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non-empty-subsets MCQ Questions for Class 11

non-empty-subsets se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

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11 questions tagged with non-empty-subsets.

Question 1/11 Hard Mathematics Relations and Functions Cartesian product of sets Class 11 Level 24

यदि (A) में (3) अवयव और (B) में (4) अवयव हैं, तो \(A\times B\) के गैर-रिक्त उपसमुच्चयों की संख्या क्या है?

If (A) has (3) elements and (B) has (4) elements, what is the number of non-empty subsets of \(A\times B\)?

Explanation opens after your attempt
Correct Answer

C. (4095)

Step 1

Concept

\(|A\times B|=12\), so non-empty subsets are \(2^{12}-1=4095\). Do not forget to subtract the empty set.

Step 2

Why this answer is correct

The correct answer is C. (4095). \(|A\times B|=12\), so non-empty subsets are \(2^{12}-1=4095\). Do not forget to subtract the empty set.

Step 3

Exam Tip

\(|A\times B|=12\), इसलिए गैर-रिक्त उपसमुच्चय \(2^{12}-1=4095\) हैं। रिक्त समुच्चय घटाना न भूलें।

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Question 2/11 Hard Mathematics Relations and Functions Cartesian product of sets Class 11 Level 23

यदि (A) में (4) अवयव और (B) में (3) अवयव हैं, तो \(A\times B\) के गैर-रिक्त उपसमुच्चयों की संख्या क्या है?

If (A) has (4) elements and (B) has (3) elements, what is the number of non-empty subsets of \(A\times B\)?

Explanation opens after your attempt
Correct Answer

D. (4095)

Step 1

Concept

\(|A\times B|=12\), so non-empty subsets are \(2^{12}-1=4095\). Do not forget to subtract the empty set.

Step 2

Why this answer is correct

The correct answer is D. (4095). \(|A\times B|=12\), so non-empty subsets are \(2^{12}-1=4095\). Do not forget to subtract the empty set.

Step 3

Exam Tip

\(|A\times B|=12\), इसलिए गैर-रिक्त उपसमुच्चय \(2^{12}-1=4095\) हैं। रिक्त समुच्चय घटाना न भूलें।

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Question 3/11 Hard Mathematics Relations and Functions Cartesian product of sets Class 11 Level 22

यदि \(A=\{1,2,3\}\) और \(B=\{4,5\}\) हैं, तो \(A\times B\) के कितने गैर-रिक्त उपसमुच्चय हैं?

If \(A=\{1,2,3\}\) and \(B=\{4,5\}\), how many non-empty subsets does \(A\times B\) have?

Explanation opens after your attempt
Correct Answer

B. (63)

Step 1

Concept

\(|A\times B|=3\cdot2=6\), so non-empty subsets are \(2^6-1=63\). Do not forget to subtract the empty set.

Step 2

Why this answer is correct

The correct answer is B. (63). \(|A\times B|=3\cdot2=6\), so non-empty subsets are \(2^6-1=63\). Do not forget to subtract the empty set.

Step 3

Exam Tip

\(|A\times B|=3\cdot2=6\), इसलिए गैर-रिक्त उपसमुच्चय \(2^6-1=63\) हैं। रिक्त समुच्चय घटाना न भूलें।

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Question 4/11 Expert Mathematics Sets Power Set and Universal Set Class 11 Level 12

यदि \(A=\{a,b,c,d\}\), तो (P(A)) के उन अवयवों की संख्या क्या है जो खाली समुच्चय नहीं हैं?

If \(A=\{a,b,c,d\}\), what is the number of elements of (P(A)) that are not empty sets?

Explanation opens after your attempt
Correct Answer

A. (15)

Step 1

Concept

Total subsets are \(2^4=16\) and one subset is empty, so there are (15) non-empty subsets. Subtract (1) for non-empty subsets.

Step 2

Why this answer is correct

The correct answer is A. (15). Total subsets are \(2^4=16\) and one subset is empty, so there are (15) non-empty subsets. Subtract (1) for non-empty subsets.

Step 3

Exam Tip

कुल उपसमुच्चय \(2^4=16\) हैं और खाली उपसमुच्चय (1) है, इसलिए (15) गैर-रिक्त उपसमुच्चय हैं। गैर-रिक्त के लिए (1) घटाएं।

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Question 5/11 Expert Mathematics Sets Power Set and Universal Set Class 11 Level 10

\(यदि (U={1,2,3,4,5,6,7,8,9,10}) और (A={x:x\in U, x\) सम है\(}) है, तो (\mathcal{P}(A')) में कितने non-empty members हैं\)?

\(If (U={1,2,3,4,5,6,7,8,9,10}) and (A={x:x\in U, x\) is even\(}), how many non-empty members are in (\mathcal{P}(A'))\)?

Explanation opens after your attempt
Correct Answer

B. (31)

Step 1

Concept

(A') contains odd numbers ({1,3,5,7,9}), so non-empty subsets are \(2^5-1=31\). In exams, subtract (1) to exclude \(\varnothing\).

Step 2

Why this answer is correct

The correct answer is B. (31). (A') contains odd numbers ({1,3,5,7,9}), so non-empty subsets are \(2^5-1=31\). In exams, subtract (1) to exclude \(\varnothing\).

Step 3

Exam Tip

(A') में odd numbers ({1,3,5,7,9}) हैं, इसलिए non-empty subsets \(2^5-1=31\) हैं। परीक्षा में \(\varnothing\) हटाने पर (1) घटाएं।

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Question 6/11 Medium Mathematics Sets Power Set and Universal Set Class 11 Level 12

यदि \(A=\{1,2,3\}\) है, तो (\mathcal{P}(A)) के कितने तत्वों में कम से कम एक तत्व है?

If \(A=\{1,2,3\}\), how many elements of (\mathcal{P}(A)) have at least one element?

Explanation opens after your attempt
Correct Answer

B. (7)

Step 1

Concept

Subsets with at least one element are non-empty subsets. From total \(2^3=8\), removing \(\varnothing\) leaves (7).

Step 2

Why this answer is correct

The correct answer is B. (7). Subsets with at least one element are non-empty subsets. From total \(2^3=8\), removing \(\varnothing\) leaves (7).

Step 3

Exam Tip

कम से कम एक तत्व वाले उपसमुच्चय अरिक्त उपसमुच्चय होते हैं। कुल \(2^3=8\) में से \(\varnothing\) हटाने पर (7) बचते हैं।

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Question 7/11 Medium Mathematics Sets Power Set and Universal Set Class 11 Level 12

यदि \(A=\{3,6,9,12\}\) है, तो (\mathcal{P}(A)) में कितने अरिक्त तत्व होंगे?

If \(A=\{3,6,9,12\}\), how many non-empty elements are there in (\mathcal{P}(A))?

Explanation opens after your attempt
Correct Answer

B. (15)

Step 1

Concept

Total subsets are \(2^4=16\). Only \(\varnothing\) is empty so there are (15) non-empty subsets.

Step 2

Why this answer is correct

The correct answer is B. (15). Total subsets are \(2^4=16\). Only \(\varnothing\) is empty so there are (15) non-empty subsets.

Step 3

Exam Tip

कुल उपसमुच्चय \(2^4=16\) हैं। केवल \(\varnothing\) रिक्त है इसलिए अरिक्त उपसमुच्चय (15) होंगे।

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Question 8/11 Medium Mathematics Sets Power Set and Universal Set Class 11 Level 11

यदि \(A=\{1,2,3\}\) है, तो (\mathcal{P}(A)) में कितने अरिक्त तत्व होंगे?

If \(A=\{1,2,3\}\), how many non-empty elements are there in (\mathcal{P}(A))?

Explanation opens after your attempt
Correct Answer

C. (7)

Step 1

Concept

Total subsets are \(2^3=8\), and only \(\varnothing\) is empty. So non-empty subsets are (8-1=7).

Step 2

Why this answer is correct

The correct answer is C. (7). Total subsets are \(2^3=8\), and only \(\varnothing\) is empty. So non-empty subsets are (8-1=7).

Step 3

Exam Tip

कुल उपसमुच्चय \(2^3=8\) हैं और केवल \(\varnothing\) रिक्त है। इसलिए अरिक्त उपसमुच्चय (8-1=7) हैं।

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Question 9/11 Medium Mathematics Sets Power Set and Universal Set Class 11 Level 11

यदि (A) में (3) तत्व हैं, तो (A) के अरिक्त उचित उपसमुच्चयों की संख्या कितनी होगी?

If (A) has (3) elements, how many non-empty proper subsets of (A) are there?

Explanation opens after your attempt
Correct Answer

B. (6)

Step 1

Concept

Total subsets are \(2^3=8\). Removing \(\varnothing\) and (A) gives (6) non-empty proper subsets.

Step 2

Why this answer is correct

The correct answer is B. (6). Total subsets are \(2^3=8\). Removing \(\varnothing\) and (A) gives (6) non-empty proper subsets.

Step 3

Exam Tip

कुल उपसमुच्चय \(2^3=8\) हैं। अरिक्त उचित उपसमुच्चयों के लिए \(\varnothing\) और (A) हटाने पर (6) बचते हैं।

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Question 10/11 Medium Mathematics Sets Power Set and Universal Set Class 11 Level 10

यदि (\mathcal{P}(A)) में (8) तत्व हैं तो (A) के खाली नहीं उपसमुच्चयों की संख्या कितनी होगी?

If (\mathcal{P}(A)) has (8) elements, how many non-empty subsets does (A) have?

Explanation opens after your attempt
Correct Answer

C. (7)

Step 1

Concept

From \(2^n=8\), (n=3), and total subsets are (8). Removing the empty subset leaves (7).

Step 2

Why this answer is correct

The correct answer is C. (7). From \(2^n=8\), (n=3), and total subsets are (8). Removing the empty subset leaves (7).

Step 3

Exam Tip

\(2^n=8\) से (n=3) है और कुल उपसमुच्चय (8) हैं। खाली उपसमुच्चय हटाने पर (7) बचते हैं।

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Question 11/11 Medium Mathematics Sets Power Set and Universal Set Class 11 Level 10

यदि \(A=\{1,2,3\}\) है तो (\mathcal{P}(A)) में खाली नहीं होने वाले उपसमुच्चयों की संख्या कितनी होगी?

If \(A=\{1,2,3\}\), how many non-empty subsets are in (\mathcal{P}(A))?

Explanation opens after your attempt
Correct Answer

B. (7)

Step 1

Concept

Total subsets are \(2^3=8\) and one subset is empty. Therefore non-empty subsets are (7).

Step 2

Why this answer is correct

The correct answer is B. (7). Total subsets are \(2^3=8\) and one subset is empty. Therefore non-empty subsets are (7).

Step 3

Exam Tip

कुल उपसमुच्चय \(2^3=8\) हैं और खाली उपसमुच्चय एक है। इसलिए खाली नहीं उपसमुच्चय (7) हैं।

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