Select the term from the options that has the same relation as given below.

Appeared in: ESIC Nursing Officer -2019 (Shift -1)

Explanation

The question requires applying the rules defined in the image to the given options.
The rule for the '@' symbol is C @ D = √(C² + D²), which is derived from the Pythagorean theorem.
Applying this rule to the correct option: 3 @ 4 = √(3² + 4²) = √(9 + 16) = √25 = 5.
The result of the calculation (5) matches the value given in the option, making it the correct statement.

Option A: According to the rule A $ B = A² + B², the calculation is 7$24 = 7² + 24² = 49 + 576 = 625. The option incorrectly states the result is 25.
Option B: Using the rule C @ D = √(C² + D²), the calculation is 4@5 = √(4² + 5²) = √(16 + 25) = √41. The option incorrectly states the result is 9.
Option C: Following the rule A $ B = A² + B², the calculation is 5$12 = 5² + 12² = 25 + 144 = 169. The option incorrectly states the result is 13.

Visual 1: Diagram. A right-angled triangle with its two shorter sides labeled '3' and '4', and the longest side (hypotenuse) labeled '5'. This visually represents the Pythagorean triplet (3, 4, 5) and explains the logic behind the '@' operation in the correct answer.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Logical Reasoning: Applying given symbolic operations to find the correct equation as background academic context rather than a clinical decision trigger.
This question tests logical and mathematical reasoning, skills that are essential for nurses in various aspects of their job, such as calculating drug dosages, interpreting lab results, and making critical decisions under pressure.
While not a direct clinical question, the ability to follow a set of rules and perform accurate calculations is a fundamental competency in nursing.
What if the rule for '@' was C @ D = C + D? Then option B (4@5 = 9) would have been correct, as 4 + 5 = 9.

How to Approach the Question

Step 1: Carefully analyze the image to understand the rules assigned to each symbol. Write them down clearly: A $ B = A² + B² and C @ D = √(C² + D²).
Step 2: Treat each option as a separate problem to be verified.
Step 3: For each option, identify the numbers and the symbol ($ or @) used.
Step 4: Apply the corresponding rule from Step 1 and perform the mathematical calculation.
Step 5: Compare your calculated result with the result given in the option.
Step 6: The option where the calculated result matches the given result is the correct answer.

Concept Tested & Keywords

Concept Tested: Logical Reasoning: Applying given symbolic operations to find the correct equation.
Stem keywords: symbolic operations, mathematical reasoning, logical deduction
Lead-in keywords: Select the term, same relation
Negative lead-in flag: false

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Practise the full ESIC Nursing Officer -2019 (Shift -1)

Attempt every question from this paper in a timed mock, then review the full solution for each one.