     Question Answers

# If ${a^b} = 4 - ab$ and ${b^a} = 1$, where a and are b positive integers, find a.${\text{A}}{\text{. 0}} \\ {\text{B}}{\text{. 1}} \\ {\text{C}}{\text{. 2}} \\ {\text{D}}{\text{. 3}} \\$  Hint- A number of the form ${b^a}$ can be equal to one only if either b = 1 or a = 0.
In this question we have been given ${a^b} = 4 - ab$ and ${b^a} = 1$
And we know that ${b^a}$ can be equal to one only if either $b = 1$ or $a = 0$.
But we are given that $a$ and are $b$ positive integers
So, $a \ne 0$ $\Rightarrow b = 1$
Now if we put $b = 1$ in the equation ${a^b} = 4 - ab$
We get,
${a^1} = 4 - a\left( 1 \right)$
$\Rightarrow 2a = 4$
So, $a = 2$
Here the correct answer is option (C).
Note- In these types of questions, the most important part is the domain of our variables, most of us miss this point and get struck as they give two answers. So, all the given constraints should be taken into consideration while solving the question.
View Notes
Biology Root Words Starting with Ab or Abs  Positive and Normative Economics  CBSE Class 8 Maths Chapter 8 - Comparing Quantities Formulas  Difference Between Gram positive and Gram negative Bacteria  CBSE Class 8 Maths Chapter 12 - Exponents and Powers Formulas  Multiplication and Division of Integers  BA Full Form  CBSE Class 8 Maths Chapter 9 - Algebraic Expressions and Identities Formulas  CBSE Class 8 Maths Chapter 13 - Direct and Inverse Proportions Formulas  CBSE Class 8 Maths Chapter 7 - Cubes and Cube Roots Formulas  