GATE CSE 2003

Consider the following C function.

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

Assume the following C variable declaration
int *A [10], B[10][10];
Of the following expressions
I A[2]
II A[2][3]
III B[1]
IV B[2][3]
which will not give compile-time errors if used as left hand sides of assignment statements in a C program?

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

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?

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

Let T(n) be the number of different binary search trees on n distinct elements.
Then T(n)=\sum_{k=1}^{n}T(k-1)T(x),
where x is

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

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.

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

For a pipelined CPU with a single ALU, consider the following situations
1. The (j + 1)-th instruction uses the result of 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?