When Meena was asked, how many mangoes was she carrying in her basket, she replied $\left( -{{a}^{2}}b+3ab+{{b}^{2}} \right)$ with a = 2 and b = 3. How many were there in Meena’s basket?

Hint: This is a very simple problem here, we are given an equation $\left( -{{a}^{2}}b+3ab+{{b}^{2}} \right)$ and we have to find the value of this equation to find the answer. We are also given the values of the variables as a = 2 and b = 3. So we will simply put these values in the equation and find the value of it. The value obtained would be our required answer.

Complete step-by-step solution
We are given that Meena was carrying a basket and the number of mangos in her basket are given by the equation $\left( -{{a}^{2}}b+3ab+{{b}^{2}} \right)$,
Where a = 2 and b = 3,
Here we need to understand that the equation $\left( -{{a}^{2}}b+3ab+{{b}^{2}} \right)$ represents the number of mangoes in Meena’s basket,
We just need to find the number of mangoes at the particular values of a and b,
And we are given those particular values as 2 and 3 for a and b respectively,
So to find the number of mangoes in her basket we have to put the values of a and b in the equation $\left( -{{a}^{2}}b+3ab+{{b}^{2}} \right)$,
So putting a = 2 and b = 3 in this equation, we get
= $\left( -{{a}^{2}}b+3ab+{{b}^{2}} \right)$
= \[\left( -{{\left( 2 \right)}^{2}}\times 3+3\times 2\times 3+{{\left( 3 \right)}^{2}} \right)\]
= $\left( -4\times 3+18+9 \right)$
= $\left( -12+18+9 \right)$
=$ 15$
Hence the number of mangoes that were in Meena’s basket we get like 15.

Note: This was a very simple problem. The part where a student can commit a mistake is the calculation part so you need to be careful while doing calculations. Do not make the silly mistake of substituting a = 3 and b = 2. You can improve your calculation skills by solving more problems of this type or larger and lengthy problems. Try to solve these kinds of problems in a short time span to make your calculations faster.