GATECS2003
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
x^y  
e^x  
ln(1 + x)  
x^x 
Discuss it
Question 1 Explanation:
See question 1 of http://www.geeksforgeeks.org/datastructuresandalgorithmsset5/
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 compiletime 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

Discuss it
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 
Discuss it
Question 3 Explanation:
Conditional probability measures the probability of an event given that another event has occurred.
P(A  B) is Probability of A given B has occurred which is 1.
P(B  A) is probability of B given that A has occurred which is 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?
2  
30  
56  
256 
Discuss it
Question 4 Explanation:
Suppose you have selected 3 elements from 8 in 8C3 ways, the remaining elements are treated as another array and merging both the arrays gives the sorted array. Here, you can select either 3 or 5.
=> 8C3 = 8C5 = 8!/(3!5!) = 7*8 = 56 Ways.
This solution is contributed by Anil Saikrishna Devarasetty
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 
Discuss it
Question 5 Explanation:
There are three options for every couple.
1) Nobody goes to gathering 2) Wife alone goes 2) Both goSince there are n couples, total possible ways of gathering are 3^{n}
Question 6 
nk+1  
nk  
nk1  
nk2 
Discuss it
Question 6 Explanation:
The idea is to make a key root, put (k1) keys in one subtree and remaining nk keys in other subtree.
A Binary Search Tree (BST) is a tree in which all the nodes follow the belowmentioned properties −
 The left subtree of a node has a key less than or equal to its parent node's key.
 The right subtree of a node has a key greater than to its parent node's key.
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 noncommutative group  
does not have a right identity element  
forms a group if the empty string is removed from ∑* 
Discuss it
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 
Discuss it
Question 8 Explanation:
Minimum: The removed vertex itself is a separate connected component. So removal of a vertex creates k1 components.
Maximum: It may be possible that the removed vertex disconnects all components. For example the removed vertex is center of a star. So removal creates n1 components.
Question 9 
Assuming all numbers are in 2's complement representation, which of the following numbers is divisible by 11111011?
11100111  
11100100  
11010111  
11011011 
Discuss it
Question 9 Explanation:
Since most significant bit is 1, all numbers are negative.
2's complement of divisor (11111011) = 1's complement + 1 = 00000100 + 1 = 00000101
So the given number is 5
The decimal value of option A is 25
Question 10 
For a pipelined CPU with a single ALU, consider the following situations
1. The j + 1st instruction uses the result of the jth instruction as an operand 2. The execution of a conditional jump instruction 3. The jth and j + 1st instructions require the ALU at the same timeWhich of the above can cause a hazard ?
1 and 2 only  
2 and 3 only  
3 only  
All of above 
Discuss it
Question 10 Explanation:
Case 1: Is of data dependency .this can’t be safe with single ALU so read after write.
Case 2:Conditional jumps are always hazardous they create conditional dependency in pipeline.
Case 3:This is write after read problem or concurrency dependency so hazardous
All the three are hazardous
So (D) is correct option.
There are 90 questions to complete.