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VITEEE 2021 Paper

Section: Mathematics

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Question : 67 of 80

Marks: +1, -0

The relation

R

defined on the set

A=\{1,2,3,4,5\}

R=\{(x, y):x^{2}-y^{2}| < 16\}

is given by

$\{(1,1),(2,1),(3,1),(4,1),(2,3)\}$
$\{(2,2),(3,2),(4,2),(2,4)\}$
$\{(3,3),(4,3),(5,4),(3,4)\}$
None of these

Solution:

We have

R=\{(x, y):|x^{2}-y^{2}|< 16\}

Let

x=1,|x^{2}-y^{2}| < 16 \Rightarrow |1-y^{2}| < 16

⇒

|y^{2}-1| < 16 \Rightarrow y=1,2,3,4

Let

x=2,|x^{2}-y^{2}| < 16 \Rightarrow |4-y^{2}| < 16

⇒

|y^{2}-4| < 16 \Rightarrow y=1,2,3,4

Let

x=3,|x^{2}-y^{2}| < 16 \Rightarrow |9-y^{2}| < 16

⇒

|y^{2}-9| < 16 \Rightarrow y=1,2,3,4

Let

x=4,|x^{2}-y^{2}| < 16 \Rightarrow |16-y^{2}| < 16

⇒

|y^{2}-16| < 6 \Rightarrow y=1,2,3,4,5

Let

x=5,|x^{2}-y^{2}| < 16 \Rightarrow |25-y^{2}|<16

⇒

|y^{2}-25| < 16 \Rightarrow y=4,5

∴

R=\{(1,1),(1,2),(1,3),

(1,4),(2,1),(2,2),(2,3),

(2,4),(3,1),(3,2),

(3,3),(3,4),(4,1),(4,2),

(4,3),(4,4),(4,5),(5,4),

(5,5)\} .

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