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universal_set MCQ Questions for Class 11

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

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217 questions tagged with universal_set.

Question 1/217 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(A\subseteq U\), तो (\(A'\cap A\)') किसके बराबर है?

If \(A\subseteq U\), what is (\(A'\cap A\)') equal to?

Explanation opens after your attempt
Correct Answer

A. (U)

Step 1

Concept

\(A'\cap A=\varnothing\). Therefore (\(A'\cap A\)'=\varnothing'=U).

Step 2

Why this answer is correct

The correct answer is A. (U). \(A'\cap A=\varnothing\). Therefore (\(A'\cap A\)'=\varnothing'=U).

Step 3

Exam Tip

\(A'\cap A=\varnothing\) होता है। इसलिए (\(A'\cap A\)'=\varnothing'=U) है।

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Question 2/217 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 19

यदि \(A \subseteq U\), तो \(A \cap U'\) किसके बराबर होगा?

If \(A \subseteq U\), what is \(A \cap U'\) equal to?

Explanation opens after your attempt
Correct Answer

A. \(\varnothing\)

Step 1

Concept

The complement of the universal set (U) is \(\varnothing\). Hence \(A \cap U' = A \cap \varnothing=\varnothing\).

Step 2

Why this answer is correct

The correct answer is A. \(\varnothing\). The complement of the universal set (U) is \(\varnothing\). Hence \(A \cap U' = A \cap \varnothing=\varnothing\).

Step 3

Exam Tip

सार्वत्रिक समुच्चय (U) का पूरक \(\varnothing\) होता है। इसलिए \(A \cap U' = A \cap \varnothing=\varnothing\) है।

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Question 3/217 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 19

यदि \(U=\{a,b,c,d,e,g,h\}\) और \(A=\{a,e,h\}\), तो (A') क्या है?

If \(U=\{a,b,c,d,e,g,h\}\) and \(A=\{a,e,h\}\), what is (A')?

Explanation opens after your attempt
Correct Answer

A. ({b,c,d,g})

Step 1

Concept

The complement contains only those letters of (U) that are not in (A). Do not add (f) because \(f \notin U\).

Step 2

Why this answer is correct

The correct answer is A. ({b,c,d,g}). The complement contains only those letters of (U) that are not in (A). Do not add (f) because \(f \notin U\).

Step 3

Exam Tip

पूरक में केवल (U) के वे अक्षर आएंगे जो (A) में नहीं हैं। (f) को नहीं जोड़ना क्योंकि \(f \notin U\) है।

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Question 4/217 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 19

यदि \(U={1,2,\ldots,12}\), \(A=\{1,2,3,4,5\}\), तो \(A' \cup A\) क्या है?

If \(U={1,2,\ldots,12}\), \(A=\{1,2,3,4,5\}\), what is \(A' \cup A\)?

Explanation opens after your attempt
Correct Answer

A. (U)

Step 1

Concept

The union of any set with its complement gives the whole (U). This is the basic identity of complement.

Step 2

Why this answer is correct

The correct answer is A. (U). The union of any set with its complement gives the whole (U). This is the basic identity of complement.

Step 3

Exam Tip

किसी भी समुच्चय का अपने पूरक के साथ संघ पूरा (U) देता है। यह पूरक की मूल पहचान है।

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Question 5/217 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 19

यदि \(A \cup A'=U\) और \(A \cap A'=\varnothing\), तो (A') का सही अर्थ क्या है?

If \(A \cup A'=U\) and \(A \cap A'=\varnothing\), what is the correct meaning of (A')?

Explanation opens after your attempt
Correct Answer

A. (U) के वे सदस्य जो (A) में नहीं हैंElements of (U) that are not in (A)

Step 1

Concept

The complement (A') always represents (U-A). It is important to identify the universal set first.

Step 2

Why this answer is correct

The correct answer is A. (U) के वे सदस्य जो (A) में नहीं हैं / Elements of (U) that are not in (A). The complement (A') always represents (U-A). It is important to identify the universal set first.

Step 3

Exam Tip

पूरक (A') हमेशा (U-A) को दर्शाता है। सार्वत्रिक समुच्चय को पहले पहचानना जरूरी है।

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Question 6/217 Hard Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U'=\varnothing\), तो (U) के बारे में कौन सा कथन सही है?

If \(U'=\varnothing\), which statement about (U) is correct?

Explanation opens after your attempt
Correct Answer

A. (U) सार्वत्रिक समुच्चय है(U) is the universal set

Step 1

Concept

The complement of the universal set is always the empty set. Thus \(U'=\varnothing\) is a basic complement identity.

Step 2

Why this answer is correct

The correct answer is A. (U) सार्वत्रिक समुच्चय है / (U) is the universal set. The complement of the universal set is always the empty set. Thus \(U'=\varnothing\) is a basic complement identity.

Step 3

Exam Tip

सार्वत्रिक समुच्चय का पूरक हमेशा रिक्त समुच्चय होता है। इसलिए \(U'=\varnothing\) पूरक की मूल पहचान है।

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Question 7/217 Hard Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(A\cap B=U\), तो \(A'\cup B'\) क्या होगा?

If \(A\cap B=U\), what is \(A'\cup B'\)?

Explanation opens after your attempt
Correct Answer

A. \(\varnothing\)

Step 1

Concept

If \(A\cap B=U\), then (A=U) and (B=U). By De Morgan, (A'\cup B'=\(A\cap B\)'=U'=\varnothing).

Step 2

Why this answer is correct

The correct answer is A. \(\varnothing\). If \(A\cap B=U\), then (A=U) and (B=U). By De Morgan, (A'\cup B'=\(A\cap B\)'=U'=\varnothing).

Step 3

Exam Tip

\(A\cap B=U\) होने पर (A=U) और (B=U) होंगे। डी मॉर्गन से (A'\cup B'=\(A\cap B\)'=U'=\varnothing)।

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Question 8/217 Hard Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(A'=\varnothing\), तो (A) क्या होगा?

If \(A'=\varnothing\), what is (A)?

Explanation opens after your attempt
Correct Answer

A. (U)

Step 1

Concept

If the complement is empty, no element of (U) lies outside (A). Therefore (A=U).

Step 2

Why this answer is correct

The correct answer is A. (U). If the complement is empty, no element of (U) lies outside (A). Therefore (A=U).

Step 3

Exam Tip

यदि पूरक रिक्त है, तो (U) का कोई भी अवयव (A) के बाहर नहीं है। इसलिए (A=U) है।

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Question 9/217 Hard Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(A\cup B=U\), तो (\(A'\cap B'\)) क्या होगा?

If \(A\cup B=U\), what is \(A'\cap B'\)?

Explanation opens after your attempt
Correct Answer

C. \(\varnothing\)

Step 1

Concept

By De Morgan, (A'\cap B'=\(A\cup B\)'). Since \(A\cup B=U\), (\(A\cup B\)'=\varnothing).

Step 2

Why this answer is correct

The correct answer is C. \(\varnothing\). By De Morgan, (A'\cap B'=\(A\cup B\)'). Since \(A\cup B=U\), (\(A\cup B\)'=\varnothing).

Step 3

Exam Tip

डी मॉर्गन से (A'\cap B'=\(A\cup B\)')। चूंकि \(A\cup B=U\), इसलिए (\(A\cup B\)'=\varnothing)।

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Question 10/217 Medium Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(A^{c}=\varnothing\), तो (A) के बारे में कौन सा कथन सही है?

If \(A^{c}=\varnothing\), which statement about (A) is correct?

Explanation opens after your attempt
Correct Answer

B. (A=U)

Step 1

Concept

If the complement is empty, then (A) covers the whole (U). Therefore, (A=U).

Step 2

Why this answer is correct

The correct answer is B. (A=U). If the complement is empty, then (A) covers the whole (U). Therefore, (A=U).

Step 3

Exam Tip

यदि पूरक खाली है, तो (A) ने पूरे (U) को कवर कर लिया है। इसलिए (A=U) होगा।

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Question 11/217 Medium Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि (A=U) है, तो \(A^{c}\) क्या होगा?

If (A=U), what is \(A^{c}\)?

Explanation opens after your attempt
Correct Answer

C. \(\varnothing\)

Step 1

Concept

When (A) contains all elements of (U), nothing remains outside it. So remember \(U^{c}=\varnothing\).

Step 2

Why this answer is correct

The correct answer is C. \(\varnothing\). When (A) contains all elements of (U), nothing remains outside it. So remember \(U^{c}=\varnothing\).

Step 3

Exam Tip

जब (A) में (U) के सभी अवयव हैं, तो बाहर कुछ नहीं बचता। इसलिए \(U^{c}=\varnothing\) याद रखें।

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Question 12/217 Medium Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि सार्वत्रिक समुच्चय \(U=\{1,2,3,4,5,6\}\) और \(A=\{2,4,6\}\) है, तो \(A^{c}\) क्या होगा?

If the universal set is \(U=\{1,2,3,4,5,6\}\) and \(A=\{2,4,6\}\), then what is \(A^{c}\)?

Explanation opens after your attempt
Correct Answer

A. ({1,3,5})

Step 1

Concept

\(A^{c}\) contains elements of (U) that are not in (A). In exams, first remove (A) from (U).

Step 2

Why this answer is correct

The correct answer is A. ({1,3,5}). \(A^{c}\) contains elements of (U) that are not in (A). In exams, first remove (A) from (U).

Step 3

Exam Tip

\(A^{c}\) में (U) के वे अवयव आते हैं जो (A) में नहीं हैं। परीक्षा में पहले (U) से (A) हटाएं।

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Question 13/217 Easy Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U=\{2,4,6,8\}\) और (A=U) है, तो \(A^c\) क्या होगा?

If \(U=\{2,4,6,8\}\) and (A=U), what is \(A^c\)?

Explanation opens after your attempt
Correct Answer

A. \(\varnothing\)empty set

Step 1

Concept

When (A=U), no element of (U) remains outside (A). Hence the complement is \(\varnothing\).

Step 2

Why this answer is correct

The correct answer is A. \(\varnothing\) / empty set. When (A=U), no element of (U) remains outside (A). Hence the complement is \(\varnothing\).

Step 3

Exam Tip

जब (A=U) होता है, तब (U) में (A) से बाहर कोई तत्व नहीं बचता। इसलिए पूरक \(\varnothing\) होता है।

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Question 14/217 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(U={1,2,\ldots,12}\), \(A=\{2,4,6,8,10,12\}\) और \(B=\{3,6,9,12\}\) हैं, तो (\(A\cup B\)') क्या है?

If \(U={1,2,\ldots,12}\), \(A=\{2,4,6,8,10,12\}\), and \(B=\{3,6,9,12\}\), what is (\(A\cup B\)')?

Explanation opens after your attempt
Correct Answer

A. ({1,5,7,11})

Step 1

Concept

\(A\cup B={2,3,4,6,8,9,10,12}\). The elements outside it in (U) are (1,5,7,11).

Step 2

Why this answer is correct

The correct answer is A. ({1,5,7,11}). \(A\cup B={2,3,4,6,8,9,10,12}\). The elements outside it in (U) are (1,5,7,11).

Step 3

Exam Tip

\(A\cup B={2,3,4,6,8,9,10,12}\) है। (U) में इसके बाहर के तत्व (1,5,7,11) हैं।

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Question 15/217 Medium Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(U=\{a,b,c,d,e,f,g\}\), \(A=\{a,c,e,g\}\) और \(B=\{b,c,e,f\}\) हैं, तो \(A\cap B\) क्या है?

If \(U=\{a,b,c,d,e,f,g\}\), \(A=\{a,c,e,g\}\), and \(B=\{b,c,e,f\}\), what is \(A\cap B\)?

Explanation opens after your attempt
Correct Answer

A. ( {c,e} )

Step 1

Concept

Both (A) and (B) contain (c) and (e). Keep only shared elements in the intersection.

Step 2

Why this answer is correct

The correct answer is A. ( {c,e} ). Both (A) and (B) contain (c) and (e). Keep only shared elements in the intersection.

Step 3

Exam Tip

(A) और (B) दोनों में (c) और (e) हैं। प्रतिच्छेद में केवल साझा अवयव रखें।

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Question 16/217 Medium Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,5,10\}\) और \(B=\{2,4,6,8,10\}\) हैं, तो \(A\cup B\) क्या है?

If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,2,5,10\}\), and \(B=\{2,4,6,8,10\}\), what is \(A\cup B\)?

Explanation opens after your attempt
Correct Answer

A. ( {1,2,4,5,6,8,10} )

Step 1

Concept

The union contains all distinct elements of (A) and (B). (U) only gives the universal boundary.

Step 2

Why this answer is correct

The correct answer is A. ( {1,2,4,5,6,8,10} ). The union contains all distinct elements of (A) and (B). (U) only gives the universal boundary.

Step 3

Exam Tip

संघ में (A) और (B) के सभी अलग-अलग अवयव आते हैं। (U) केवल सार्वत्रिक सीमा देता है।

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Question 17/217 Medium Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,3,5,7\}\) और \(B=\{2,3,5,8\}\) हैं, तो \(A\cup B\) क्या है?

If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,3,5,7\}\), and \(B=\{2,3,5,8\}\), what is \(A\cup B\)?

Explanation opens after your attempt
Correct Answer

A. ( {1,2,3,5,7,8} )

Step 1

Concept

The union contains all distinct elements of (A) and (B). (U) only shows the universal boundary.

Step 2

Why this answer is correct

The correct answer is A. ( {1,2,3,5,7,8} ). The union contains all distinct elements of (A) and (B). (U) only shows the universal boundary.

Step 3

Exam Tip

संघ में (A) और (B) के सभी अलग-अलग अवयव शामिल होते हैं। (U) केवल सार्वत्रिक सीमा बताता है।

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Question 18/217 Easy Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(U=\{10,20,30,40,50\}\), \(A=\{10,20,40\}\) और \(B=\{20,30\}\) है, तो (A-B) क्या है?

If \(U=\{10,20,30,40,50\}\), \(A=\{10,20,40\}\), and \(B=\{20,30\}\), what is (A-B)?

Explanation opens after your attempt
Correct Answer

A. ( {10,40} )

Step 1

Concept

The common element (20) is removed from (A), leaving ({10,40}). Even when (U) is given, find the difference from (A) and (B).

Step 2

Why this answer is correct

The correct answer is A. ( {10,40} ). The common element (20) is removed from (A), leaving ({10,40}). Even when (U) is given, find the difference from (A) and (B).

Step 3

Exam Tip

(A) से (B) का समान अवयव (20) हटता है और ({10,40}) बचता है। (U) दिए होने पर भी अंतर (A) और (B) से निकालें।

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Question 19/217 Easy Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(U=\{a,b,c,d,e,f\}\), \(A=\{a,c,e\}\) और \(B=\{b,c,e,f\}\) है, तो \(A\cap B\) क्या है?

If \(U=\{a,b,c,d,e,f\}\), \(A=\{a,c,e\}\), and \(B=\{b,c,e,f\}\), what is \(A\cap B\)?

Explanation opens after your attempt
Correct Answer

A. ( {c,e} )

Step 1

Concept

The common elements of (A) and (B) are (c) and (e). The universal set only gives the reference.

Step 2

Why this answer is correct

The correct answer is A. ( {c,e} ). The common elements of (A) and (B) are (c) and (e). The universal set only gives the reference.

Step 3

Exam Tip

(A) और (B) में सामान्य अवयव (c) और (e) हैं। सार्वत्रिक समुच्चय केवल संदर्भ देता है।

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Question 20/217 Easy Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,7\}\) और \(B=\{2,4,6\}\) है, तो \(A\cup B\) क्या है?

If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,7\}\), and \(B=\{2,4,6\}\), what is \(A\cup B\)?

Explanation opens after your attempt
Correct Answer

A. ( {1,2,4,6,7} )

Step 1

Concept

\(A\cup B\) contains all distinct elements of (A) and (B). (U) is only the universal set; the answer is not always the whole (U).

Step 2

Why this answer is correct

The correct answer is A. ( {1,2,4,6,7} ). \(A\cup B\) contains all distinct elements of (A) and (B). (U) is only the universal set; the answer is not always the whole (U).

Step 3

Exam Tip

\(A\cup B\) में (A) और (B) के सभी अलग-अलग अवयव हैं। (U) केवल सार्वत्रिक समुच्चय है, उत्तर हमेशा पूरा (U) नहीं होता।

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Question 21/217 Easy Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(U=\{a,b,c,d,e\}\), \(A=\{a,b,d\}\) और \(B=\{b,c\}\) है, तो (A-B) क्या है?

If \(U=\{a,b,c,d,e\}\), \(A=\{a,b,d\}\), and \(B=\{b,c\}\), what is (A-B)?

Explanation opens after your attempt
Correct Answer

A. ( {a,d} )

Step 1

Concept

The common element (b) is removed from (A), leaving ({a,d}). Even when a universal set is given, find the difference only between the asked sets.

Step 2

Why this answer is correct

The correct answer is A. ( {a,d} ). The common element (b) is removed from (A), leaving ({a,d}). Even when a universal set is given, find the difference only between the asked sets.

Step 3

Exam Tip

(A) से (B) का समान अवयव (b) हटता है और ({a,d}) बचता है। सार्वत्रिक समुच्चय दिए होने पर भी अंतर केवल दिए गए दो समुच्चयों से निकालें।

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Question 22/217 Easy Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,3,5\}\) और \(B=\{2,3,4\}\) है, तो \(A\cup B\) क्या है?

If \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,3,5\}\), and \(B=\{2,3,4\}\), what is \(A\cup B\)?

Explanation opens after your attempt
Correct Answer

A. ( {1,2,3,4,5} )

Step 1

Concept

\(A\cup B\) contains all distinct elements of (A) and (B). (U) is only the universal set; the answer is not always the whole (U).

Step 2

Why this answer is correct

The correct answer is A. ( {1,2,3,4,5} ). \(A\cup B\) contains all distinct elements of (A) and (B). (U) is only the universal set; the answer is not always the whole (U).

Step 3

Exam Tip

\(A\cup B\) में (A) और (B) के सभी अलग-अलग अवयव आते हैं। (U) केवल संदर्भ समुच्चय है, हर बार पूरा (U) उत्तर नहीं होता।

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Question 23/217 Easy Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\) और \(B=\{3,4\}\) हैं, तो (\(A\cup B\)) क्या है?

If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), and \(B=\{3,4\}\), what is (\(A\cup B\))?

Explanation opens after your attempt
Correct Answer

A. ( {1,2,3,4} )

Step 1

Concept

\(A\cup B\) contains all distinct elements of (A) and (B). (U) only gives the universal set here.

Step 2

Why this answer is correct

The correct answer is A. ( {1,2,3,4} ). \(A\cup B\) contains all distinct elements of (A) and (B). (U) only gives the universal set here.

Step 3

Exam Tip

\(A\cup B\) में (A) और (B) के सभी अलग-अलग अवयव आते हैं। (U) यहां केवल सार्वत्रिक समुच्चय की जानकारी देता है।

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Question 24/217 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

किसी वेन आरेख में (n\(A\cup B\cup C\)=215), (n(\(A\cup B\cup C\)')=35), और ठीक दो समुच्चयों में (62) तत्व हैं। यदि (n(U)) पूछा जाए, तो उत्तर क्या होगा?

In a Venn diagram, (n\(A\cup B\cup C\)=215), (n(\(A\cup B\cup C\)')=35), and exactly two sets have (62) elements. If (n(U)) is asked, what is the answer?

Explanation opens after your attempt
Correct Answer

A. (250)

Step 1

Concept

The universal set is the sum of the union and outside region, so (215+35=250). The exactly-two data is extra in this question.

Step 2

Why this answer is correct

The correct answer is A. (250). The universal set is the sum of the union and outside region, so (215+35=250). The exactly-two data is extra in this question.

Step 3

Exam Tip

सार्वत्रिक समुच्चय संघ और बाहरी भाग का योग है, इसलिए (215+35=250) है। ठीक दो वाला आंकड़ा इस प्रश्न में अतिरिक्त है।

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Question 25/217 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n\(A\cap B'\)=36), (n\(A'\cap B\)=44), (n\(A\cap B\)=25) और (n(\(A\cup B\)')=18) है, तो (n(U)) कितना है?

If (n\(A\cap B'\)=36), (n\(A'\cap B\)=44), (n\(A\cap B\)=25) and (n(\(A\cup B\)')=18), then what is (n(U))?

Explanation opens after your attempt
Correct Answer

A. (123)

Step 1

Concept

The sum of the four disjoint regions is (36+44+25+18=123). The universal set includes both inside and outside regions.

Step 2

Why this answer is correct

The correct answer is A. (123). The sum of the four disjoint regions is (36+44+25+18=123). The universal set includes both inside and outside regions.

Step 3

Exam Tip

चारों अलग क्षेत्रों का योग (36+44+25+18=123) है। सार्वत्रिक समुच्चय में अंदर और बाहर दोनों क्षेत्र आते हैं।

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Question 26/217 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

किसी वेन आरेख में (n\(A\cup B\cup C\)=190), (n(\(A\cup B\cup C\)')=25), और ठीक दो समुच्चयों में (54) तत्व हैं। यदि (n(U)) पूछा जाए, तो उत्तर क्या होगा?

In a Venn diagram, (n\(A\cup B\cup C\)=190), (n(\(A\cup B\cup C\)')=25), and exactly two sets have (54) elements. If (n(U)) is asked, what is the answer?

Explanation opens after your attempt
Correct Answer

A. (215)

Step 1

Concept

The universal set (U) is the sum of the union and the outside region, so (190+25=215). The exactly-two data is extra here.

Step 2

Why this answer is correct

The correct answer is A. (215). The universal set (U) is the sum of the union and the outside region, so (190+25=215). The exactly-two data is extra here.

Step 3

Exam Tip

सार्वत्रिक समुच्चय (U) संघ और उसके बाहर वाले भाग का योग है, इसलिए (190+25=215) है। ठीक दो वाला आंकड़ा इस प्रश्न में अनावश्यक है।

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Question 27/217 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cap B'\)=29), (n\(A'\cap B\)=33), (n\(A\cap B\)=17) और (n(\(A\cup B\)')=21) है, तो (n(U)) कितना है?

If (n\(A\cap B'\)=29), (n\(A'\cap B\)=33), (n\(A\cap B\)=17) and (n(\(A\cup B\)')=21), then what is (n(U))?

Explanation opens after your attempt
Correct Answer

A. (100)

Step 1

Concept

The sum of all four disjoint regions is (29+33+17+21=100). The universal set includes both inside and outside regions.

Step 2

Why this answer is correct

The correct answer is A. (100). The sum of all four disjoint regions is (29+33+17+21=100). The universal set includes both inside and outside regions.

Step 3

Exam Tip

सभी चार अलग क्षेत्रों का योग (29+33+17+21=100) है। सार्वत्रिक समुच्चय में अंदर और बाहर दोनों क्षेत्र आते हैं।

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Question 28/217 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cup B\)=n(U)) है, तो वेन आरेख में कौन सा क्षेत्र खाली होगा?

If (n\(A\cup B\)=n(U)), which region is empty in the Venn diagram?

Explanation opens after your attempt
Correct Answer

A. (\(A\cup B\)')

Step 1

Concept

When the union equals the whole (U), no element remains outside the union. Therefore, (\(A\cup B\)') is empty.

Step 2

Why this answer is correct

The correct answer is A. (\(A\cup B\)'). When the union equals the whole (U), no element remains outside the union. Therefore, (\(A\cup B\)') is empty.

Step 3

Exam Tip

जब संघ पूरे (U) के बराबर हो, तो संघ के बाहर कोई तत्व नहीं रहता। इसलिए (\(A\cup B\)') खाली होगा।

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Question 29/217 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

एक वेन आरेख में (A) और (B) के बाहर (14), केवल (A) में (22), केवल (B) में (18), और दोनों में (11) हैं। (n(U)) कितना है?

In a Venn diagram, outside (A) and (B) there are (14), only (A) has (22), only (B) has (18), and both have (11). What is (n(U))?

Explanation opens after your attempt
Correct Answer

A. (65)

Step 1

Concept

The universal set is the sum of all regions (14+22+18+11=65). The outside region is also included in (U).

Step 2

Why this answer is correct

The correct answer is A. (65). The universal set is the sum of all regions (14+22+18+11=65). The outside region is also included in (U).

Step 3

Exam Tip

सार्वत्रिक समुच्चय सभी क्षेत्रों का योग (14+22+18+11=65) है। बाहर का भाग भी (U) में शामिल होता है।

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Question 30/217 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

एक सर्वे में (n(U)=200), (n\(A\cup B\cup C\)=164) है। किसी भी समुच्चय में न आने वालों की संख्या कितनी है?

In a survey (n(U)=200), (n\(A\cup B\cup C\)=164). How many people are in none of the sets?

Explanation opens after your attempt
Correct Answer

A. (36)

Step 1

Concept

None of the sets is (n(\(A\cup B\cup C\)')=200-164=36). The outside region is always total universal set minus the union.

Step 2

Why this answer is correct

The correct answer is A. (36). None of the sets is (n(\(A\cup B\cup C\)')=200-164=36). The outside region is always total universal set minus the union.

Step 3

Exam Tip

किसी में नहीं (n(\(A\cup B\cup C\)')=200-164=36) है। बाहर का क्षेत्र हमेशा सार्वत्रिक समुच्चय से संघ घटाकर मिलता है।

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