Question

Which of the following is not a binary operation on $R$?

• A. $a\times b=ab$
• B. $a\times b=a-b$
• C. $a\times b=\sqrt{ab}$
• D. $a\times b=\sqrt{a^2+b^2}$

Answer 1

Answer: (C)

$a\times b=\sqrt{ab}$

When you will multiply, add , subtract, any two real number the resulting

number will be real number, so option $A$ and $B$ are binary operations.

Also if $a$ and $b$ are real number then $\sqrt{a^2+b^2}$ will be a real number, so option $D$ is also binary operation

Check option 'C', If sign of product of $a$ and $b$ will be negative, then $\sqrt{ab}$ will not be real number,

Hence it is not a binary operation

Therefore option $C$ is correct choice