Comprehension

Using the relation, answer the questions given below.
\(@(A,B) =\) average of A & B
\\((A,B) =\) product of A & B
\(×(A,B) =\) the result when A is divided by B.

Question: 1

The sum of $A$ \& $B$ is given by:

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Average $\times$ number of terms = sum of the terms.
Updated On: Aug 5, 2025
  • $\backslash(@(A,B), 2)$
  • $@( \backslash(A,B), 2)$
  • $@(x(A,B), 2)$
  • None of these
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The Correct Option is A

Solution and Explanation

Given: - $@(A,B)$ = average of $A$ and $B$ = $\dfrac{A+B}{2}$. - $\backslash(P,Q)$ = product of $P$ and $Q$. The sum $A+B$ = $2 \times$ average$(A,B)$ = $2 \times @(A,B)$. In given notation, multiplying $@(A,B)$ by $2$ means: \[ \backslash(@(A,B), 2) \] Thus (1) is correct. \[ \boxed{\backslash(@(A,B), 2)} \]
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Question: 2

The average of $A, B, C$ is given by:

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Break the operation into smaller steps matching each symbolic definition.
Updated On: Aug 5, 2025
  • $@(x(\backslash(@(A,B), 2), C), 3)$
  • $\backslash(x(\backslash(@(A,B)), C), 2)$
  • $x(@(\backslash(@(A,B), 2), C), 3)$
  • $@(\backslash(@(A,B), 2), C)$
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The Correct Option is C

Solution and Explanation

Step 1: $\backslash(@(A,B), 2)$ = product of $@(A,B)$ and 2 = $A+B$. Step 2: $@(\ A+B, \ C)$ = average of $A+B$ and $C$ = $\dfrac{(A+B) + C}{2} = \dfrac{A+B+C}{2}$. Step 3: To get average of $A,B,C$, divide sum by 3: Average = $\dfrac{A+B+C}{3}$, so divide the sum $(A+B+C)$ by 3: \[ x(@(\backslash(@(A,B), 2), C), 3) \] Thus (3) is correct. \[ \boxed{x(@(\backslash(@(A,B), 2), C), 3)} \]
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