Question 1 |

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 approximatesx^{y} | |

e^{x} | |

ln(1+x) | |

x^{x} |

Question 1 Explanation:

Question 2 |

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?

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?

I, II, and IV only | |

II, III, and IV only | |

II and IV only | |

IV only |

Question 2 Explanation:

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 3 Explanation:

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?

(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?

2 | |

30 | |

56 | |

256 |

Question 4 Explanation:

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

\binom{2n}{n}*2^{n} | |

3^{n} | |

\frac{(2n)!}{2^{n}}
| |

\binom{2n}{n} |

Question 5 Explanation:

Question 6 |

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

Then T(n)=\sum_{k=1}^{n}T(k-1)T(x),

where x is

n-k+1 | |

n-k | |

n-k-1 | |

n-k-2 |

Question 6 Explanation:

Question 7 |

Consider the set \Sigma ^{*} of all strings over the alphabet \Sigma ={0,1}. \Sigma ^{*} 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 \Sigma ^{*} |

Question 7 Explanation:

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 8 Explanation:

Question 9 |

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

11100111 | |

11100100 | |

11010111 | |

11011011 |

Question 9 Explanation:

Question 10 |

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?

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?

1 and 2 only | |

2 and 3 only | |

3 only | |

All the three |

Question 10 Explanation:

There are 10 questions to complete.