GATE-CS-2003

Question 1

Consider the following C function. 

C

float f(float x, int y)
{
  float p, s; int i;
  for (s=1, p=1, i=1; i < y; i ++)
  {
    p*= x/i;
    s+=p;
  }
  return s;
}  

For large values of y, the return value of the function f best approximates

• x^y

• e^x

• ln(1 + x)

• x^x

Question 2

Assume the following C variable declaration 

C

 int *A [10], B[10][10];  

Of the following expressions :

1. A[2] 
2. A[2][3] 
3. B[1]
4. B[2][3] 

which will not give compile-time errors if used as left hand sides of assignment statements in a C program?

• I, II, and IV only

• II, III, and IV only

• II and IV only

• IV only

Question 3

Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = 1/2, the values of P(A | B) and P(B | A) respectively are

• 1/4, 1/2
• 1/2, 1/14
• 1/2, 1
• 1, 1/2

Question 4

Let A be a sequence of 8 distinct integers sorted in ascending order. How many distinct pairs of sequences, B and C are there such that (i) each is sorted in ascending order, (ii) B has 5 and C has 3 elements, and (iii) the result of merging B and C gives A?

• 256
  

• 56
  

• 30
  

• 2
  

Question 5

n couples are invited to a party with the condition that every husband should be accompanied by his wife. However, a wife need not be accompanied by her husband. The number of different gatherings possible at the party is

• A
• B
• C
• D

Question 6

Let T(n) be the number of different binary search trees on n distinct elements. Then , where x is

• n-k+1
• n-k
• n-k-1
• n-k-2

Question 7

Consider the set ∑* of all strings over the alphabet ∑ = {0, 1}. ∑* with the concatenation operator for strings

• does not form a group
• forms a non-commutative group
• does not have a right identity element
• forms a group if the empty string is removed from ∑*

Question 8

Let G be an arbitrary graph with n nodes and k components. If a vertex is removed from G, the number of components in the resultant graph must necessarily lie between

• k and n
• k - 1 and k + 1
• k - 1 and n - 1
• k + 1 and n - k

Question 9

Assuming all numbers are in 2\'s complement representation, which of the following numbers is divisible by 11111011?

• 11100111
• 11100100
• 11010111
• 11011011

Question 10

For a pipelined CPU with a single ALU, consider the following situations

1. The j + 1-st instruction uses the result of the j-th instruction
    as an operand
2. The execution of a conditional jump instruction
3. The j-th and j + 1-st instructions require the ALU at the same 
   time

Which of the above can cause a hazard ?

• 1 and 2 only
• 2 and 3 only
• 3 only
• All of above