Consider the binary operation * on a defined by x * y = 1 + 12x + xy, ∀ x, y ∈ Q, then 2 * 3 equals

The correct option is 31.

To find the value of $2*3$, we use the definition of the binary operation $*$ given in the problem statement.
The binary operation is defined for any rational numbers $x$ and $y$ in $Q$ as:
$x*y=1+12x+xy$

To evaluate $2*3$, we substitute $x=2$ and $y=3$ into the formula:
$2*3=1+12\left(2\right)+\left(2\right)\left(3\right)$

Now, perform the multiplications:
$12\times 2=24$
$2\times 3=6$

Substitute these values back into the equation:
$2*3=1+24+6$

Finally, add the numbers together:
$2*3=31$

Therefore, the result of the binary operation $2*3$ is 31.