Class CBSE Class 12 Mathematics Applications of Derivatives Q #1477
KNOWLEDGE BASED
APPLY
3 Marks 2025 AISSCE(Board Exam) SA
Amongst all pairs of positive integers with product as 289, find which of the two numbers add up to the least.
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Detailed Solution

Step 1: Find the factor pairs of 289

We need to find all pairs of positive integers whose product is 289. The factors of 289 are 1, 17, and 289. Therefore, the pairs are (1, 289) and (17, 17).

Step 2: Calculate the sum of each pair

Now, we calculate the sum of each pair:\nPair (1, 289): Sum = 1 + 289 = 290\nPair (17, 17): Sum = 17 + 17 = 34

Step 3: Determine the pair with the least sum

Comparing the sums, 34 is less than 290. Therefore, the pair (17, 17) has the least sum.

Step 4: State the two numbers

The two numbers that add up to the least sum are 17 and 17.

Final Answer: 17 and 17

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply their knowledge of factors and sums to find the pair of numbers that satisfy the given condition.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concept of factors and how they relate to the product of two numbers, as well as the concept of summation.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly relates to number theory concepts that are foundational and may appear in various contexts within the curriculum.

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