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 , where x is

Consider the set ∑* of all strings over the alphabet ∑ = {0, 1}. ∑* 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 numbers is divisible by 11111011?

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

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

Which of the above can cause a hazard?

Consider an array multiplier for multiplying two n bit numbers. If each gate in the circuit has a unit delay, the total delay of the multiplier is

Ram and Shyam have been asked to show that a certain problem Π is NP-complete. Ram shows a polynomial time reduction from the 3-SAT problem to Π, and Shyam shows a polynomial time reduction from Π to 3-SAT. Which of the following can be inferred from these reductions?

Nobody knows yet if P = NP. Consider the language L defined as follows:

Which of the following statements is true?

The regular expression 0*(10*)* denotes the same set as

If the strings of a language L can be effectively enumerated in lexicographic (i.e., alphabetic) order, which of the following statements is true?

Which of the following suffices to convert an arbitrary CFG to an LL(1) grammar?

Assume that the SLR parser for a grammar G has n₁ states and the LALR parser for G has n₂ states. The relationship between n₁ and n₂ is:

In a bottom-up evaluation of a syntax directed definition, inherited attributes can

Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that order into an initially empty binary search tree. The binary search tree uses the usual ordering on natural numbers. What is the in-order traversal sequence of the resultant tree?

Consider the following three claims

I. (n + k)m = Θ(nm), where k and m are constants
II. 2n+1 = O(2n)
III. 22n+1 = O(2n) 

Which of these claims are correct?

Consider the following graph

Among the following sequences:

(I) a b e g h f    (II) a b f e h g    (III) a b f h g e    (IV) a f g h b e 

Which are depth first traversals of the above graph?

The usual Θ(n²) implementation of Insertion Sort to sort an array uses linear search to identify the position where an element is to be inserted into the already sorted part of the array. If, instead, we use binary search to identify the position, the worst case running time will