CS and IT GATE 2015 Set-2 Questions with Answer

Ques 40 Mathematics

The larger of the two eigenvalues of the matrix

Ques 41 Mathematics

In a triangle PQR, PS is the angle bisector of ∠QPR and ∠QPS = 60°. What is the length of PS?

Ques 42 Mathematics

Let f(x) = x^-(1/3) and A denote the area of the region bounded by f(x) and the X-axis, when x varies from -1 to 1. Which of the following statements is/are TRUE?
I) f is continuous in [-1, 1]
II) f is not bounded in [-1, 1]
III) A is nonzero and finite

Ques 43 Mathematics

Perform the following operations on the matrix

Ques 44 Mathematics

The number of onto functions (surjective functions) from set X = {1, 2, 3, 4} to set Y = {a, b, c} is _______.

Ques 45 Mathematics

Let X and Y denote the sets containing 2 and 20 distinct objects respectively and F denote the set of all possible functions defined from X to Y. Let f be randomly chosen from F. The probability of f being one-to-one is _______.

Ques 46 Numerical Analysis

The secant method is used to find the root of an equation f(x) = 0. It is started from two distinct estimates x_a and x_b for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if f(x_b) is very small and then x_b is the solution. The procedure is given below. Observe that there is an expression which is missing and is marked by?. Which is the suitable expression that is to be put in place of? so that it follows all steps of the secant method?

Ques 47 Operating Systems

A system has 6 identical resources and N processes competing for them. Each process can request at most 2 resources. Which one of the following values of N could lead to a deadlock?

Ques 48 Operating Systems

Consider six memory partitions of sizes 200 KB, 400 KB, 600 KB, 500 KB, 300 KB and 250 KB, where KB refers to kilobyte. These partitions need to be allotted to four processes of sizes 357 KB, 210 KB, 468 KB and 491 KB in that order. If the best fit algorithm is used, which partitions are NOT allotted to any process?

Ques 49 Operating Systems

Consider a typical disk that rotates at 15000 rotations per minute (RPM) and has a transfer rate of 50 x 10⁶ bytes/sec. If the average seek time of the disk is twice the average rotational delay and the controller's transfer time is 10 times the disk transfer time, the average time (in milliseconds) to read or write a 512-byte sector of the disk is _______.

Ques 50 Programming and Data Structures

Suppose you are provided with the following function declaration in the C programming language.
int partition(int a, int n);
The function treats the first element of a as a pivot, and rearranges the array so that all elements less than or equal to the pivot is in the left part of the array, and all elements greater than the pivot is in the right part. In addition, it moves the pivot so that the pivot is the last element of the left part. The return value is the number of elements in the left part.
The following partially given function in the C programming language is used to find the kth smallest element in an array a of size n using the partition function. We assume k ≤ n.

Ques 51 Programming and Data Structures

Consider the C program below.

Ques 52 Software Engineering

Consider the basic COCOMO model where E is the effort applied in person-months, D is the development time in chronological months, KLOC is the estimated number of delivered lines of code (in thousands) and a_b, b_b, c_b, d_b have their usual meanings. The basic COCOMO equations are of the form.