Question:
Functions are defined for numbers A, B and C: \( @(A,B) \) = average of A and B; \( *(A,B) \) = product of A and B; \( /(A,B) \) = A divided by B.
The sum of A and B is given by
Functions are defined for numbers A, B and C: \( @(A,B) \) = average of A and B; \( *(A,B) \) = product of A and B; \( /(A,B) \) = A divided by B.
The sum of A and B is given by
The sum of A and B is given by
Show Hint
The average of A and B is half their sum, so doubling the average gives the sum.
Updated On: Nov 5, 2026
- \( *(@(A,B),2) \)
- \( /(@(A,B),2) \)
- \( @(*(A,B),2) \)
- \( @(/(A,B),2) \)
Show Solution
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The Correct Option is A
Solution and Explanation
Step 1: Recall the definitions:
\( @(A,B) = \frac{A+B}{2} \), \( *(A,B) = AB \), \( /(A,B) = \frac{A}{B} \).
Step 2: Evaluate each option:
(1) \( *(@(A,B),2) = \frac{A+B}{2}\times 2 = A + B \). This is the sum.
(2) \( /(@(A,B),2) = \frac{A+B}{2}\div 2 = \frac{A+B}{4} \). No.
(3) \( @(*(A,B),2) = \frac{AB + 2}{2} \). No.
(4) \( @(/(A,B),2) = \frac{A/B + 2}{2} \). No.
Final Answer:
The correct option is (1): \( *(@(A,B),2) \).
\( @(A,B) = \frac{A+B}{2} \), \( *(A,B) = AB \), \( /(A,B) = \frac{A}{B} \).
Step 2: Evaluate each option:
(1) \( *(@(A,B),2) = \frac{A+B}{2}\times 2 = A + B \). This is the sum.
(2) \( /(@(A,B),2) = \frac{A+B}{2}\div 2 = \frac{A+B}{4} \). No.
(3) \( @(*(A,B),2) = \frac{AB + 2}{2} \). No.
(4) \( @(/(A,B),2) = \frac{A/B + 2}{2} \). No.
Final Answer:
The correct option is (1): \( *(@(A,B),2) \).
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