Question

Choose the right answer from the following if $ A = 1 $ and $ B = 0 $ , what is the value of $ A.A + B $ ?
(A) $ 1 $
(B) $ - 1 $
(C) $ 0 $
(D) $ 2 $

Answer 1

Hint: In the given question, we are required to simplify an algebraic expression provided to us in the problem. We are also given the value of variables in the problem itself. We have to simply substitute the values of variables in the algebraic expression and find the final answer. We can use arithmetic rules and properties in order to simplify the given expression.

Complete step-by-step answer:
So, the expression given to us in the question is $ A.A + B $ .
Also, we are given the value of variables as $ A = 1 $ and $ B = 0 $ .
We would use the BODMAS rule in order to simplify the expression. BODMAS is an acronym for the sequence in which the mathematical operations are to be done. In BODMAS, B stands for brackets, O stands for of, D stands for division, M stands for multiplication, A stands for addition, and S stands for subtraction.
So, we simply substitute the values of variables in the algebraic expression. Hence, we get,
 $ A.A + B = 1 \times 1 + 0 $
Now, we know that multiplying a number by itself means squaring the number. So, we get,
 $ \Rightarrow A.A + B = {1^2} + 0 $
Now, we know that the value of any power of one is one itself. So, we get,
 $ \Rightarrow A.A + B = 1 + 0 $
We also know that the sum of zero with any number gives us that number itself. So, we get,
 $ \Rightarrow A.A + B = 1 $
Hence, the value of expression $ A.A + B $ is $ 1 $ if $ A = 1 $ and $ B = 0 $ .
So, option (A) is the correct answer.
So, the correct answer is “Option A”.

Note: The given problem deals with algebraic expression. We must know how to substitute the values of variables in the mathematical expression so as to solve the problem. Care should be taken while doing the calculation steps. Algebraic identities and simplification rules like BODMAS may also be used as and when required as they help simplify complex and tedious tasks. Nowadays, another acronym PEMDAS is also coming into use for describing the sequence of arithmetic operations.