1

GATE CSE 2019

MCQ (Single Correct Answer)

+1

-0.33

Let G be an arbitrary group. Consider the following relations on G :

R1: ∀a,b ∈ G, aR

R2: ∀a,b ∈ G, aR

Which of the above is/are equivalence relation/relations?

R1: ∀a,b ∈ G, aR

_{1}b if and only if ∃g ∈ G such that a = g^{-1}bgR2: ∀a,b ∈ G, aR

_{2}b if and only if a = b^{-1}Which of the above is/are equivalence relation/relations?

2

GATE CSE 2019

MCQ (Single Correct Answer)

+1

-0.33

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

I. |A| = n2

II. |A| = $$\sum\limits_{k = 1}^n {k\left( {\matrix{ n \cr k \cr } } \right)} $$

Which of the above statements is/are TRUE?

I. |A| = n2

^{n–1}II. |A| = $$\sum\limits_{k = 1}^n {k\left( {\matrix{ n \cr k \cr } } \right)} $$

Which of the above statements is/are TRUE?

3

GATE CSE 2015 Set 3

MCQ (Single Correct Answer)

+1

-0.3

Suppose $$𝑈$$ is the power set of the set $$S = \left\{ {1,2,3,4,5,6,} \right\}$$. For any $$T \in U,$$ let $$\left| T \right|$$ denote the number of elements in $$𝑇$$ and $$T'$$ denote the complement of $$𝑇.$$ For any $$T,R \in U,$$ let $$T\backslash R$$ be the set of all elements in $$𝑇$$ which are not in $$𝑅.$$ Which one of the following is true?

4

GATE CSE 2015 Set 2

MCQ (Single Correct Answer)

+1

-0.3

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 other than $$1.$$ Which one of the following statements about $$𝑅$$ is true?

Questions Asked from Set Theory & Algebra (Marks 1)

Number in Brackets after Paper Indicates No. of Questions

GATE CSE 2020 (2)
GATE CSE 2019 (2)
GATE CSE 2015 Set 3 (1)
GATE CSE 2015 Set 2 (2)
GATE CSE 2015 Set 1 (1)
GATE CSE 2014 Set 3 (1)
GATE CSE 2013 (2)
GATE CSE 2010 (2)
GATE CSE 2009 (2)
GATE CSE 2008 (1)
GATE CSE 2007 (2)
GATE CSE 2006 (4)
GATE CSE 2005 (4)
GATE CSE 2004 (3)
GATE CSE 2001 (1)
GATE CSE 1999 (1)
GATE CSE 1998 (3)
GATE CSE 1997 (1)
GATE CSE 1996 (4)
GATE CSE 1995 (2)
GATE CSE 1993 (2)
GATE CSE 1987 (2)

GATE CSE Subjects

Theory of Computation

Operating Systems

Algorithms

Database Management System

Data Structures

Computer Networks

Software Engineering

Compiler Design

Web Technologies

General Aptitude

Discrete Mathematics

Programming Languages