Question

If the operation $ \oplus $is defined by a$ \oplus $b=${a^2} + {b^2}$ for all real numbers ‘a’ and ‘b’
Then (2$ \oplus $3) $ \oplus $4 is
A. 181
B. 182
C. 184
D. 185

Answer 1

Hint: In this question, we will use the given logic to find the value of the expression given in the bracket. After this we assume the number obtained as ‘a’ and other number 4 as ‘b’ and again apply the logic to get the final answer.

Complete step-by-step answer:
We have given the logic a$ \oplus $b=${a^2} + {b^2}$ and with the help of this we are going to find the value of (2$ \oplus $3) $ \oplus $4.
So now first of all we have to solve (2$ \oplus $3).
So , let a= 2 and b=3
On applying the logic a$ \oplus $b=${a^2} + {b^2}$, we get:
(2$ \oplus $3) = ${2^2} + {3^2}$
Putting the value of ${2^2}$and ${3^2}$, we get:
(2$ \oplus $3) = 4+9 =13

Now again on putting the obtained value in given expression, we have:
(2$ \oplus $3) $ \oplus $4. = (13$ \oplus $3).
So, now we will find the value of (13$ \oplus $3)
Let a= 13 and b=4.
On applying the logic a$ \oplus $b=${a^2} + {b^2}$, we get:
(13$ \oplus $4) = ${13^2} + {4^2}$
Putting the value of ${13^2}$and ${4^2}$, we get:
(13$ \oplus $4) = 169+16 =185
And hence 185 will be the answer to the given question.

So, the correct answer is “Option D”.

Note: In this type of question carefully note down the meaning or logic of the symbol given and then use it to simplify the expression. Talking about simplification, you should know the rule of ‘BODMAS’. The priority order goes from left to right.
B- Bracket
O- Of
D- Division
M- Multiplication
A- Addition
S- Subtraction.