Gate IT 2008

Question 71

A binary tree with n > 1 nodes has n₁, n₂ and n₃ nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors.
Starting with the above tree, while there remains a node v of degree two in the tree, add an edge between the two neighbors of v and then remove v from the tree. How many edges will remain at the end of the process?

• 2 * n₁ - 3
• n₂ + 2 * n₁ - 2
• n₃ - n₂
• n₂ + n₁ - 2

Question 72

A CFG G is given with the following productions where S is the start symbol, A is a non-terminal and a and b are terminals.
S→aS∣A
A→aAb∣bAa∣ϵ
Which of the following strings is generated by the grammar above?

• aabbaba
• aabaaba
• abababb
• aabbaab

Question 73

A CFG G is given with the following productions where S is the start symbol, A is a non-terminal and a and b are terminals.
S→aS∣A
A→aAb∣bAa∣ϵ
For the correct answer in Q75, how many steps are required to derive the string and how many parse trees are there?

• 6 and 1
• 6 and 2
• 7 and 2
• 4 and 2

Question 74

Consider a computer with a 4-ways set-associative mapped cache of the following characteristics: a total of 1 MB of main memory, a word size of 1 byte, a block size of 128 words and a cache size of 8 KB. The number of bits in the TAG, SET and WORD fields, respectively are:

• 7, 6, 7
• 8, 5, 7
• 8, 6, 6
• 9, 4, 7

Question 75

Consider a computer with a 4-ways set-associative mapped cache of the following character­istics: a total of 1 MB of main memory, a word size of 1 byte, a block size of 128 words and a cache size of 8 KB. While accessing the memory location 0C795H by the CPU, the contents of the TAG field of the corresponding cache line is

• 000011000
• 110001111
• 00011000
• 110010101

Question 76

Consider the code fragment written in JAVA below : 

Java

void f (int n)
{ 
  if (n <=1)  {
   System.out.print(n);
  }
  else {
   f (n/2);
   System.out.print(n%2);
  }
}

What does f(173) print?

• 010110101

• 010101101

• 10110101

• 10101101