List of top Questions asked in GATE CS

Consider the following ANSI C function: 

int SomeFunction(int x, int y) 
{
if ((x == 1) || (y == 1)) return 1; 
if (x == y) return x; 
if (x > y) return SomeFunction(x - y, y); 
if (y > x) return SomeFunction(x, y - x); 
} 

The value returned by SomeFunction(15, 255) is \(\underline{\hspace{2cm}}\).

Consider the string abbccddeee. Each letter in the string must be assigned a binary code satisfying the following properties:
1. For any two letters, the code assigned to one letter must not be a prefix of the code assigned to the other letter. 
2. For any two letters of the same frequency, the letter which occurs earlier in the dictionary order is assigned a code whose length is at most the length of the code assigned to the other letter. 
Among the set of all binary code assignments which satisfy the above two properties, what is the minimum length of the encoded string?

In a directed acyclic graph with source vertex \( s \), the quality-score of a directed path is the product of the weights of the edges on the path. 
For a vertex \( v \neq s \), the quality-score of \( v \) is the maximum among the quality-scores of all paths from \( s \) to \( v \). The quality-score of \( s \) is assumed to be 1. 
The sum of the quality-scores of all the vertices in the graph is \(\underline{\hspace{2cm}}\). 

A polygon is convex if, for every pair of points inside the polygon, the line segment joining them lies completely inside or on the polygon. Which one of the following is NOT a convex polygon? 

A circular sheet of paper is folded along the lines in the directions shown. The paper, after being punched in the final folded state as shown and unfolded in the reverse order of folding, will look like \(\underline{\hspace{2cm}}\) 

Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost. 
The formula for Profit Percentage is: 
\[ \text{Profit \%} = \frac{\text{Selling Price} - \text{Cost}}{\text{Cost}} \times 100 \] The discount on item Q, as a percentage of its marked price, is: 

Consider the following ANSI C code segment: 

z = x + 3 + y->f1 + y->f2; 
for (i = 0; i < 200; i = i + 2){ 
	if (z > i) { 
		p = p + x + 3; 
		q = q + y->f1; 
	} else { 
		p = p + y->f2; 
		q = q + x + 3; 
	} 
}  

Assume that the variable \(y\) points to a struct (allocated on the heap) containing two fields \(f1\) and \(f2\), and the local variables \(x, y, z, p, q,\) and \(i\) are allotted registers. Common sub-expression elimination (CSE) optimization is applied on the code. The number of addition and dereference operations (of the form \(y \rightarrow f1\) or \(y \rightarrow f2\)) in the optimized code, respectively, are: 
 

The relation scheme given below is used to store information about the employees of a company, where empId is the key and deptId indicates the department to which the employee is assigned. Each employee is assigned to exactly one department. 
\[ \text{emp}(\text{empId},\ \text{name},\ \text{gender},\ \text{salary},\ \text{deptId}) \] 

Consider the following SQL query: 

select deptId, count(*) 
from emp 
where gender = "female" and salary > (select avg(salary) from emp) 
group by deptId; 

The above query gives, for each department in the company, the number of female employees whose salary is greater than the average salary of

Consider the following ANSI C program: 

#include <stdio.h> 
#include <stdlib.h> 
struct Node{ 
	int value; 
	struct Node *next; }; 
int main(){ 
	struct Node *boxE, *head, *boxN; int index = 0; 
	boxE = head = (struct Node *) malloc(sizeof(struct Node)); 
	head->value = index; 
	for (index = 1; index <= 3; index++){ 
		boxN = (struct Node *) malloc(sizeof(struct Node)); 
		boxE->next = boxN; 
		boxN->value = index; 
		boxE = boxN; } 
	for (index = 0; index <= 3; index++) { 
		printf("Value at index %d is %d\n", index, head->value); 
		head = head->next; 
		printf("Value at index %d is %d\n", index+1, head->value); } } 

Which one of the statements below is correct about the program?