r<=2e/3 2. r<=2e/3e 3. r<=3e/2 4. r<=3/2e 136. If a connected planar graph G has e edges, v vertices and r regions, then 1. v+e+r=2 2. v-e+r=2 3. v-e-r=2 4. v+e-r=2 137. If a connected graph G has e edges and v vertices, then 1. 3v+e>6 2. 3v-e>6 3. 3v-e>=6 4. 3v+e>=6 138. A complete graph kn is planar if and only if 1. n<=5 2. n>=5 3. n>5 4. n<5 139. A complete bipartite graph km,n is planar if and only if 1. m>3 or n>3 2. m<3 or n>3 3. m<=3 or n<=3 4. m>=3 or n>3 b 140. A plane connected graph in which each region has degree equal to or greater than 3
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and each vertex has degree equal to or greater than 3 is called a ___ graph. 1. critical planar 2. polyhedral 3. homeomorphic 4. isomorphic A graph G is said to be ___ if G is non planar but any subgraph obtained by removing by vertex of G is planar. 1. critical planar 2. polyhedral 3. homeomorphic 4. isomorphic A graph G=(V,E) is called a _____ graph if its vertices V can be partitioned into two subsets V1 and V2 such that each edge of G connects a vertex of V1 to a vertex of V2. 1. simple 2. bipartite 3. complete bipartite 4. multi graph A graph G=(V,E) is called a _____ graph if its vertices V can be partitioned into two subsets V1 and V2 such that each vertex of V1 is connected to each vertex of V2. 1. simple 2. bipartite 3. complete bipartite 4. multi graph A planar graph has only ___ infinite region(s). 1. one 2. two 3. three 4. four A simple graph with n vertices must be connected if it has more than _____ edges. 1. (n-1)(n-2)/2 2. n(n-1)/2 3. (n-2)/2 4. n(n-2)/2 A non directed graph G has 8 edges. Find the number of vertices, if the degree of each vertex is 2. 1. 7 2. 8 3. 9 4. 10 What is the largest number of vertices in a graph with 35 edges if all vertices are degree atleast 3. 1. 9 2. 10
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3. 11 4. 12 A complete graph with n vertices will have ____ edges. 1. (n-1)(n-2)/2 2. n(n-1)/2 3. (n-2)/2 4. n(n-2)/2 If G is a simple graph with n vertices and k components, then G can have at most ___ edges. 1. (n-k)(n+k+1)/2 2. (n-k)(n-k+1)/2 3. (n+k)(n+k+1)/2 4. (n-k)(n-k-1)/2 Kuratowski's first graph is the non planar complete graph with the smallest number of vertices. The number of vertices is 1. 4 2. 5 3. 6 4. 7 If a graph G does not contain either Kuratowaki's two graphs or any graph isomorphic to them, the graph G is then 1. planar graph 2. non planar graph 3. Eular graph 4. Regular graph Circuit rank of a graph with n vertices and m edges is 1. m-n+1 2. m+n+1 3. m-n-1 4. m+n-1 Spanning tree of below graph 1. 2. 3. 4. The spanning tree of below graph is
1. 2. 3. 4. 155. Adjacency matrix representation of below graph is
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1. 0 1 1 1 1011 1101 1110 2. 0 1 1 1 1011 1110 1110 3. 0 1 1 1 1001 1101 1110 4. 0 1 0 1 1011 1110 1110 Two graphs G1 and G2 are called _____ graph if there is a one-to-one correspondence between their vertices and between their edges. 1. Homeomorphic 2. isomorphic 3. complete 4. planar A graph which allows more than one edge to join a pair of vertices is called a ____. 1. simple graph 2. null graph 3. multi graph 4. pseudograph If G is a connected graph with n vertices and m edges, a spanning tree of g must have ______ edges. 1. n 2. n+1 3. n+3 4. n-1 The number of edges that must be removed before a spanning tree is obtained with n vertices and m edges must be 1. m-n+1 2. m+n+1 3. m-n-1 4. m+n-1 How many ways can we get a sum of 6 or 9 when two distinguishable dice are rolled? 1. 6 2. 7 3. 12
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4. 15 The length of a Hamiltonian path in a connected graph of n vertices is 1. n-1 2. n 3. n+1 4. n/2 In a railway compartment 6 seats are vacant on a bench. In how many ways can 3 passengers can sit on their? 1. 120 2. 110 3. 100 4. 90 There are 10 busses plying between on a bench. In how many ways can 3 passengers can sit on them? 1. 120 2. 110 3. 100 4. 90 If there are 12 boys and 16 girls in a class find the number of ways of selecting one student as class representative? 1. 24 2. 26 3. 28 4. 30 A given connected graph is a Eular graph if and only if all vertices of G are of 1. same degree 2. even degree 3. odd degree 4. different degree An ____ through a graph is a path whose edge list contains each edge of the graph exactly once. 1. Eular path 2. Eular circuit 3. Eular graph 4. Eular region An ____ is a path through a graph, in which the initial vertex appears second time as the terminal vertex. 1. Eular path 2. Eular circuit 3. Eular graph 4. Eular region An ____ is a graph that possesses a Eular circuit. 1. Eular path
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2. Eular circuit 3. Eular graph 4. Eular region How many ways can we get a sum of 8 when two in distinguishable dice are rolled? 1. 9 2. 10 3. 11 4. 12 AUB= 1. A Π B 2. A U A 3. B U A 4. B U B Commutative law is 1. A U B = B U A 2. A = A 3. (A U B) U C = A U (B U C) 4. B = B 40 computer programmers interviewed for a job. 25 knew JAVA, 28 knew ORACLE, and 7 knew neither language. How many knew both languages? 1. 18 2. 20 3. 22 4. 24 AUΦ= 1. Φ 2. A 3. A' 4. 2A AUA= 1. Φ 2. A 3. A' 4. 2A The length of Hamilton in a connected graph of n vertices i 1. n-1 2. n 3. n+1 4. n/2 A circuit in a connected graph which includes every vertex of the graph is known as 1. Eular 2. Universal 3. Hamiltonian
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4. Clique If G is agraph within vertices, then a Hamiltonian cycle in G will contain exactly ___ edges. 1. n-1 2. n 3. n+1 4. n+2 The length of a Hamiltonian path in a connected graph of n vertices is 1. n-1 2. n 3. n+1 4. n+2 A circuit in a connected graph which includes every vertex of the graph is known as 1. Eular 2. Universal 3. Hamiltonian 4. Clique If a graph requires k different colors for its proper coloring then the chromatic number of the graph is 1. k/2 2. k-1 3. k 4. 1 The number of colors required to properly color the vertices of every planar graph is 1. 2 2. 3 3. 4 4. 5 The vertices of a planar graph with less than 30 edges is ____ colorable. 1. 1 2. 2 3. 3 4. 4 A simple connected planar graph with 17 edges and 10 vertices cannot be ____ colorable. 1. 1 2. 2 3. 3 4. 4 Every graph with a chromatic number of ___ is bipartite. 1. 1 2. 2 3. 3
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4. 4 The chromatic number of an isolated vertex is 1. one 2. two 3. three 4. four The Chromatic number of a graph having atleast one edge is atleast 1. one 2. two 3. three 4. four Every tree with ___ or more vertices is 2-chromatic 1. one 2. two 3. three 4. four Every _____ graph is 5-colorable. 1. simple 2. bipartite 3. planar 4. Eular The chromatic number of below graph is
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