Cartesian Product
If set A has 3 elements and set B has 4 elements, then the number of subsets of the Cartesian product A × B that contain exactly 2 ordered pairs equals which value?
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- cartesian product
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
66
The Cartesian product A × B consists of all ordered pairs with first entry from A and second from B, so it has 3×4 = 12 elements, a basic JEE Advanced set-construction fact. A subset containing exactly 2 ordered pairs is a choice of 2 elements from these 12, counted by the combination C(12, 2). Compute C(12, 2) = (12·11)/2 = 66. This converts a subset-size question into a straightforward combination, the standard archetype. Option 12 counts the elements of A × B, not pairs of them. Option 144 = 12^2 counts ordered selections with repetition, overcounting. Option 78 = C(13,2) uses the wrong product size. Hence the number of 2-element subsets is 66. Plausibility check: C(12,2) must be less than the total subsets 2^12 and equals the number of unordered pairs from 12 items; 66 is consistent with the handshake count for 12 objects, confirming the combinatorial reasoning.
This easy difficulty mathematics question is from the chapter sets, relations and functions, covering the topic of cartesian product. It appeared in the 2025 exam.
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