GATE CSE 2019

## GATE CSE

Consider a sequence of 14 elements: A = [-5, -10, 6, 3, -1, -2, 13, 4, -9, -1, 4, 12, -3, 0]. The subsequence sum $$S\le

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An array of 25 distinct elements is to be sorted using quicksort. Assume that the pivot element is chosen uniformly at r

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Consider the following statements:
I. The smallest element in a max-heap is always at a leaf node
II. The second larg

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There are n unsorted arrays: A1, A2, ..., An. Assume that n is odd. Each of A1, A2, ..., An contains n distinct elements

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Consider the grammar given below:
S → Aa
A → BD
B → b | ε
D → d | ε
Let a, b, d, and $ be indexed as follows:
Compute t

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Which one of the following kinds of derivation is used by LR parsers?

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Consider the augmented grammar given below :
S' → S
S → 〈L〉 | id
L → L,S | S
Let I0 = CLOSURE ({[S' → ●S]}). Th

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Which of the following protocol pairs can be used to send and retrieve e-mails (in that order)?

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The value of 351 mod 5 is_________.

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In an RSA cryptosystem, the value of the public modulus parameter n is 3007. If it is also known that $$\varphi $$(n) =

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Consider that 15 machines need to be connected in a LAN using 8-port Ethernet switches. Assume that these switches do no

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The chip select logic for a certain DRAM chip in a memory system design is shown below. Assume that the memory system ha

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A certain processor uses a fully associative cache of size 16 kB. The cache block size is 16 bytes. Assume that the main

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Let T be a full binary tree with 8 leaves. (A full binary tree has every level full). Suppose two leaves a and b of T ar

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Which one of the following statements is NOT correct about the B+ tree data structure used for creating an index of a re

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Consider the following two statements about database transaction schedules:
I. Strict two-phase locking protocol genera

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Consider the following relations P(X,Y,Z), Q(X,Y,T) and R(Y,V).
How many tuples will be returned by the following relat

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A relational database contains two tables Student and Performance as shown below:
The primary key of the Student table

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Let the set of functional dependencies F = {QR → S, R → P, S → Q} hold on a relation schema X = (PQRS). X is not in BCNF

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In 16-bit 2's complement representation, the decimal number -28 is :

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Which one of the following is NOT a valid identity?

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Consider Z = X - Y, where X, Y and Z are all in sign-magnitude form. X and Y are each represented in n bits. To avoid ov

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What is the minimum number of 2-input NOR gates required to implement a 4-variable function function expressed in sum-of

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Consider three 4-variable functions f1, f2 and f3, which are expressed in sum-of-minterms as
f1 = Σ(0, 2, 5, 8, 14),
f

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Compute $$\mathop {\lim }\limits_{x \to 3} {{{x^4} - 81} \over {2{x^2} - 5x - 3}}$$

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Two numbers are chosen independently and uniformly at random from the set {1, 2, ...., 13}. The probability (rounded off

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Let G be an arbitrary group. Consider the following relations on G :
R1: ∀a,b ∈ G, aR1b if and only if ∃g ∈ G such that

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Let X be a square matrix. Consider the following two statements on X.
I. X is invertible.
II. Determinant of X is non-z

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Let G be an undirected complete graph on n vertices, where n > 2. Then, the number of different Hamiltonian cycles in

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Let U = {1, 2 ,..., n}. Let A = {(x, X) | x ∈ X, X ⊆ U}. Consider the following two statements on |A|.
I. |A| = n2n–1
II

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Suppose Y is distributed uniformly in the open interval (1,6). The probability that the polynomial 3x2 + 6xY + 3Y + 6 ha

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Consider the first order predicate formula φ:
∀x[(∀z z|x ⇒ ((z = x) ∨ (z = 1))) ⇒ ∃w (w > x) ∧ (∀z z|w ⇒ ((w = z) ∨ (

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Consider three concurrent processes P1, P2 and P3 as shown below, which access a shared variable D that has been initial

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The following C program is executed on a Unix/Linux system:
#include < unistd.h >
int mai

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Assume that in a certain computer, the virtual addresses are 64 bits long and the physical addresses are 48 bits long. T

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Consider the following four processes with arrival times (in milliseconds) and their length of CPU bursts (in millisecon

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Consider the following C program :
#include < stdio.h >
int main () {
int arr [] = {1,2,3,4,5,6,7,8,

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Consider the following C program:
#include < stdio.h >
int jumble (int x, int y) {

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Consider the following C program:
#include < stdio.h >
int main()
{
int a[] = {2,

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If L is a regular language over Σ = {a,b}, which one of the following languages is NOT regular?

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For Σ = {a, b}, let us consider the regular language L = {x | x = a2+3k or x = b10+12k, k ≥ 0}. Which one of the followi

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## General Aptitude

The expenditure on the project _____ as follows; equipment Rs.20 lakhs, salaries Rs.12 lakhs, and contingency Rs.3 lakhs

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Ten freiends planned to share equally the cost of buying a gift for their teacher. When two of them decided not to contr

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A court is to a judge as _______ is to a teacher.

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The search engine's business model _____ around the fulcrum of trust.

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Two cars start at the same time from the same location and go in the same direction. The speed of the first car is 50 Km

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In a college, there are three student clubs. Sixty students are only in the Drama club, 80 students are only in the Danc

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The police arrested four criminals - P, Q, R and S. The criminals knew each other. They made the following statements:

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"A recent High Court judgement has sought to dispel the idea of begging as a disease — which leads to its stigmatization

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Three of the five students allocated to a hostel put in special requests to the warden. Given the floor plan of the vaca

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In the given diagram, teachers are represented in the triangle, researchers in the circle and administrators in the rect

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