1.  The power set of the set { φ} is 
a.  {φ} 
b.  { φ, { φ}} 
c.  {0} 
d.  {0, φ, { φ}} 
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Answer: (b).{ φ, { φ}})

2.  The number of bit strings of length eight that will either start with a 1 bit or end with two bits 00 shall be 
a.  32 
b.  64 
c.  128 
d.  160 
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Answer: (a).32)

3.  In which tree, for every node the height of its left subtree and right subtree differ almost by one ? 
a.  Binary search tree 
b.  AVL tree 
c.  Threaded Binary Tree 
d.  Complete Binary Tree 
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Answer: (b).AVL tree)

4.  Suppose that someone starts with a chain letter. Each person who receives the letter is asked to send it on to 4 other people. Some people do this, while some do not send any letter. How many people have seen the letter, including the first person, if no one receives more than one letter and if the chain letter ends after there have been 100 people who read it but did not send it out ? Also find how many people sent out the letter ? 
a.  122 & 22 
b.  111 & 11 
c.  133 & 33 
d.  144 & 44 
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Answer: (c).133 & 33)

5.  The maximum number of keys stored in a Btree of order m and depth d is 
a.  m^d + 1  1 
b.  m^d+1  1/(m  1) 
c.  (m  1) (m^d + 1  1) 
d.  m^d1 
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Answer: (d).m^d1)

6.  Which of the following is the most powerful parring method ? 
a.  LL(I) 
b.  Canonical LR 
c.  SLR 
d.  LALR 
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Answer: (b).Canonical LR)

7.  The graph K3,4 has 
a.  3 edges 
b.  4 edges 
c.  7 edges 
d.  12 edges 
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Answer: (d).12 edges)

8.  The time complexities of some standard graph algorithms are given. Match each algorithm with its time complexity ? (n and m are no. of nodes and edges respectively)
a. Bellman Ford algorithm 1. O (m log n) b. Kruskals algorithm 2. O (n3) c. Floyd Warshall algorithm 3. O(mn) d. Topological sorting 4. O(n + m) Codes : a b c d 
a.  3 1 2 4 
b.  2 4 3 1 
c.  3 4 1 2 
d.  2 1 3 4 
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Answer: (a).3 1 2 4)

9.  Let V1 = 2I – J + K and V2 = I + J – K, then the angle between V1 & V2 and a vector perpendicular to both V1 & V2 shall be : 
a.  90 degrees and (–2I + J – 3K) 
b.  60 degrees and (2I + J + 3K) 
c.  90 degrees and (2I + J – 3K) 
d.  90 degrees and (–2I – J + 3K) 
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Answer: (d).90 degrees and (–2I – J + 3K))

10.  Let T(n) be the function defined by T(n) = 1 and T(n) = 2T (n/2) + n, which of the following is TRUE ? 
a.  T(n) = O(n) 
b.  T(n) = O(log2n) 
c.  T(n) = O(n) 
d.  T(n) = O(n2) 
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Answer: (c).T(n) = O(n))
