Let ‘*’ be a binary operation on N defined by a*b=a-b+ab2, then find 4*5

The correct option is 99.

To find the value of $4*5$, we need to use the definition of the binary operation $*$ given in the problem.

The binary operation is defined for any two natural numbers $a$ and $b$ as:
$$a*b=a-b+a{b}^2$$

Here, we want to evaluate $4*5$. By comparing $4*5$ with $a*b$, we substitute $a=4$ and $b=5$ into the formula.

Let us perform the calculation step-by-step:
1. Identify the terms:
    • $a=4$
    • $b=5$
2. Substitute these values into the expression $a-b+a{b}^2$:
$$4*5=4-5+4\cdot \left(5^2\right)$$
3. First, calculate the exponent part, $5^2$:
$$5^2=25$$
4. Substitute this value back into the expression:
$$4*5=4-5+4\cdot 25$$
5. Next, perform the multiplication:
$$4\cdot 25=100$$
6. Now, substitute this result and simplify the addition and subtraction from left to right:
$$4*5=4-5+100$$
$$4*5=-1+100$$
$$4*5=99$$

Therefore, the value of $4*5$ is $99$.