Q. In the set of real numbers $R$ which of the following is a not binary operation

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A

$a * b =\frac{a}{b+2}$

B

$a * b =\sqrt{a^{2}+b^{2}}$

C

$a * b =\frac{a+2 b}{a^{2}+b^{2}+1}$

D

$a * b=3 a-2 b$

Solution:

For every $a, b \in R, 3 a-2 b \in R$ (b) (c) are also b.o.
$\therefore a * b =\frac{a}{b+2}$ not a b.o. because $b$ can be $-2$. is a binary operation

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