GATE CSE 2003

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 approximates
A
x^{y}
B
e^{x}
C
ln(1+x)
D
x^{x}
C Programming   Loop
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?
A
I, II, and IV only
B
II, III, and IV only
C
II and IV only
D
IV only
C Programming   Array and Pointer
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
A
1/4,1/2
B
1/2, 1/14
C
1/2, 1
D
1, 1/2
Discrete Mathematics   Probability Theory
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?
A
2
B
30
C
56
D
256
Discrete Mathematics   Combination
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
\binom{2n}{n}*2^{n}
B
3^{n}
C
\frac{(2n)!}{2^{n}}
D
\binom{2n}{n}
Discrete Mathematics   Combination
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
A
n-k+1
B
n-k
C
n-k-1
D
n-k-2
Data Structure   Binary Search Tree
Question 7
Consider the set \Sigma ^{*} of all strings over the alphabet \Sigma ={0,1}. \Sigma ^{*} with the concatenation operator for strings
A
does not form a group
B
forms a non-commutative group
C
does not have a right identity element
D
forms a group if the empty string is removed from \Sigma ^{*}
Discrete Mathematics   Group Theory
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.
A
k and n
B
k-1 and k+1
C
k-1 and n-1
D
k+1 and n-k
Discrete Mathematics   Graph Theory
Question 9
Assuming all numbers are in 2's complement representation, which of the following number is divisible by 11111011?
A
11100111
B
11100100
C
11010111
D
11011011
Digital Logic   Number System
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?
A
1 and 2 only
B
2 and 3 only
C
3 only
D
All the three
Computer Organization   Pipeline Processor
There are 10 questions to complete.

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