1

GATE CSE 2015 Set 2

Numerical

+2

-0

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 ________.

Your input ____

2

GATE CSE 2015 Set 3

MCQ (Single Correct Answer)

+2

-0.6

Let $$R$$ be a relation on the set of ordered pairs of positive integers such that $$\left( {\left( {p,q} \right),\left( {r,s} \right)} \right) \in R$$ if and only if $$p - s = q - r.$$ Which one of the following is true about $$R$$?

3

GATE CSE 2014 Set 1

Numerical

+2

-0

Let S denote the set of all functions $$f:\,{\{ 0,\,1\} ^4}\, \to \,\{ 0,\,1\} $$. Denote by N the number of functions from S to the set {0, 1}. The value of $${\log _2}$$ $${\log _2}$$ N is___________________

Your input ____

4

GATE CSE 2014 Set 3

MCQ (Single Correct Answer)

+2

-0.6

Consider the set of all functions $$f:\left\{ {0,\,1,.....,2014} \right\} \to \left\{ {0,\,1,.....,2014} \right\}$$ such that $$f\left( {f\left( i \right)} \right) = i,\,\,\,$$ for all $$0 \le i \le 2014.$$ Consider the following statements:

$$P$$. For each such function it must be the case that for every $$i$$, $$f\left( i \right) = i$$

$$Q$$. For each such function it must be the case that for some $$i$$, $$f\left( i \right) = 1$$

$$R$$. Each such function must be onto.

$$P$$. For each such function it must be the case that for every $$i$$, $$f\left( i \right) = i$$

$$Q$$. For each such function it must be the case that for some $$i$$, $$f\left( i \right) = 1$$

$$R$$. Each such function must be onto.

Which one of the following id CORRECT?

Questions Asked from Set Theory & Algebra (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE CSE 2023 (1)
GATE CSE 2021 Set 1 (1)
GATE CSE 2019 (1)
GATE CSE 2018 (1)
GATE CSE 2016 Set 2 (2)
GATE CSE 2016 Set 1 (1)
GATE CSE 2015 Set 2 (2)
GATE CSE 2015 Set 3 (1)
GATE CSE 2014 Set 1 (1)
GATE CSE 2014 Set 3 (2)
GATE CSE 2014 Set 2 (1)
GATE CSE 2012 (1)
GATE CSE 2009 (1)
GATE CSE 2007 (4)
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GATE CSE 2005 (3)
GATE CSE 2004 (2)
GATE CSE 2002 (1)
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GATE CSE 1999 (1)
GATE CSE 1998 (3)
GATE CSE 1996 (3)
GATE CSE 1995 (1)
GATE CSE 1994 (1)
GATE CSE 1989 (1)
GATE CSE 1988 (1)

GATE CSE Subjects

Theory of Computation

Operating Systems

Algorithms

Database Management System

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Computer Networks

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Compiler Design

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General Aptitude

Discrete Mathematics

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