(D) Given the relation $3 a+2 b=27$ where $a, b \in N$ (natural numbers). $2 b = 27 - 3 a$ $b = \frac{3(9 - a)}{2}$ Since $b$ must be a natural number

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$\{(1, 12), (3, 9), (5, 6), (7, 3)\}$

(D) Given the relation $3 a+2 b=27$ where $a, b \in N$ (natural numbers). $2 b = 27 - 3 a$ $b = \frac{3(9 - a)}{2}$ Since $b$ must be a natural number,$3(9 - a)$ must be even and positive. For $a = 1, b = \frac{3(8)}{2} = 12$. For $a = 3, b = \frac{3(6)}{2} = 9$. For $a = 5, b = \frac{3(4)}{2} = 6$. For $a = 7, b = \frac{3(2)}{2} = 3$. For $a = 9, b = 0$ (not a natural number). Thus,$R = \{(1, 12), (3, 9), (5, 6), (7, 3)\}$.

Class 11 Mathematics Relations and Functions Relations

Easy

Let the relation $R$ be defined on the set of natural numbers $N$ by $a R b$ if $3 a+2 b=27$. Then $R$ is:

KCET 2023 All KCET

KCET 2022 All KCET

A
$\{(0, 13.5), (1, 12), (3, 9), (5, 6), (7, 3)\}$
B
$\{(1, 12), (3, 9), (5, 6), (7, 3), (9, 0)\}$
C
$\{(2, 1), (9, 3), (6, 5), (3, 7)\}$
D
$\{(1, 12), (3, 9), (5, 6), (7, 3)\}$

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Let the relation $R$ be defined on the set of natural numbers $N$ by $a R b$ if $3 a+2 b=27$. Then $R$ is:

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