GATE CS — Computer Science & IT

GATE CS 2014 Set 1 — Question 20

Numerical answer 1 mark Discrete Mathematics 2014

The maximum number of edges in a bipartite graph on 12 vertices is ______.

GATE CS 2014 Set 3 — Question 13

Multiple choice 1 mark Discrete Mathematics 2014

If \(G\) is a forest with \(n\) vertices and \(k\) connected components, how many edges does \(G\) have?

GATE CS 2015 Set 2 — Question 25

Multiple choice 1 mark Discrete Mathematics 2015

Let \(R\) be the relation on the set of positive integers such that \(aRb\) if and only if \(a\) and \(b\) are distinct and have a common divisor…

GATE CS 2005 — Question 42

Multiple choice 2 marks Discrete Mathematics 2005

Let \(R\) and \(S\) be any two equivalence relations on a non-empty set \(A\). Which one of the following statements is TRUE?

GATE CS 2018 — Question 40

Multiple choice 2 marks Discrete Mathematics 2018

Let \(\mathbb{N}\) be the set of natural numbers. Consider the following sets.P: Set of rational numbers (positive and negative)Q: Set of functions from \(\{0, 1\}\) to \(\mathbb{N}\)R: Set of functions from \(\mathbb{N}\) to \(\{0, 1\}\)S: Set of finite subsets of \(\mathbb{N}\)Which of the sets above are countable?

GATE CS 2015 Set 3 — Question 22

Numerical answer 1 mark Discrete Mathematics 2015

The cardinality of the power set of \(\{0, 1, 2, \ldots, 10\}\) is ______.

GATE CS 2020 — Question 7

Numerical answer 1 mark Digital Logic 2020

A multiplexer is placed between a group of 32 registers and an accumulator to regulate data movement such that at any given point in time the content of…

GATE CS 2019 — Question 11

Multiple choice 1 mark Digital Logic 2019

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 overflow, the representation of \(Z\)…

GATE CS 2018 — Question 39

Numerical answer 2 marks Digital Logic 2018

Consider the minterm list form of a Boolean function \(F\) given below.\(F(P,Q,R,S) = \sum m(0,\,2,\,5,\,7,\,9,\,11) + d(3,\,8,\,10,\,12,\,14)\)Here, \(m\) denotes a minterm and \(d\) denotes a don't care term. The number of essential…

GATE CS 2017 Set 2 — Question 5

Multiple choice 1 mark Digital Logic 2017

Consider the Boolean operator \(\#\) with the following properties:\(x \# 0 = x\),   \(x \# 1 = \overline{x}\),   \(x \# x = 0\)   and   \(x \# \overline{x} = 1\).Then \(x \# y\) is equivalent to: