GATE CSE 2013 | Set Theory & Algebra Question 35 | Discrete Mathematics

GATE CSE 2013

MCQ (Single Correct Answer)

-0.3

Which one of the following functions is continuous at $$x = 3$$?

$$f\left( x \right) = \left\{ {\matrix{ {2,} & {if} & {x = 3} \cr {x - 1} & {if} & {x > 3} \cr {{{x + 3} \over 3},} & {if} & {x < 3} \cr } } \right.$$

$$f\left( x \right) = \left\{ {\matrix{ {4,} & {if} & {x = 3} \cr {8 - x} & {if} & {x \ne 3} \cr } } \right.$$

$$f\left( x \right) = \left\{ {\matrix{ {x + 3,} & {if} & {x \le 3} \cr {x - 4} & {if} & {x > 3} \cr } } \right.$$

$$f\left( x \right) = \matrix{ {{1 \over {{x^3} - 27}},} & {if} & {x \ne 3} \cr } $$

GATE CSE 2010

MCQ (Single Correct Answer)

-0.3

Consider the set $$S = \left\{ {1,\,\omega ,\,{\omega ^2}} \right\},$$ where $$\omega $$ and $${{\omega ^2}}$$, are cube roots of unity. If $$ * $$ denotes the multiplication operation, the structure $$\left\{ {S,\, * } \right\}$$ forms

a group

a ring

an integral domain

a field

GATE CSE 2010

MCQ (Single Correct Answer)

-0.3

What is the possible number of reflexive relations on a set $$5$$ elements?

2¹⁰

2¹⁵

2²⁰

2²⁵

GATE CSE 2009

MCQ (Single Correct Answer)

-0.3

consider the binary relation $$R = \left\{ {\left( {x,y} \right),\,\left( {x,z} \right),\,\left( {z,x} \right),\,\left( {z,y} \right)} \right\}$$ on the set $$\left\{ {x,\,y,\,z} \right\}$$. which one of the following is TRUE?

$$R$$ is symmetric but $$NOT$$ antisymmetric

$$R$$ is NOT symmetric but antisymmetric

$$R$$ is both symmetric and antisymmetric.

$$R$$ is neither symmetric nor antisymmetric.

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