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यदि (U) में (10) तत्व हैं, तो \(\mathcal {P}(U)\) में ऐसे members कितने हैं जो (U) के किसी निश्चित (4)-तत्वीय subset से disjoint हैं?

If (U) has (10) elements, how many members of \(\mathcal{P}(U)) are disjoint from a fixed (4)-element subset of (U)?

Explanation opens after your attempt
Correct Answer

C. (64)

Step 1

Concept

A member disjoint from the fixed (4)-element subset can be formed only from the remaining (6) elements. Therefore the number is \(2^6=64\).

Step 2

Why this answer is correct

The correct answer is C. (64). A member disjoint from the fixed (4)-element subset can be formed only from the remaining (6) elements. Therefore the number is \(2^6=64\).

Step 3

Exam Tip

Fixed (4)-element subset से disjoint member केवल शेष (6) तत्वों से बनेगा। इसलिए संख्या \(2^6=64\) है।

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यदि (U) में (10) तत्व हैं, तो \(\mathcal {P}(U)\) में ऐसे members कितने हैं जो (U) के किसी निश्चित (4)-तत्वीय subset से disjoint हैं? / If (U) has (10) elements, how many members of \(\mathcal{P}(U)) are disjoint from a fixed (4)-element subset of (U)?

Correct Answer: C. (64). Explanation: Fixed (4)-element subset से disjoint member केवल शेष (6) तत्वों से बनेगा। इसलिए संख्या \(2^6=64\) है। / A member disjoint from the fixed (4)-element subset can be formed only from the remaining (6) elements. Therefore the number is \(2^6=64\).

Which concept should I revise for this Mathematics MCQ?

A member disjoint from the fixed (4)-element subset can be formed only from the remaining (6) elements. Therefore the number is \(2^6=64\).

What exam hint can help solve this Mathematics question?

Fixed (4)-element subset से disjoint member केवल शेष (6) तत्वों से बनेगा। इसलिए संख्या \(2^6=64\) है।