Concept-wise Practice

disjoint-subsets MCQ Questions for Class 11

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Practice Questions

5 questions tagged with disjoint-subsets.

Question 1/5 Expert Mathematics Sets Class 11 Level 11

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 \(A=\{1,2,3,4,5\}\) है, तो (\mathcal{P}(A)) में ऐसे subsets कितने हैं जो ({1,2}) से disjoint हैं?

If \(A=\{1,2,3,4,5\}\), how many subsets in (\mathcal{P}(A)) are disjoint from ({1,2})?

Explanation opens after your attempt
Correct Answer

B. (8)

Step 1

Concept

Disjoint subsets are formed only from ({3,4,5}), so there are \(2^3=8\). In exams, remove forbidden elements for a disjoint condition.

Step 2

Why this answer is correct

The correct answer is B. (8). Disjoint subsets are formed only from ({3,4,5}), so there are \(2^3=8\). In exams, remove forbidden elements for a disjoint condition.

Step 3

Exam Tip

Disjoint subsets केवल ({3,4,5}) से बनेंगे, इसलिए \(2^3=8\) हैं। परीक्षा में disjoint condition के लिए forbidden elements हटा दें।

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यदि \(A=\{1,2,3,4\}\) है, तो (\mathcal{P}(A)) में ऐसे members कितने हैं जो ({1,2}) से disjoint हैं?

If \(A=\{1,2,3,4\}\), how many members of (\mathcal{P}(A)) are disjoint from ({1,2})?

Explanation opens after your attempt
Correct Answer

B. (4)

Step 1

Concept

Disjoint subsets are formed only from ({3,4}), so the number is \(2^2=4\). In exams, remove forbidden elements for a disjoint condition.

Step 2

Why this answer is correct

The correct answer is B. (4). Disjoint subsets are formed only from ({3,4}), so the number is \(2^2=4\). In exams, remove forbidden elements for a disjoint condition.

Step 3

Exam Tip

Disjoint subsets केवल ({3,4}) से बनेंगे, इसलिए संख्या \(2^2=4\) है। परीक्षा में disjoint condition के लिए forbidden elements हटाएं।

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यदि \(A=\{a,b,c,d\}\), तो (\mathcal{P}(A)) के कितने तत्व ( {a,d}) से असंयुक्त नहीं हैं?

If \(A=\{a,b,c,d\}\), how many elements of (\mathcal{P}(A)) are not disjoint from ({a,d})?

Explanation opens after your attempt
Correct Answer

C. (12)

Step 1

Concept

Subsets disjoint from ({a,d}) are formed only from (b,c), so there are \(2^2=4\). Hence not disjoint subsets are (16-4=12).

Step 2

Why this answer is correct

The correct answer is C. (12). Subsets disjoint from ({a,d}) are formed only from (b,c), so there are \(2^2=4\). Hence not disjoint subsets are (16-4=12).

Step 3

Exam Tip

({a,d}) से असंयुक्त उपसमुच्चय केवल (b,c) से बनेंगे, जो \(2^2=4\) हैं। इसलिए असंयुक्त नहीं होने वाले (16-4=12) हैं।

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यदि \(A=\{x,y,z,w\}\), तो (\mathcal{P}(A)) में ऐसे कितने तत्व हैं जो ({x,z}) से असंयुक्त हैं?

If \(A=\{x,y,z,w\}\), how many elements of (\mathcal{P}(A)) are disjoint from ({x,z})?

Explanation opens after your attempt
Correct Answer

B. (4)

Step 1

Concept

A disjoint subset cannot contain (x) or (z). Only (y,w) may be chosen, so there are \(2^2=4\).

Step 2

Why this answer is correct

The correct answer is B. (4). A disjoint subset cannot contain (x) or (z). Only (y,w) may be chosen, so there are \(2^2=4\).

Step 3

Exam Tip

असंयुक्त उपसमुच्चय में (x) और (z) नहीं आ सकते। केवल (y,w) चुने जा सकते हैं, इसलिए \(2^2=4\) हैं।

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