यदि \(A=\{a,b,c,d,e\}\) है, तो (\mathcal{P}(A)) में ऐसे subsets कितने हैं जिनमें (a) और (b) में से ठीक एक हो?

If \(A=\{a,b,c,d,e\}\), how many subsets in (\mathcal{P}(A)) contain exactly one of (a) and (b)?

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Correct Answer

B. (16)

Step 1

Concept

There are (2) ways to choose exactly one of (a,b), and the remaining (3) elements are free. Hence \(2\cdot2^3=16\).

Step 2

Why this answer is correct

The correct answer is B. (16). There are (2) ways to choose exactly one of (a,b), and the remaining (3) elements are free. Hence \(2\cdot2^3=16\).

Step 3

Exam Tip

(a,b) में से ठीक एक चुनने के (2) तरीके हैं और बाकी (3) तत्व स्वतंत्र हैं। इसलिए \(2\cdot2^3=16\)।

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Mathematics Answer, Explanation and Revision Hints

यदि \(A=\{a,b,c,d,e\}\) है, तो (\mathcal{P}(A)) में ऐसे subsets कितने हैं जिनमें (a) और (b) में से ठीक एक हो? / If \(A=\{a,b,c,d,e\}\), how many subsets in (\mathcal{P}(A)) contain exactly one of (a) and (b)?

Correct Answer: B. (16). Explanation: (a,b) में से ठीक एक चुनने के (2) तरीके हैं और बाकी (3) तत्व स्वतंत्र हैं। इसलिए \(2\cdot2^3=16\)। / There are (2) ways to choose exactly one of (a,b), and the remaining (3) elements are free. Hence \(2\cdot2^3=16\).

Which concept should I revise for this Mathematics MCQ?

There are (2) ways to choose exactly one of (a,b), and the remaining (3) elements are free. Hence \(2\cdot2^3=16\).

What exam hint can help solve this Mathematics question?

(a,b) में से ठीक एक चुनने के (2) तरीके हैं और बाकी (3) तत्व स्वतंत्र हैं। इसलिए \(2\cdot2^3=16\)।