JUNE 2013 - Paper 3

11:  
The golden ratio φ and its conjugate φ both satisfy the equation
 
A.

x3-x-1=0

B.

x3+x-1=0

C.

x2-x-1=0

D.

x2+x-1=0

 
 

Option: C

Explanation :

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φ and its conjugate φ both satisfy the equation
 
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12:  

The solution of recurrence relation, 
T(n) = 2T(floor (√n) ) + log n  is 

A.
 O(n log log logn)
B.
 O(n log logn)
C.

O(log log n)

D.

O(log n log logn)

 
 

Option: B

Explanation :

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√n) ) + log n  is 

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13:  

In any n-element heap, the number of nodes of height h is

A.

 less then equal to [n/2h]

B.

greater then [n/2h

C.

greater then [n / 2h+1 

D.

less then equal to  [n / 2h+1 

 
 

Option: C

Explanation :

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14:  

A data file of 1,00,000 , characters contains only the characters g-1, with the frequencies as indicated in table :

 

g

h

i

j

k

l

Frequency in Thousand

45

13

12

16

9

5


using the variable-length code by Huffman codes, the file can be encoded with
 
A.
 2,52,000 bits
B.
2,64,000 bits
C.
2,46,000 bits
D.

 2,24,000 bits

 
 

Option: D

Explanation :

Question is incomplete . In this we need an additional field as  follows
               

 

g

h

i

j

k

l

Variable-length codeword

0

101

100

111

1101

1100


Now according to Huffman coding algorithem
                A data file of 100,000 characters contains only the characters g-l , with the frequencies indicated. If we assign each character a 3-bit codeword, we can encode the le in 300,000 bits. Using the variablelength code shown, we can encode the fi le in only 224,000 bits.
 
 

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15:  

A vertex cover of an undirected graph G(V, E) is a subset V1 ⊆ V vertices such that  

A.

 Each pair of vertices in V, is connected by an edge

B.

If (u, v)   E then u  ε  V1 and v  ⊂ V1

C.

If (u, v)   E  then u  V1 or  v ∈ V1

D.

All pairs of vertices in V1 are not connected by an edge

 
 

Option: C

Explanation :

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⊆ V vertices such that  

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