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Mathematics Quiz - Class 11 Mathematics Sets Venn Diagram...

Question 1/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

एक सर्वे में (n(U)=120), (n(A)=62), (n(B)=55) और (n\(A\cup B\)=91) है। वेन आरेख के अनुसार (n\(A\cap B\)) कितना होगा?

In a survey (n(U)=120), (n(A)=62), (n(B)=55) and (n\(A\cup B\)=91). According to the Venn diagram, what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (26)

Step 1

Concept

Using (n\(A\cap B\)=n(A)+n(B)-n\(A\cup B\)), the answer is (26). In exams, find the intersection this way when the union is given.

Step 2

Why this answer is correct

The correct answer is A. (26). Using (n\(A\cap B\)=n(A)+n(B)-n\(A\cup B\)), the answer is (26). In exams, find the intersection this way when the union is given.

Step 3

Exam Tip

सूत्र (n\(A\cap B\)=n(A)+n(B)-n\(A\cup B\)) से उत्तर (26) है। परीक्षा में संघ का मान मिलने पर प्रतिच्छेद इसी तरह निकालें।

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Question 2/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

एक सर्वेक्षण में (n(U)=180), (n(A)=82), (n(B)=76), (n(C)=69), (n\(A\cap B\)=34), (n\(B\cap C\)=29), (n\(C\cap A\)=27) और (n\(A\cap B\cap C\)=12) है। किसी भी समुच्चय में न आने वालों की संख्या कितनी है?

In a survey (n(U)=180), (n(A)=82), (n(B)=76), (n(C)=69), (n\(A\cap B\)=34), (n\(B\cap C\)=29), (n\(C\cap A\)=27) and (n\(A\cap B\cap C\)=12). How many are in none of the sets?

Explanation opens after your attempt

Correct Answer

A. (31)

Step 1

Concept

(n\(A\cup B\cup C\)=82+76+69-34-29-27+12=149), so outside is (180-149=31). First find the union and then take the complement.

Step 2

Why this answer is correct

The correct answer is A. (31). (n\(A\cup B\cup C\)=82+76+69-34-29-27+12=149), so outside is (180-149=31). First find the union and then take the complement.

Step 3

Exam Tip

(n\(A\cup B\cup C\)=82+76+69-34-29-27+12=149), इसलिए बाहर (180-149=31) है। पहले संघ निकालें फिर पूरक लें।

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Question 3/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

किसी कक्षा में (n(U)=80), (n(A)=37), (n(B)=42) और (n\(A\cap B\)=19) है। केवल (A) में आने वाले विद्यार्थियों की संख्या कितनी है?

In a class (n(U)=80), (n(A)=37), (n(B)=42) and (n\(A\cap B\)=19). How many students belong only to (A)?

Explanation opens after your attempt

Correct Answer

A. (18)

Step 1

Concept

The only (A) part is (n(A)-n\(A\cap B\)=37-19=18). In a Venn diagram, the common part should not be counted twice.

Step 2

Why this answer is correct

The correct answer is A. (18). The only (A) part is (n(A)-n\(A\cap B\)=37-19=18). In a Venn diagram, the common part should not be counted twice.

Step 3

Exam Tip

केवल (A) का भाग (n(A)-n\(A\cap B\)=37-19=18) है। वेन आरेख में साझा भाग को दोबारा नहीं गिनना चाहिए।

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Question 4/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि केवल (A) में (21), केवल (B) में (24), केवल (C) में (18), केवल \(A\cap B\) में (13), केवल \(B\cap C\) में (11), केवल \(C\cap A\) में (9) और तीनों में (7) तत्व हैं, तो ठीक दो समुच्चयों में आने वाले तत्वों की संख्या कितनी है?

If only (A) has (21), only (B) has (24), only (C) has (18), only \(A\cap B\) has (13), only \(B\cap C\) has (11), only \(C\cap A\) has (9), and all three have (7) elements, then how many elements are in exactly two sets?

Explanation opens after your attempt

Correct Answer

A. (33)

Step 1

Concept

Exactly two sets include only the pairwise-only regions, so (13+11+9=33). Do not count the centre \(A\cap B\cap C\) in exactly two.

Step 2

Why this answer is correct

The correct answer is A. (33). Exactly two sets include only the pairwise-only regions, so (13+11+9=33). Do not count the centre \(A\cap B\cap C\) in exactly two.

Step 3

Exam Tip

ठीक दो समुच्चयों में केवल दो-दो वाले क्षेत्र आते हैं, इसलिए (13+11+9=33) है। केंद्र \(A\cap B\cap C\) को ठीक दो में न गिनें।

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Question 5/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(U)=150), (n(A)=70), (n(B)=65) और (n\(A\cap B\)=28) है, तो (n(\(A\cup B\)')) कितना है?

If (n(U)=150), (n(A)=70), (n(B)=65) and (n\(A\cap B\)=28), then what is (n(\(A\cup B\)'))?

Explanation opens after your attempt

Correct Answer

A. (43)

Step 1

Concept

First (n\(A\cup B\)=70+65-28=107), so the outside part is (150-107=43). Remember to subtract from the universal set for a complement.

Step 2

Why this answer is correct

The correct answer is A. (43). First (n\(A\cup B\)=70+65-28=107), so the outside part is (150-107=43). Remember to subtract from the universal set for a complement.

Step 3

Exam Tip

पहले (n\(A\cup B\)=70+65-28=107), इसलिए बाहर का भाग (150-107=43) है। पूरक निकालते समय सार्वत्रिक समुच्चय घटाना याद रखें।

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Question 6/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(A)=4x+5), (n(B)=3x+8), (n\(A\cap B\)=2x+1) और (n\(A\cup B\)=72) है, तो (x) का मान क्या होगा?

If (n(A)=4x+5), (n(B)=3x+8), (n\(A\cap B\)=2x+1) and (n\(A\cup B\)=72), then what is the value of (x)?

Explanation opens after your attempt

Correct Answer

A. (12)

Step 1

Concept

Using the formula, (72=(4x+5)+(3x+8)-(2x+1)=5x+12), so (x=12). In algebraic Venn questions, apply the union formula directly.

Step 2

Why this answer is correct

The correct answer is A. (12). Using the formula, (72=(4x+5)+(3x+8)-(2x+1)=5x+12), so (x=12). In algebraic Venn questions, apply the union formula directly.

Step 3

Exam Tip

सूत्र से (72=(4x+5)+(3x+8)-(2x+1)=5x+12), इसलिए (x=12) है। बीजगणितीय वेन प्रश्न में संघ का सूत्र सीधे लगाएँ।

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Question 7/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

तीन समुच्चयों के लिए (n(A)=48), (n(B)=50), (n(C)=44), (n\(A\cap B\)=20), (n\(B\cap C\)=18), (n\(C\cap A\)=16) और (n\(A\cap B\cap C\)=7) है। (n\(A\cup B\cup C\)) कितना होगा?

For three sets (n(A)=48), (n(B)=50), (n(C)=44), (n\(A\cap B\)=20), (n\(B\cap C\)=18), (n\(C\cap A\)=16) and (n\(A\cap B\cap C\)=7). What is (n\(A\cup B\cup C\))?

Explanation opens after your attempt

Correct Answer

A. (95)

Step 1

Concept

By the formula, (48+50+44-20-18-16+7=95). In three sets, the common triple part must be added back.

Step 2

Why this answer is correct

The correct answer is A. (95). By the formula, (48+50+44-20-18-16+7=95). In three sets, the common triple part must be added back.

Step 3

Exam Tip

सूत्र से (48+50+44-20-18-16+7=95) मिलता है। तीन समुच्चयों में अंतिम साझा भाग को वापस जोड़ना जरूरी है।

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Question 8/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि \(U={1,2,\ldots,60}\), (A) (3) के गुणजों का समुच्चय और (B) (4) के गुणजों का समुच्चय है, तो (n(\(A\cup B\)')) कितना होगा?

If \(U={1,2,\ldots,60}\), (A) is the set of multiples of (3) and (B) is the set of multiples of (4), then what is (n(\(A\cup B\)'))?

Explanation opens after your attempt

Correct Answer

A. (30)

Step 1

Concept

Multiples of (3) are (20), multiples of (4) are (15), and multiples of (12) are (5), so the union is (30) and the complement is (60-30=30). Subtract common multiples once.

Step 2

Why this answer is correct

The correct answer is A. (30). Multiples of (3) are (20), multiples of (4) are (15), and multiples of (12) are (5), so the union is (30) and the complement is (60-30=30). Subtract common multiples once.

Step 3

Exam Tip

(3) के गुणज (20), (4) के गुणज (15), और (12) के गुणज (5) हैं, इसलिए संघ (30) और पूरक (60-30=30) है। साझा गुणजों को एक बार घटाएँ।

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Question 9/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cap B\cap C\)=9), केवल \(A\cap B\) में (14), केवल \(B\cap C\) में (11), और केवल \(C\cap A\) में (13) तत्व हैं, तो (n(\(A\cap B\)\cup\(B\cap C\)\cup\(C\cap A\))) कितना है?

If (n\(A\cap B\cap C\)=9), only \(A\cap B\) has (14), only \(B\cap C\) has (11), and only \(C\cap A\) has (13) elements, then what is (n(\(A\cap B\)\cup\(B\cap C\)\cup\(C\cap A\)))?

Explanation opens after your attempt

Correct Answer

A. (47)

Step 1

Concept

Elements in at least two sets are (14+11+13+9=47). In the Venn diagram, count the centre only once.

Step 2

Why this answer is correct

The correct answer is A. (47). Elements in at least two sets are (14+11+13+9=47). In the Venn diagram, count the centre only once.

Step 3

Exam Tip

कम से कम दो समुच्चयों में आने वाले तत्व (14+11+13+9=47) हैं। वेन आरेख में केंद्र को एक बार ही गिनें।

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Question 10/150 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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Question 11/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cup B\)=76), (n(A-B)=31) और (n(B-A)=27) है, तो (n\(A\cap B\)) कितना होगा?

If (n\(A\cup B\)=76), (n(A-B)=31) and (n(B-A)=27), then what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (18)

Step 1

Concept

The union is the sum of three disjoint parts, so the intersection is (76-31-27=18). For region-based questions, split the Venn diagram into parts.

Step 2

Why this answer is correct

The correct answer is A. (18). The union is the sum of three disjoint parts, so the intersection is (76-31-27=18). For region-based questions, split the Venn diagram into parts.

Step 3

Exam Tip

संघ तीन अलग भागों का योग है, इसलिए प्रतिच्छेद (76-31-27=18) है। क्षेत्र आधारित प्रश्नों में वेन आरेख को भागों में बाँटें।

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Question 12/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

वेन आरेख में (A) के केवल भाग में (23), (B) के केवल भाग में (17), (C) के केवल भाग में (19), केवल दो-दो के भागों में (8,9,10) और केंद्र में (5) हैं। (n\(A\cup B\cup C\)) कितना है?

In a Venn diagram, only (A) has (23), only (B) has (17), only (C) has (19), the only two-set regions have (8,9,10), and the centre has (5). What is (n\(A\cup B\cup C\))?

Explanation opens after your attempt

Correct Answer

A. (91)

Step 1

Concept

The union is the sum of all disjoint inside regions (23+17+19+8+9+10+5=91). Add each separate region exactly once.

Step 2

Why this answer is correct

The correct answer is A. (91). The union is the sum of all disjoint inside regions (23+17+19+8+9+10+5=91). Add each separate region exactly once.

Step 3

Exam Tip

संघ सभी अंदरूनी अलग क्षेत्रों का योग (23+17+19+8+9+10+5=91) है। अलग क्षेत्रों को एक-एक बार जोड़ना सही तरीका है।

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Question 13/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि \(A\subseteq B\), (n(A)=32), (n(B)=57) और (n(U)=90) है, तो (n(B-A)) कितना होगा?

If \(A\subseteq B\), (n(A)=32), (n(B)=57) and (n(U)=90), then what is (n(B-A))?

Explanation opens after your attempt

Correct Answer

A. (25)

Step 1

Concept

Since \(A\subseteq B\), (B-A) has (57-32=25) elements. In subset diagrams, the smaller circle lies inside the larger one.

Step 2

Why this answer is correct

The correct answer is A. (25). Since \(A\subseteq B\), (B-A) has (57-32=25) elements. In subset diagrams, the smaller circle lies inside the larger one.

Step 3

Exam Tip

क्योंकि \(A\subseteq B\), इसलिए (B-A) में (57-32=25) तत्व होंगे। उपसमुच्चय वाले आरेख में छोटा वृत्त बड़े के भीतर होता है।

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Question 14/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि \(A\cap B=\varnothing\), (n(A)=41), (n(B)=39) और (n(U)=100) है, तो (n(\(A\cup B\)')) कितना है?

If \(A\cap B=\varnothing\), (n(A)=41), (n(B)=39) and (n(U)=100), then what is (n(\(A\cup B\)'))?

Explanation opens after your attempt

Correct Answer

A. (20)

Step 1

Concept

For disjoint sets, (n\(A\cup B\)=41+39=80), so the complement is (20). When sets are disjoint, take the intersection as zero.

Step 2

Why this answer is correct

The correct answer is A. (20). For disjoint sets, (n\(A\cup B\)=41+39=80), so the complement is (20). When sets are disjoint, take the intersection as zero.

Step 3

Exam Tip

असंबद्ध समुच्चयों में (n\(A\cup B\)=41+39=80), इसलिए पूरक (20) है। असंबद्ध होने पर प्रतिच्छेद शून्य मानें।

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Question 15/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

किसी परीक्षा में (120) विद्यार्थियों में से (72) गणित, (64) भौतिकी और (38) दोनों पढ़ते हैं। केवल एक विषय पढ़ने वालों की संख्या कितनी है?

In an exam group of (120) students, (72) study Mathematics, (64) study Physics and (38) study both. How many study exactly one subject?

Explanation opens after your attempt

Correct Answer

A. (60)

Step 1

Concept

Exactly one subject is ((72-38)+(64-38)=60). For exactly one, subtract the common part from both sides.

Step 2

Why this answer is correct

The correct answer is A. (60). Exactly one subject is ((72-38)+(64-38)=60). For exactly one, subtract the common part from both sides.

Step 3

Exam Tip

केवल एक विषय ((72-38)+(64-38)=60) है। ठीक एक में साझा भाग को दोनों तरफ से घटाएँ।

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Question 16/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(A)=45), (n(B)=52), (n\(A\cup B\)=73) है, तो (n\(A\triangle B\)) कितना होगा, जहाँ \(A\triangle B=(A-B)\cup(B-A)\)?

If (n(A)=45), (n(B)=52), (n\(A\cup B\)=73), then what is (n\(A\triangle B\)), where \(A\triangle B=(A-B)\cup(B-A)\)?

Explanation opens after your attempt

Correct Answer

A. (49)

Step 1

Concept

First (n\(A\cap B\)=45+52-73=24), then (n\(A\triangle B\)=73-24=49). The symmetric difference excludes the common part.

Step 2

Why this answer is correct

The correct answer is A. (49). First (n\(A\cap B\)=45+52-73=24), then (n\(A\triangle B\)=73-24=49). The symmetric difference excludes the common part.

Step 3

Exam Tip

पहले (n\(A\cap B\)=45+52-73=24), फिर (n\(A\triangle B\)=73-24=49) है। सममित अंतर में साझा भाग शामिल नहीं होता।

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Question 17/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(U)=110), (n(A)=58), (n(B)=49) और (n(A-B)=21) है, तो (n(\(A\cup B\)')) कितना है?

If (n(U)=110), (n(A)=58), (n(B)=49) and (n(A-B)=21), then what is (n(\(A\cup B\)'))?

Explanation opens after your attempt

Correct Answer

A. (24)

Step 1

Concept

(n\(A\cap B\)=58-21=37), so (n\(A\cup B\)=58+49-37=70) and outside is (110-70=40). Check calculations carefully to avoid option traps.

Step 2

Why this answer is correct

The correct answer is A. (24). (n\(A\cap B\)=58-21=37), so (n\(A\cup B\)=58+49-37=70) and outside is (110-70=40). Check calculations carefully to avoid option traps.

Step 3

Exam Tip

(n\(A\cap B\)=58-21=37), इसलिए (n\(A\cup B\)=58+49-37=70) और बाहर (40) नहीं बल्कि (110-70=40) होगा। सही विकल्पों में त्रुटि से बचने के लिए गणना जाँचें।

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Question 18/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(U)=110), (n(A)=58), (n(B)=49) और (n(A-B)=21) है, तो (n(\(A\cup B\)')) के लिए सही मान चुनें।

If (n(U)=110), (n(A)=58), (n(B)=49) and (n(A-B)=21), choose the correct value of (n(\(A\cup B\)')).

Explanation opens after your attempt

Correct Answer

A. (40)

Step 1

Concept

\(A\cap B\) has (58-21=37) elements, so the union is (70) and the complement is (40). Fill inner regions first and then find the outside part.

Step 2

Why this answer is correct

The correct answer is A. (40). \(A\cap B\) has (58-21=37) elements, so the union is (70) and the complement is (40). Fill inner regions first and then find the outside part.

Step 3

Exam Tip

\(A\cap B\) में (58-21=37) तत्व हैं, इसलिए संघ (70) और पूरक (40) है। पहले आरेख के अंदर के क्षेत्र भरें फिर बाहर का भाग निकालें।

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Question 19/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

तीन विषयों के सर्वे में (n(M)=60), (n(P)=54), (n(C)=50), (n\(M\cap P\)=25), (n\(P\cap C\)=22), (n\(C\cap M\)=20), (n\(M\cap P\cap C\)=10) है। केवल (M) पढ़ने वाले कितने हैं?

In a survey of three subjects (n(M)=60), (n(P)=54), (n(C)=50), (n\(M\cap P\)=25), (n\(P\cap C\)=22), (n\(C\cap M\)=20), (n\(M\cap P\cap C\)=10). How many study only (M)?

Explanation opens after your attempt

Correct Answer

A. (25)

Step 1

Concept

Only (M=60-25-20+10=25). In three sets, the centre is subtracted twice and must be added back.

Step 2

Why this answer is correct

The correct answer is A. (25). Only (M=60-25-20+10=25). In three sets, the centre is subtracted twice and must be added back.

Step 3

Exam Tip

केवल (M=60-25-20+10=25) है। तीन समुच्चयों में केंद्र को घटाने के बाद वापस जोड़ना पड़ता है।

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Question 20/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि केवल (A) में (12), केवल (B) में (15), केवल (C) में (18), केवल \(A\cap B\) में (9), केवल \(B\cap C\) में (7), केवल \(C\cap A\) में (6), और \(A\cap B\cap C\) में (4) हैं, तो (n(A\cap\(B\cup C\))) कितना है?

If only (A) has (12), only (B) has (15), only (C) has (18), only \(A\cap B\) has (9), only \(B\cap C\) has (7), only \(C\cap A\) has (6), and \(A\cap B\cap C\) has (4), then what is (n(A\cap\(B\cup C\)))?

Explanation opens after your attempt

Correct Answer

A. (19)

Step 1

Concept

(A\cap\(B\cup C\)) includes \(A\cap B\), \(A\cap C\), and the centre, so (9+6+4=19). The only (A) region is not included.

Step 2

Why this answer is correct

The correct answer is A. (19). (A\cap\(B\cup C\)) includes \(A\cap B\), \(A\cap C\), and the centre, so (9+6+4=19). The only (A) region is not included.

Step 3

Exam Tip

(A\cap\(B\cup C\)) में \(A\cap B\), \(A\cap C\) और केंद्र आते हैं, इसलिए (9+6+4=19) है। केवल (A) इसमें शामिल नहीं होगा।

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Question 21/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

कौन सा वेन आरेखीय संबंध (A-\(B\cup C\)) को दर्शाता है?

Which Venn diagram region represents (A-\(B\cup C\))?

Explanation opens after your attempt

Correct Answer

A. केवल (A) का भागOnly the part of (A)

Step 1

Concept

(A-\(B\cup C\)) means being in (A) but outside both (B) and (C). In the Venn diagram, it is the only (A) region.

Step 2

Why this answer is correct

The correct answer is A. केवल (A) का भाग / Only the part of (A). (A-\(B\cup C\)) means being in (A) but outside both (B) and (C). In the Venn diagram, it is the only (A) region.

Step 3

Exam Tip

(A-\(B\cup C\)) का अर्थ (A) में रहकर (B) और (C) से बाहर होना है। वेन आरेख में यह केवल (A) वाला क्षेत्र है।

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Question 22/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (A) और (B) अतिव्यापी समुच्चय हैं, तो \(A\cup B\) के वेन आरेख में कौन सा भाग छायांकित होगा?

If (A) and (B) are overlapping sets, which region is shaded for \(A\cup B\) in a Venn diagram?

Explanation opens after your attempt

Correct Answer

A. (A) और (B) दोनों वृत्तों का पूरा अंदरूनी भागEntire inside of both (A) and (B) circles

Step 1

Concept

\(A\cup B\) means (A) or (B) or both. Therefore, all inside regions of both circles are shaded.

Step 2

Why this answer is correct

The correct answer is A. (A) और (B) दोनों वृत्तों का पूरा अंदरूनी भाग / Entire inside of both (A) and (B) circles. \(A\cup B\) means (A) or (B) or both. Therefore, all inside regions of both circles are shaded.

Step 3

Exam Tip

\(A\cup B\) का अर्थ (A) या (B) या दोनों है। इसलिए दोनों वृत्तों के सभी अंदरूनी क्षेत्र छायांकित होंगे।

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Question 23/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cap B\)=n(A)) और (n(A)>0) है, तो वेन आरेख में (A) और (B) का संबंध क्या होगा?

If (n\(A\cap B\)=n(A)) and (n(A)>0), what is the relation between (A) and (B) in a Venn diagram?

Explanation opens after your attempt

Correct Answer

A. \(A\subseteq B\)

Step 1

Concept

If all of (A) is common with (B), then (A) lies completely inside (B). Hence \(A\subseteq B\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(A\subseteq B\). If all of (A) is common with (B), then (A) lies completely inside (B). Hence \(A\subseteq B\) is correct.

Step 3

Exam Tip

यदि (A) का पूरा भाग (B) से साझा है, तो (A) पूरी तरह (B) के अंदर है। इसलिए \(A\subseteq B\) सही है।

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Question 24/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

(n(U)=95), (n(A')=47), (n(B')=52) और (n\(A\cap B\)=18) है। (n\(A\cup B\)) कितना है?

(n(U)=95), (n(A')=47), (n(B')=52) and (n\(A\cap B\)=18). What is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (66)

Step 1

Concept

(n(A)=95-47=48) and (n(B)=95-52=43), so the union is (48+43-18=73), not (66). Recheck the formula before matching options.

Step 2

Why this answer is correct

The correct answer is A. (66). (n(A)=95-47=48) and (n(B)=95-52=43), so the union is (48+43-18=73), not (66). Recheck the formula before matching options.

Step 3

Exam Tip

(n(A)=95-47=48) और (n(B)=95-52=43), इसलिए संघ (48+43-18=73) नहीं बल्कि (73) है। विकल्पों से मिलान करते समय सूत्र दोबारा देखें।

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Question 25/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(U)=95), (n(A')=47), (n(B')=52) और (n\(A\cap B\)=18) है, तो (n\(A\cup B\)) का सही मान चुनें।

If (n(U)=95), (n(A')=47), (n(B')=52) and (n\(A\cap B\)=18), choose the correct value of (n\(A\cup B\)).

Explanation opens after your attempt

Correct Answer

A. (73)

Step 1

Concept

(n(A)=48), (n(B)=43), so (n\(A\cup B\)=48+43-18=73). First obtain the original set sizes from complements.

Step 2

Why this answer is correct

The correct answer is A. (73). (n(A)=48), (n(B)=43), so (n\(A\cup B\)=48+43-18=73). First obtain the original set sizes from complements.

Step 3

Exam Tip

(n(A)=48), (n(B)=43), इसलिए (n\(A\cup B\)=48+43-18=73) है। पूरक से मूल समुच्चय निकालना पहला कदम रखें।

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Question 26/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cap B'\)=24), (n\(A'\cap B\)=31) और (n\(A\cap B\)=16) है, तो (n\(A\cup B\)) कितना है?

If (n\(A\cap B'\)=24), (n\(A'\cap B\)=31) and (n\(A\cap B\)=16), then what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (71)

Step 1

Concept

The three disjoint parts of the union are (24), (31), and (16), whose sum is (71). In a Venn diagram, separate regions can be added directly.

Step 2

Why this answer is correct

The correct answer is A. (71). The three disjoint parts of the union are (24), (31), and (16), whose sum is (71). In a Venn diagram, separate regions can be added directly.

Step 3

Exam Tip

संघ के तीन अलग भाग (24), (31) और (16) हैं, जिनका योग (71) है। वेन आरेख में अलग-अलग क्षेत्रों को सीधे जोड़ सकते हैं।

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Question 27/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

किसी सर्वे में (90) लोगों में (52) चाय, (47) कॉफी और (25) दोनों पसंद करते हैं। न चाय न कॉफी पसंद करने वाले कितने हैं?

In a survey of (90) people, (52) like tea, (47) like coffee and (25) like both. How many like neither tea nor coffee?

Explanation opens after your attempt

Correct Answer

A. (16)

Step 1

Concept

The union is (52+47-25=74), so outside is (90-74=16). In such questions, neither means the complement.

Step 2

Why this answer is correct

The correct answer is A. (16). The union is (52+47-25=74), so outside is (90-74=16). In such questions, neither means the complement.

Step 3

Exam Tip

संघ (52+47-25=74) है, इसलिए बाहर (90-74=16) है। ऐसे प्रश्नों में किसी भी नहीं का अर्थ पूरक होता है।

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Question 28/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

(100) विद्यार्थियों में (40) केवल (A), (28) केवल (B) और (12) दोनों में हैं। कम से कम एक में आने वाले कितने हैं?

Among (100) students, (40) are only in (A), (28) are only in (B), and (12) are in both. How many are in at least one?

Explanation opens after your attempt

Correct Answer

A. (80)

Step 1

Concept

At least one means the union, so (40+28+12=80). Add the only regions and the both region separately.

Step 2

Why this answer is correct

The correct answer is A. (80). At least one means the union, so (40+28+12=80). Add the only regions and the both region separately.

Step 3

Exam Tip

कम से कम एक का अर्थ संघ है, इसलिए (40+28+12=80) है। केवल और दोनों वाले भागों को अलग-अलग जोड़ें।

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Question 29/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि \(A\cap B\cap C=\varnothing\), (n(A)=30), (n(B)=34), (n(C)=36), (n\(A\cap B\)=8), (n\(B\cap C\)=10), (n\(C\cap A\)=6) है, तो (n\(A\cup B\cup C\)) कितना है?

If \(A\cap B\cap C=\varnothing\), (n(A)=30), (n(B)=34), (n(C)=36), (n\(A\cap B\)=8), (n\(B\cap C\)=10), (n\(C\cap A\)=6), then what is (n\(A\cup B\cup C\))?

Explanation opens after your attempt

Correct Answer

A. (76)

Step 1

Concept

The union of three sets is (30+34+36-8-10-6+0=76). If the centre is empty, keep the final addition as (0).

Step 2

Why this answer is correct

The correct answer is A. (76). The union of three sets is (30+34+36-8-10-6+0=76). If the centre is empty, keep the final addition as (0).

Step 3

Exam Tip

तीन समुच्चयों का संघ (30+34+36-8-10-6+0=76) है। यदि केंद्र खाली हो तो अंतिम जोड़ (0) रखें।

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Question 30/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cup B\cup C\)=118), (n(A)=45), (n(B)=50), (n(C)=55), (n\(A\cap B\)=18), (n\(B\cap C\)=20), (n\(C\cap A\)=16) है, तो (n\(A\cap B\cap C\)) कितना है?

If (n\(A\cup B\cup C\)=118), (n(A)=45), (n(B)=50), (n(C)=55), (n\(A\cap B\)=18), (n\(B\cap C\)=20), (n\(C\cap A\)=16), then what is (n\(A\cap B\cap C\))?

Explanation opens after your attempt

Correct Answer

A. (22)

Step 1

Concept

Using the formula (118=45+50+55-18-20-16+x), so (x=22). Let the unknown centre be (x) to form an equation easily.

Step 2

Why this answer is correct

The correct answer is A. (22). Using the formula (118=45+50+55-18-20-16+x), so (x=22). Let the unknown centre be (x) to form an equation easily.

Step 3

Exam Tip

सूत्र में (118=45+50+55-18-20-16+x), इसलिए (x=22) है। अज्ञात केंद्र को (x) मानकर समीकरण बनाना आसान है।

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Question 31/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(A)=3x+2), (n(B)=2x+5), (n\(A\cap B\)=x+1) और (n\(A\cup B\)=30) है, तो (x) का मान कितना है?

If (n(A)=3x+2), (n(B)=2x+5), (n\(A\cap B\)=x+1) and (n\(A\cup B\)=30), then what is (x)?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

(30=(3x+2)+(2x+5)-(x+1)=4x+6), so (x=6). In algebraic Venn questions, first apply the union formula.

Step 2

Why this answer is correct

The correct answer is A. (6). (30=(3x+2)+(2x+5)-(x+1)=4x+6), so (x=6). In algebraic Venn questions, first apply the union formula.

Step 3

Exam Tip

(30=(3x+2)+(2x+5)-(x+1)=4x+6), इसलिए (x=6) है। बीजगणितीय वेन प्रश्न में पहले संघ का सूत्र लगाएँ।

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Question 32/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(A-B)=2x+3), (n(B-A)=x+7), (n\(A\cap B\)=x-1) और (n\(A\cup B\)=45) है, तो (x) कितना है?

If (n(A-B)=2x+3), (n(B-A)=x+7), (n\(A\cap B\)=x-1) and (n\(A\cup B\)=45), then what is (x)?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

The union is (2x+3+x+7+x-1=4x+9=45), so (x=9). The sum of disjoint regions directly gives the union.

Step 2

Why this answer is correct

The correct answer is A. (9). The union is (2x+3+x+7+x-1=4x+9=45), so (x=9). The sum of disjoint regions directly gives the union.

Step 3

Exam Tip

संघ (2x+3+x+7+x-1=4x+9=45), इसलिए (x=9) है। अलग क्षेत्रों का योग सीधे संघ देता है।

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Question 33/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

\(यदि (A={x:x\in \mathbb{N},x\le 12}), (B={x:x\) is even\(,x\le 12}) और (C={x:x\) is a multiple of \(3,x\le 12}) है, तो (n(B\cap C)) कितना है\)?

\(If (A={x:x\in \mathbb{N},x\le 12}), (B={x:x\) is even\(,x\le 12}) and (C={x:x\) is a multiple of \(3,x\le 12}), then what is (n(B\cap C))\)?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

\(B\cap C\) contains (6) and (12), so the count is (2). For intersection, both conditions must be satisfied together.

Step 2

Why this answer is correct

The correct answer is A. (2). \(B\cap C\) contains (6) and (12), so the count is (2). For intersection, both conditions must be satisfied together.

Step 3

Exam Tip

\(B\cap C\) में (6) और (12) हैं, इसलिए संख्या (2) है। प्रतिच्छेद के लिए दोनों शर्तें साथ में पूरी होनी चाहिए।

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Question 34/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि \(U={1,2,\ldots,20}\), (A) अभाज्य संख्याओं का समुच्चय और (B) विषम संख्याओं का समुच्चय है, तो (A-B) क्या होगा?

If \(U={1,2,\ldots,20}\), (A) is the set of prime numbers and (B) is the set of odd numbers, then what is (A-B)?

Explanation opens after your attempt

Correct Answer

A. ({2})

Step 1

Concept

(A-B) contains primes that are not odd, so only (2) remains. In set difference, remove the elements of the second set.

Step 2

Why this answer is correct

The correct answer is A. ({2}). (A-B) contains primes that are not odd, so only (2) remains. In set difference, remove the elements of the second set.

Step 3

Exam Tip

(A-B) में वे अभाज्य होंगे जो विषम नहीं हैं, इसलिए केवल (2) बचेगा। समुच्चय अंतर में दूसरे समुच्चय के तत्व हटा दें।

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Question 35/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि \(U={1,2,\ldots,30}\), (A) (2) के गुणजों का और (B) (5) के गुणजों का समुच्चय है, तो (n\(A\cup B\)) कितना है?

If \(U={1,2,\ldots,30}\), (A) is the set of multiples of (2) and (B) is the set of multiples of (5), then what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (18)

Step 1

Concept

Multiples of (2) are (15), multiples of (5) are (6), and multiples of (10) are (3), so the union is (15+6-3=18). Subtract common multiples once.

Step 2

Why this answer is correct

The correct answer is A. (18). Multiples of (2) are (15), multiples of (5) are (6), and multiples of (10) are (3), so the union is (15+6-3=18). Subtract common multiples once.

Step 3

Exam Tip

(2) के गुणज (15), (5) के गुणज (6), और (10) के गुणज (3) हैं, इसलिए संघ (15+6-3=18) है। साझा गुणजों को एक बार घटाएँ।

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Question 36/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि \(U={1,2,\ldots,50}\), (A) (4) के गुणजों का और (B) (6) के गुणजों का समुच्चय है, तो (n\(A\cap B\)) कितना है?

If \(U={1,2,\ldots,50}\), (A) is the set of multiples of (4) and (B) is the set of multiples of (6), then what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

Common multiples are multiples of (\operatorname{lcm}(4,6)=12), namely (12,24,36,48). Hence the count is (4).

Step 2

Why this answer is correct

The correct answer is A. (4). Common multiples are multiples of (\operatorname{lcm}(4,6)=12), namely (12,24,36,48). Hence the count is (4).

Step 3

Exam Tip

साझा गुणज (\operatorname{lcm}(4,6)=12) के गुणज होंगे, जो (12,24,36,48) हैं। इसलिए संख्या (4) है।

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Question 37/150 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 38/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cup B\)=84) और (n\(A\cap B\)=27) है, तो (n(A-B)+n(B-A)) कितना है?

If (n\(A\cup B\)=84) and (n\(A\cap B\)=27), then what is (n(A-B)+n(B-A))?

Explanation opens after your attempt

Correct Answer

A. (57)

Step 1

Concept

The sum of the two only regions is union minus intersection (84-27=57). This is also the size of the symmetric difference.

Step 2

Why this answer is correct

The correct answer is A. (57). The sum of the two only regions is union minus intersection (84-27=57). This is also the size of the symmetric difference.

Step 3

Exam Tip

दोनों केवल भागों का योग संघ से प्रतिच्छेद घटाकर (84-27=57) है। यह सममित अंतर की संख्या भी है।

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Question 39/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

किसी सर्वे में (160) लोगों में (92) मोबाइल, (78) लैपटॉप और (51) दोनों रखते हैं। ठीक एक उपकरण रखने वाले कितने हैं?

In a survey of (160) people, (92) have a mobile, (78) have a laptop and (51) have both. How many have exactly one device?

Explanation opens after your attempt

Correct Answer

A. (68)

Step 1

Concept

Exactly one is ((92-51)+(78-51)=68). People having both are not counted in exactly one.

Step 2

Why this answer is correct

The correct answer is A. (68). Exactly one is ((92-51)+(78-51)=68). People having both are not counted in exactly one.

Step 3

Exam Tip

ठीक एक (=(92-51)+(78-51)=68) है। दोनों रखने वालों को ठीक एक में नहीं गिना जाता।

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Question 40/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (70) में से (45) विद्यार्थी हिंदी, (40) अंग्रेजी और (30) दोनों पढ़ते हैं, तो कम से कम एक भाषा पढ़ने वाले कितने हैं?

If out of (70) students, (45) study Hindi, (40) study English and (30) study both, then how many study at least one language?

Explanation opens after your attempt

Correct Answer

A. (55)

Step 1

Concept

At least one is (45+40-30=55). The intersection is subtracted to avoid double counting.

Step 2

Why this answer is correct

The correct answer is A. (55). At least one is (45+40-30=55). The intersection is subtracted to avoid double counting.

Step 3

Exam Tip

कम से कम एक (45+40-30=55) है। प्रतिच्छेद को दो बार गिनने से बचने के लिए घटाते हैं।

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Question 41/150 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 42/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि \(A\cap B=\varnothing\) और \(B\cap C=\varnothing\), तो क्या \(A\cap C=\varnothing\) अवश्य होगा?

If \(A\cap B=\varnothing\) and \(B\cap C=\varnothing\), must \(A\cap C=\varnothing\)?

Explanation opens after your attempt

Correct Answer

A. नहीं, (A) और (C) अतिव्यापी हो सकते हैंNo, (A) and (C) may overlap

Step 1

Concept

(B) can be separate from both, while (A) and (C) may still overlap. In Venn diagrams, understand independent relations separately.

Step 2

Why this answer is correct

The correct answer is A. नहीं, (A) और (C) अतिव्यापी हो सकते हैं / No, (A) and (C) may overlap. (B) can be separate from both, while (A) and (C) may still overlap. In Venn diagrams, understand independent relations separately.

Step 3

Exam Tip

(B) दोनों से अलग हो सकता है, लेकिन (A) और (C) आपस में मिल सकते हैं। वेन आरेख में स्वतंत्र संबंधों को अलग-अलग समझें।

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Question 43/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (A) और (B) असंबद्ध हैं, तो (\(A\cup B\)') किसके बराबर है?

If (A) and (B) are disjoint, then (\(A\cup B\)') is equal to what?

Explanation opens after your attempt

Correct Answer

A. \(A'\cap B'\)

Step 1

Concept

By De Morgan's law, (\(A\cup B\)'=A'\cap B'). This rule is true for both disjoint and general cases.

Step 2

Why this answer is correct

The correct answer is A. \(A'\cap B'\). By De Morgan's law, (\(A\cup B\)'=A'\cap B'). This rule is true for both disjoint and general cases.

Step 3

Exam Tip

डी मॉर्गन नियम के अनुसार (\(A\cup B\)'=A'\cap B') है। यह नियम असंबद्ध और सामान्य दोनों स्थितियों में सही है।

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Question 44/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(U)=60), (n(A)=35), (n(B)=32) है, तो (n\(A\cap B\)) का न्यूनतम संभव मान कितना है?

If (n(U)=60), (n(A)=35), (n(B)=32), then what is the minimum possible value of (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (7)

Step 1

Concept

The minimum intersection is (35+32-60=7). If the sum exceeds (U), that much overlap is necessary.

Step 2

Why this answer is correct

The correct answer is A. (7). The minimum intersection is (35+32-60=7). If the sum exceeds (U), that much overlap is necessary.

Step 3

Exam Tip

न्यूनतम प्रतिच्छेद (35+32-60=7) होगा। यदि योग (U) से अधिक हो तो उतना अतिव्यापन अनिवार्य है।

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Question 45/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(U)=100), (n(A)=64), (n(B)=58) है, तो (n\(A\cup B\)) का न्यूनतम संभव मान कितना है?

If (n(U)=100), (n(A)=64), (n(B)=58), then what is the minimum possible value of (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (64)

Step 1

Concept

The minimum union can be as small as the larger set, which is (64). This happens when \(B\subseteq A\) is possible.

Step 2

Why this answer is correct

The correct answer is A. (64). The minimum union can be as small as the larger set, which is (64). This happens when \(B\subseteq A\) is possible.

Step 3

Exam Tip

संघ का न्यूनतम मान बड़े समुच्चय जितना हो सकता है, यानी (64)। यह तब होगा जब \(B\subseteq A\) हो सकता है।

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Question 46/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(A)=46), (n(B)=39) है, तो (n\(A\cap B\)) का अधिकतम संभव मान कितना है?

If (n(A)=46), (n(B)=39), then what is the maximum possible value of (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (39)

Step 1

Concept

The maximum intersection cannot exceed the smaller set, so it is (39). In maximum overlap, the smaller set can lie inside the larger set.

Step 2

Why this answer is correct

The correct answer is A. (39). The maximum intersection cannot exceed the smaller set, so it is (39). In maximum overlap, the smaller set can lie inside the larger set.

Step 3

Exam Tip

प्रतिच्छेद का अधिकतम मान छोटे समुच्चय से अधिक नहीं हो सकता, इसलिए (39) है। अधिकतम अतिव्यापन में छोटा समुच्चय बड़े में समा सकता है।

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Question 47/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(A)=30), (n(B)=28) और (n\(A\cup B\)=52) है, तो (n(A-B)) कितना है?

If (n(A)=30), (n(B)=28) and (n\(A\cup B\)=52), then what is (n(A-B))?

Explanation opens after your attempt

Correct Answer

A. (24)

Step 1

Concept

First (n\(A\cap B\)=30+28-52=6), then (A-B=30-6=24). Identify the common part before finding difference.

Step 2

Why this answer is correct

The correct answer is A. (24). First (n\(A\cap B\)=30+28-52=6), then (A-B=30-6=24). Identify the common part before finding difference.

Step 3

Exam Tip

पहले (n\(A\cap B\)=30+28-52=6), फिर (A-B=30-6=24) है। अंतर निकालने से पहले साझा भाग पहचानें।

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Question 48/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(A-B)=18), (n(B-C)=25), (n(C-A)=20) दिए हों, तो क्या केवल इनसे (n\(A\cup B\cup C\)) निश्चित किया जा सकता है?

If (n(A-B)=18), (n(B-C)=25), (n(C-A)=20) are given, can (n\(A\cup B\cup C\)) be determined uniquely from only these?

Explanation opens after your attempt

Correct Answer

A. नहीं, साझा क्षेत्रों की जानकारी चाहिएNo, information about common regions is needed

Step 1

Concept

These differences do not give all Venn regions. To find the union, complete information about common and only regions is needed.

Step 2

Why this answer is correct

The correct answer is A. नहीं, साझा क्षेत्रों की जानकारी चाहिए / No, information about common regions is needed. These differences do not give all Venn regions. To find the union, complete information about common and only regions is needed.

Step 3

Exam Tip

इन अंतरों से सभी वेन क्षेत्रों की जानकारी नहीं मिलती। संघ के लिए साझा और केवल क्षेत्रों का पूरा विवरण चाहिए।

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Question 49/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

एक वेन आरेख में (n\(A\cap B\)=14) और (n\(A\cap B\cap C\)=6) है। केवल \(A\cap B\) में कितने तत्व हैं?

In a Venn diagram, (n\(A\cap B\)=14) and (n\(A\cap B\cap C\)=6). How many elements are only in \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

Only \(A\cap B\) has (14-6=8) elements. A two-set intersection includes the centre also.

Step 2

Why this answer is correct

The correct answer is A. (8). Only \(A\cap B\) has (14-6=8) elements. A two-set intersection includes the centre also.

Step 3

Exam Tip

केवल \(A\cap B\) में (14-6=8) तत्व होंगे। दो-समुच्चय प्रतिच्छेद में केंद्र भी शामिल होता है।

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Question 50/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cup B\cup C\)=140), ठीक एक समुच्चय में (65) और ठीक दो समुच्चयों में (51) तत्व हैं, तो (n\(A\cap B\cap C\)) कितना है?

If (n\(A\cup B\cup C\)=140), exactly one set has (65) elements and exactly two sets have (51) elements, then what is (n\(A\cap B\cap C\))?

Explanation opens after your attempt

Correct Answer

A. (24)

Step 1

Concept

Union equals exactly one plus exactly two plus all three, so all three is (140-65-51=24). In region-sum questions, keep the parts separate.

Step 2

Why this answer is correct

The correct answer is A. (24). Union equals exactly one plus exactly two plus all three, so all three is (140-65-51=24). In region-sum questions, keep the parts separate.

Step 3

Exam Tip

संघ (=) ठीक एक (+) ठीक दो (+) तीनों, इसलिए तीनों (140-65-51=24) है। क्षेत्र-आधारित योग प्रश्नों में हिस्सों को अलग रखें।

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Question 51/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

एक सर्वे में (n(U)=210), (n(A)=96), (n(B)=88), (n(C)=74), (n\(A\cap B\)=39), (n\(B\cap C\)=31), (n\(C\cap A\)=28) और (n\(A\cap B\cap C\)=14) है। किसी भी समुच्चय में न आने वालों की संख्या कितनी है?

In a survey (n(U)=210), (n(A)=96), (n(B)=88), (n(C)=74), (n\(A\cap B\)=39), (n\(B\cap C\)=31), (n\(C\cap A\)=28) and (n\(A\cap B\cap C\)=14). How many are in none of the sets?

Explanation opens after your attempt

Correct Answer

A. (36)

Step 1

Concept

(n\(A\cup B\cup C\)=96+88+74-39-31-28+14=174), so outside is (210-174=36). First find the union and then take the complement.

Step 2

Why this answer is correct

The correct answer is A. (36). (n\(A\cup B\cup C\)=96+88+74-39-31-28+14=174), so outside is (210-174=36). First find the union and then take the complement.

Step 3

Exam Tip

(n\(A\cup B\cup C\)=96+88+74-39-31-28+14=174), इसलिए बाहर (210-174=36) है। पहले संघ निकालकर ही पूरक लें।

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Question 52/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cup B\cup C\)=155), (n\(A\cup B\)=118), (n\(B\cup C\)=124), (n\(C\cup A\)=121) और (n(B)=64) है, तो (n(\(A\cap C\)-B)) कितना होगा?

If (n\(A\cup B\cup C\)=155), (n\(A\cup B\)=118), (n\(B\cup C\)=124), (n\(C\cup A\)=121) and (n(B)=64), then what is (n(\(A\cap C\)-B))?

Explanation opens after your attempt

Correct Answer

A. (30)

Step 1

Concept

(n(\(A\cap C\)-B)=n\(A\cup B\)+n\(B\cup C\)-n(B)-n\(A\cup B\cup C\)=118+124-64-155=23), not (30). Check the formula before matching options.

Step 2

Why this answer is correct

The correct answer is A. (30). (n(\(A\cap C\)-B)=n\(A\cup B\)+n\(B\cup C\)-n(B)-n\(A\cup B\cup C\)=118+124-64-155=23), not (30). Check the formula before matching options.

Step 3

Exam Tip

(n(\(A\cap C\)-B)=n\(A\cup B\)+n\(B\cup C\)-n(B)-n\(A\cup B\cup C\)=118+124-64-155=23) नहीं, इसलिए विकल्पों से पहले सूत्र जाँचें; सही क्षेत्र (155-118) और (155-124) जैसे बाहर वाले हिस्सों से नहीं निकलेगा।

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Question 53/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A)=78), (n(B)=69), (n(C)=63), (n\(A\cap B\)=30), (n\(B\cap C\)=25), (n\(C\cap A\)=21) और (n\(A\cap B\cap C\)=9) है, तो केवल (A) में कितने तत्व हैं?

If (n(A)=78), (n(B)=69), (n(C)=63), (n\(A\cap B\)=30), (n\(B\cap C\)=25), (n\(C\cap A\)=21) and (n\(A\cap B\cap C\)=9), then how many elements are only in (A)?

Explanation opens after your attempt

Correct Answer

A. (36)

Step 1

Concept

Only (A=78-30-21+9=36). In three sets, the centre is subtracted twice, so add it back.

Step 2

Why this answer is correct

The correct answer is A. (36). Only (A=78-30-21+9=36). In three sets, the centre is subtracted twice, so add it back.

Step 3

Exam Tip

केवल (A=78-30-21+9=36) है। तीन समुच्चयों में केंद्र दो बार घटता है इसलिए उसे वापस जोड़ें।

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Question 54/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

किसी वेन आरेख में केवल (A) में (18), केवल (B) में (22), केवल (C) में (16), केवल \(A\cap B\) में (11), केवल \(B\cap C\) में (13), केवल \(C\cap A\) में (9) और तीनों में (6) तत्व हैं। कम से कम दो समुच्चयों में आने वाले तत्व कितने हैं?

In a Venn diagram, only (A) has (18), only (B) has (22), only (C) has (16), only \(A\cap B\) has (11), only \(B\cap C\) has (13), only \(C\cap A\) has (9), and all three have (6) elements. How many elements are in at least two sets?

Explanation opens after your attempt

Correct Answer

A. (39)

Step 1

Concept

At least two sets contain (11+13+9+6=39) elements. In this type of question, the centre region is also included.

Step 2

Why this answer is correct

The correct answer is A. (39). At least two sets contain (11+13+9+6=39) elements. In this type of question, the centre region is also included.

Step 3

Exam Tip

कम से कम दो में (11+13+9+6=39) तत्व हैं। इस प्रकार के प्रश्न में तीनों वाला केंद्र भी शामिल होता है।

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Question 55/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cup B\)=112), (n(A-B)=43) और (n(B-A)=37) है, तो (n\(A\cap B\)) कितना होगा?

If (n\(A\cup B\)=112), (n(A-B)=43) and (n(B-A)=37), then what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (32)

Step 1

Concept

The union is the sum of three disjoint parts, so the intersection is (112-43-37=32). Count each separate region once in a Venn diagram.

Step 2

Why this answer is correct

The correct answer is A. (32). The union is the sum of three disjoint parts, so the intersection is (112-43-37=32). Count each separate region once in a Venn diagram.

Step 3

Exam Tip

संघ तीन अलग भागों का योग है, इसलिए प्रतिच्छेद (112-43-37=32) है। वेन आरेख में अलग क्षेत्रों को एक-एक बार गिनें।

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Question 56/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(U)=140), (n(A')=58), (n(B')=71) और (n\(A\cap B\)=34) है, तो (n\(A\cup B\)) कितना है?

If (n(U)=140), (n(A')=58), (n(B')=71) and (n\(A\cap B\)=34), then what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (117)

Step 1

Concept

(n(A)=140-58=82) and (n(B)=140-71=69), so the union is (82+69-34=117). Getting original sizes from complements is the first step.

Step 2

Why this answer is correct

The correct answer is A. (117). (n(A)=140-58=82) and (n(B)=140-71=69), so the union is (82+69-34=117). Getting original sizes from complements is the first step.

Step 3

Exam Tip

(n(A)=140-58=82) और (n(B)=140-71=69), इसलिए संघ (82+69-34=117) है। पूरक से मूल संख्या निकालना पहला कदम है।

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Question 57/150 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 58/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

एक कक्षा में (95) विद्यार्थियों में (56) गणित, (49) विज्ञान और (27) दोनों पढ़ते हैं। ठीक एक विषय पढ़ने वाले कितने हैं?

In a class of (95) students, (56) study Mathematics, (49) study Science and (27) study both. How many study exactly one subject?

Explanation opens after your attempt

Correct Answer

A. (51)

Step 1

Concept

Exactly one subject is ((56-27)+(49-27)=51). Do not include those who study both in exactly one.

Step 2

Why this answer is correct

The correct answer is A. (51). Exactly one subject is ((56-27)+(49-27)=51). Do not include those who study both in exactly one.

Step 3

Exam Tip

ठीक एक विषय ((56-27)+(49-27)=51) है। दोनों पढ़ने वालों को ठीक एक में शामिल न करें।

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Question 59/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A)=64), (n(B)=59) और (n\(A\cup B\)=91) है, तो (n\(A\triangle B\)) कितना है?

If (n(A)=64), (n(B)=59) and (n\(A\cup B\)=91), then what is (n\(A\triangle B\))?

Explanation opens after your attempt

Correct Answer

A. (59)

Step 1

Concept

First (n\(A\cap B\)=64+59-91=32), then (n\(A\triangle B\)=91-32=59). The symmetric difference does not include the common part.

Step 2

Why this answer is correct

The correct answer is A. (59). First (n\(A\cap B\)=64+59-91=32), then (n\(A\triangle B\)=91-32=59). The symmetric difference does not include the common part.

Step 3

Exam Tip

पहले (n\(A\cap B\)=64+59-91=32), फिर (n\(A\triangle B\)=91-32=59) है। सममित अंतर में साझा भाग नहीं आता।

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Question 60/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि \(A\subseteq B\), (n(B)=83), (n(A)=47) और (n(U)=120) है, तो (n(B-A)) कितना होगा?

If \(A\subseteq B\), (n(B)=83), (n(A)=47) and (n(U)=120), then what is (n(B-A))?

Explanation opens after your attempt

Correct Answer

A. (36)

Step 1

Concept

Since \(A\subseteq B\), (B-A=83-47=36). In a subset Venn diagram, the smaller circle lies inside the larger one.

Step 2

Why this answer is correct

The correct answer is A. (36). Since \(A\subseteq B\), (B-A=83-47=36). In a subset Venn diagram, the smaller circle lies inside the larger one.

Step 3

Exam Tip

क्योंकि \(A\subseteq B\), इसलिए (B-A=83-47=36) होगा। उपसमुच्चय वाले वेन आरेख में छोटा वृत्त बड़े के अंदर होता है।

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Question 61/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि \(A\cap B=\varnothing\), (n(A)=44), (n(B)=52) और (n(U)=130) है, तो (n(\(A\cup B\)')) कितना है?

If \(A\cap B=\varnothing\), (n(A)=44), (n(B)=52) and (n(U)=130), then what is (n(\(A\cup B\)'))?

Explanation opens after your attempt

Correct Answer

A. (34)

Step 1

Concept

For disjoint sets, the union is (44+52=96), so the complement is (130-96=34). Disjoint sets have zero common part.

Step 2

Why this answer is correct

The correct answer is A. (34). For disjoint sets, the union is (44+52=96), so the complement is (130-96=34). Disjoint sets have zero common part.

Step 3

Exam Tip

असंबद्ध समुच्चयों में संघ (44+52=96) है, इसलिए पूरक (130-96=34) है। असंबद्ध होने पर साझा भाग शून्य होता है।

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Question 62/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

तीन क्लबों में (n(A)=72), (n(B)=68), (n(C)=61), (n\(A\cap B\)=29), (n\(B\cap C\)=24), (n\(C\cap A\)=26) और (n\(A\cap B\cap C\)=11) है। केवल (B) में आने वाले सदस्य कितने हैं?

In three clubs (n(A)=72), (n(B)=68), (n(C)=61), (n\(A\cap B\)=29), (n\(B\cap C\)=24), (n\(C\cap A\)=26) and (n\(A\cap B\cap C\)=11). How many members are only in (B)?

Explanation opens after your attempt

Correct Answer

A. (26)

Step 1

Concept

Only (B=68-29-24+11=26). While subtracting two intersections, the centre is removed twice.

Step 2

Why this answer is correct

The correct answer is A. (26). Only (B=68-29-24+11=26). While subtracting two intersections, the centre is removed twice.

Step 3

Exam Tip

केवल (B=68-29-24+11=26) है। दो प्रतिच्छेद घटाते समय केंद्र दो बार घट जाता है।

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Question 63/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cup B\cup C\)=135), ठीक एक समुच्चय में (58) और ठीक दो समुच्चयों में (49) तत्व हैं, तो (n\(A\cap B\cap C\)) कितना है?

If (n\(A\cup B\cup C\)=135), exactly one set has (58) elements and exactly two sets have (49) elements, then what is (n\(A\cap B\cap C\))?

Explanation opens after your attempt

Correct Answer

A. (28)

Step 1

Concept

Union equals exactly one plus exactly two plus all three, so all three is (135-58-49=28). In region-based questions, keep the parts separate.

Step 2

Why this answer is correct

The correct answer is A. (28). Union equals exactly one plus exactly two plus all three, so all three is (135-58-49=28). In region-based questions, keep the parts separate.

Step 3

Exam Tip

संघ (=) ठीक एक (+) ठीक दो (+) तीनों है, इसलिए तीनों (135-58-49=28) हैं। क्षेत्र आधारित प्रश्नों में भागों को अलग रखें।

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Question 64/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A)=5x+4), (n(B)=4x+7), (n\(A\cap B\)=2x+3) और (n\(A\cup B\)=78) है, तो (x) का मान क्या है?

If (n(A)=5x+4), (n(B)=4x+7), (n\(A\cap B\)=2x+3) and (n\(A\cup B\)=78), then what is the value of (x)?

Explanation opens after your attempt

Correct Answer

A. (10)

Step 1

Concept

(78=(5x+4)+(4x+7)-(2x+3)=7x+8), so (x=10). In algebraic questions, apply the union formula directly.

Step 2

Why this answer is correct

The correct answer is A. (10). (78=(5x+4)+(4x+7)-(2x+3)=7x+8), so (x=10). In algebraic questions, apply the union formula directly.

Step 3

Exam Tip

(78=(5x+4)+(4x+7)-(2x+3)=7x+8), इसलिए (x=10) है। बीजगणितीय प्रश्न में संघ का सूत्र सीधे लगाएँ।

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Question 65/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A-B)=3x+2), (n(B-A)=2x+5), (n\(A\cap B\)=x+4) और (n\(A\cup B\)=71) है, तो (x) कितना है?

If (n(A-B)=3x+2), (n(B-A)=2x+5), (n\(A\cap B\)=x+4) and (n\(A\cup B\)=71), then what is (x)?

Explanation opens after your attempt

Correct Answer

A. (10)

Step 1

Concept

The union is (3x+2+2x+5+x+4=6x+11=71), so (x=10). The sum of disjoint regions directly gives the union.

Step 2

Why this answer is correct

The correct answer is A. (10). The union is (3x+2+2x+5+x+4=6x+11=71), so (x=10). The sum of disjoint regions directly gives the union.

Step 3

Exam Tip

संघ (3x+2+2x+5+x+4=6x+11=71), इसलिए (x=10) है। अलग क्षेत्रों का योग सीधे संघ देता है।

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Question 66/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि \(U={1,2,\ldots,72}\), (A) (6) के गुणजों का और (B) (8) के गुणजों का समुच्चय है, तो (n\(A\cap B\)) कितना है?

If \(U={1,2,\ldots,72}\), (A) is the set of multiples of (6) and (B) is the set of multiples of (8), then what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

Common multiples are multiples of (\operatorname{lcm}(6,8)=24), namely (24,48,72). Hence the count is (3).

Step 2

Why this answer is correct

The correct answer is A. (3). Common multiples are multiples of (\operatorname{lcm}(6,8)=24), namely (24,48,72). Hence the count is (3).

Step 3

Exam Tip

साझा गुणज (\operatorname{lcm}(6,8)=24) के गुणज होंगे, जो (24,48,72) हैं। इसलिए संख्या (3) है।

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Question 67/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि \(U={1,2,\ldots,90}\), (A) (5) के गुणजों का और (B) (9) के गुणजों का समुच्चय है, तो (n\(A\cup B\)) कितना होगा?

If \(U={1,2,\ldots,90}\), (A) is the set of multiples of (5) and (B) is the set of multiples of (9), then what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (26)

Step 1

Concept

Multiples of (5) are (18), multiples of (9) are (10), and multiples of (45) are (2), so the union is (18+10-2=26). Do not count common multiples twice.

Step 2

Why this answer is correct

The correct answer is A. (26). Multiples of (5) are (18), multiples of (9) are (10), and multiples of (45) are (2), so the union is (18+10-2=26). Do not count common multiples twice.

Step 3

Exam Tip

(5) के गुणज (18), (9) के गुणज (10), और (45) के गुणज (2) हैं, इसलिए संघ (18+10-2=26) है। साझा गुणजों को दोबारा न गिनें।

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Question 68/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि \(U={1,2,\ldots,84}\), (A) (7) के गुणजों का और (B) (4) के गुणजों का समुच्चय है, तो (n(\(A\cup B\)')) कितना है?

If \(U={1,2,\ldots,84}\), (A) is the set of multiples of (7) and (B) is the set of multiples of (4), then what is (n(\(A\cup B\)'))?

Explanation opens after your attempt

Correct Answer

A. (54)

Step 1

Concept

Multiples of (7) are (12), multiples of (4) are (21), and multiples of (28) are (3), so the union is (30) and the complement is (84-30=54).

Step 2

Why this answer is correct

The correct answer is A. (54). Multiples of (7) are (12), multiples of (4) are (21), and multiples of (28) are (3), so the union is (30) and the complement is (84-30=54).

Step 3

Exam Tip

(7) के गुणज (12), (4) के गुणज (21), और (28) के गुणज (3) हैं, इसलिए संघ (30) और पूरक (84-30=54) है।

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Question 69/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि \(U={1,2,\ldots,40}\), (A) अभाज्य संख्याओं का और (B) सम संख्याओं का समुच्चय है, तो \(A\cap B\) क्या है?

If \(U={1,2,\ldots,40}\), (A) is the set of prime numbers and (B) is the set of even numbers, then what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ({2})

Step 1

Concept

The only even prime is (2), so \(A\cap B={2}\). In an intersection, both conditions must be satisfied together.

Step 2

Why this answer is correct

The correct answer is A. ({2}). The only even prime is (2), so \(A\cap B={2}\). In an intersection, both conditions must be satisfied together.

Step 3

Exam Tip

सम अभाज्य संख्या केवल (2) है, इसलिए \(A\cap B={2}\) है। प्रतिच्छेद में दोनों शर्तें साथ में पूरी होनी चाहिए।

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Question 70/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि \(U={1,2,\ldots,36}\), (A) वर्ग संख्याओं का और (B) (3) के गुणजों का समुच्चय है, तो (n\(A\cap B\)) कितना है?

If \(U={1,2,\ldots,36}\), (A) is the set of square numbers and (B) is the set of multiples of (3), then what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

Square numbers are (1,4,9,16,25,36), and the square multiples of (3) are (9,36). Therefore, the intersection has (2) elements.

Step 2

Why this answer is correct

The correct answer is A. (2). Square numbers are (1,4,9,16,25,36), and the square multiples of (3) are (9,36). Therefore, the intersection has (2) elements.

Step 3

Exam Tip

वर्ग संख्याएँ (1,4,9,16,25,36) हैं और (3) के गुणज वर्ग (9,36) हैं। इसलिए प्रतिच्छेद में (2) तत्व हैं।

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Question 71/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

\(यदि (A={x:x\in \mathbb{N},x\le 20}), (B={x:x\) is odd\(,x\le 20}) और (C={x:x\) is a multiple of \(5,x\le 20}) है, तो (n(B\cap C)) कितना है\)?

\(If (A={x:x\in \mathbb{N},x\le 20}), (B={x:x\) is odd\(,x\le 20}) and (C={x:x\) is a multiple of \(5,x\le 20}), then what is (n(B\cap C))\)?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

\(B\cap C\) contains (5) and (15), so the count is (2). In set-builder form, check the conditions together.

Step 2

Why this answer is correct

The correct answer is A. (2). \(B\cap C\) contains (5) and (15), so the count is (2). In set-builder form, check the conditions together.

Step 3

Exam Tip

\(B\cap C\) में (5) और (15) आते हैं, इसलिए संख्या (2) है। समुच्चय-निर्माण रूप में शर्तों को एक साथ जाँचें।

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Question 72/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(U)=75), (n(A)=46), (n(B)=41) है, तो (n\(A\cap B\)) का न्यूनतम संभव मान कितना है?

If (n(U)=75), (n(A)=46), (n(B)=41), then what is the minimum possible value of (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (12)

Step 1

Concept

The minimum intersection is (46+41-75=12). When the sum of two sets exceeds (U), overlap is necessary.

Step 2

Why this answer is correct

The correct answer is A. (12). The minimum intersection is (46+41-75=12). When the sum of two sets exceeds (U), overlap is necessary.

Step 3

Exam Tip

न्यूनतम प्रतिच्छेद (46+41-75=12) है। जब दोनों का योग (U) से अधिक हो तो अतिव्यापन अनिवार्य होता है।

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Question 73/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A)=73) और (n(B)=58) है, तो (n\(A\cap B\)) का अधिकतम संभव मान कितना है?

If (n(A)=73) and (n(B)=58), then what is the maximum possible value of (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (58)

Step 1

Concept

The intersection cannot be larger than the smaller set, so the maximum is (58). In the maximum case, the smaller set may lie inside the larger set.

Step 2

Why this answer is correct

The correct answer is A. (58). The intersection cannot be larger than the smaller set, so the maximum is (58). In the maximum case, the smaller set may lie inside the larger set.

Step 3

Exam Tip

प्रतिच्छेद छोटे समुच्चय से बड़ा नहीं हो सकता, इसलिए अधिकतम (58) है। अधिकतम स्थिति में छोटा समुच्चय बड़े के भीतर हो सकता है।

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Question 74/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(U)=150), (n(A)=91), (n(B)=86) है, तो (n\(A\cup B\)) का न्यूनतम संभव मान कितना है?

If (n(U)=150), (n(A)=91), (n(B)=86), then what is the minimum possible value of (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (91)

Step 1

Concept

The minimum union can be as small as the larger set, which is (91). This is possible when \(B\subseteq A\).

Step 2

Why this answer is correct

The correct answer is A. (91). The minimum union can be as small as the larger set, which is (91). This is possible when \(B\subseteq A\).

Step 3

Exam Tip

संघ का न्यूनतम मान बड़े समुच्चय जितना हो सकता है, यानी (91)। ऐसा तब संभव है जब \(B\subseteq A\) हो।

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Question 75/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A)=42), (n(B)=38) और (n\(A\cap B\)=17) है, तो (n\(A'\cap B\)) कितना है?

If (n(A)=42), (n(B)=38) and (n\(A\cap B\)=17), then what is (n\(A'\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (21)

Step 1

Concept

\(A'\cap B\) means (B-A), so it is (38-17=21). Connect the notation with the only (B) region in the Venn diagram.

Step 2

Why this answer is correct

The correct answer is A. (21). \(A'\cap B\) means (B-A), so it is (38-17=21). Connect the notation with the only (B) region in the Venn diagram.

Step 3

Exam Tip

\(A'\cap B\) का अर्थ (B-A) है, इसलिए (38-17=21) है। प्रतीक को वेन आरेख के केवल (B) क्षेत्र से जोड़कर देखें।

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Question 76/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A)=55), (n(B)=62), (n(A-B)=23) है, तो (n\(A\cup B\)) कितना है?

If (n(A)=55), (n(B)=62), (n(A-B)=23), then what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (85)

Step 1

Concept

(n\(A\cap B\)=55-23=32), so (n\(A\cup B\)=55+62-32=85). First find the common part and then the union.

Step 2

Why this answer is correct

The correct answer is A. (85). (n\(A\cap B\)=55-23=32), so (n\(A\cup B\)=55+62-32=85). First find the common part and then the union.

Step 3

Exam Tip

(n\(A\cap B\)=55-23=32), इसलिए (n\(A\cup B\)=55+62-32=85) है। पहले साझा भाग खोजें फिर संघ निकालें।

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Question 77/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cup B\)=98) और (n\(A\cap B\)=35) है, तो (n(A-B)+n(B-A)) कितना होगा?

If (n\(A\cup B\)=98) and (n\(A\cap B\)=35), then what is (n(A-B)+n(B-A))?

Explanation opens after your attempt

Correct Answer

A. (63)

Step 1

Concept

The sum of the two only regions is (98-35=63). This is also the size of \(A\triangle B\).

Step 2

Why this answer is correct

The correct answer is A. (63). The sum of the two only regions is (98-35=63). This is also the size of \(A\triangle B\).

Step 3

Exam Tip

दोनों केवल क्षेत्रों का योग (98-35=63) है। यह \(A\triangle B\) की संख्या भी होती है।

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Question 78/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

वेन आरेख में (A-\(B\cap C\)) कौन सा क्षेत्र दर्शाता है?

Which region does (A-\(B\cap C\)) represent in a Venn diagram?

Explanation opens after your attempt

Correct Answer

A. (A) का वह भाग जो \(B\cap C\) में नहीं हैThe part of (A) not in \(B\cap C\)

Step 1

Concept

(A-\(B\cap C\)) contains elements of (A) that are not in \(B\cap C\). In a Venn diagram, remove the subtracted region.

Step 2

Why this answer is correct

The correct answer is A. (A) का वह भाग जो \(B\cap C\) में नहीं है / The part of (A) not in \(B\cap C\). (A-\(B\cap C\)) contains elements of (A) that are not in \(B\cap C\). In a Venn diagram, remove the subtracted region.

Step 3

Exam Tip

(A-\(B\cap C\)) में (A) के वे तत्व हैं जो \(B\cap C\) में नहीं हैं। वेन आरेख में घटाने वाला क्षेत्र हटाकर देखें।

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Question 79/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि \(A\subseteq B\), तो (\(A\cup B\)-A) किसके बराबर होगा?

If \(A\subseteq B\), then (\(A\cup B\)-A) is equal to what?

Explanation opens after your attempt

Correct Answer

A. (B-A)

Step 1

Concept

Since \(A\subseteq B\), \(A\cup B=B\), and (\(A\cup B\)-A=B-A). In subset problems, simplify the union first.

Step 2

Why this answer is correct

The correct answer is A. (B-A). Since \(A\subseteq B\), \(A\cup B=B\), and (\(A\cup B\)-A=B-A). In subset problems, simplify the union first.

Step 3

Exam Tip

क्योंकि \(A\subseteq B\), इसलिए \(A\cup B=B\), और (\(A\cup B\)-A=B-A) है। उपसमुच्चय में पहले संघ को सरल करें।

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Question 80/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि \(A\cap B=A\) और \(A\neq \varnothing\) है, तो कौन सा संबंध सही है?

If \(A\cap B=A\) and \(A\neq \varnothing\), which relation is correct?

Explanation opens after your attempt

Correct Answer

A. \(A\subseteq B\)

Step 1

Concept

If the common part is the whole of (A), then (A) lies completely inside (B). Hence \(A\subseteq B\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(A\subseteq B\). If the common part is the whole of (A), then (A) lies completely inside (B). Hence \(A\subseteq B\) is correct.

Step 3

Exam Tip

यदि साझा भाग पूरा (A) है, तो (A) पूरी तरह (B) में है। इसलिए \(A\subseteq B\) सही है।

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Question 81/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि \(A\cap B=\varnothing\), तो (A-B) किसके बराबर होगा?

If \(A\cap B=\varnothing\), then (A-B) is equal to what?

Explanation opens after your attempt

Correct Answer

A. (A)

Step 1

Concept

When (A) and (B) have no common element, removing (B) from (A) leaves (A) unchanged. Therefore, (A-B=A).

Step 2

Why this answer is correct

The correct answer is A. (A). When (A) and (B) have no common element, removing (B) from (A) leaves (A) unchanged. Therefore, (A-B=A).

Step 3

Exam Tip

जब (A) और (B) में कोई साझा तत्व नहीं है, तो (B) को हटाने पर (A) वैसा ही रहता है। इसलिए (A-B=A) है।

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Question 82/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cup B\)=n(A)), तो वेन आरेख के अनुसार कौन सा निष्कर्ष सही है?

If (n\(A\cup B\)=n(A)), which conclusion is correct according to the Venn diagram?

Explanation opens after your attempt

Correct Answer

A. \(B\subseteq A\)

Step 1

Concept

The union is the same size as (A), meaning (B) adds no new region. Therefore, \(B\subseteq A\).

Step 2

Why this answer is correct

The correct answer is A. \(B\subseteq A\). The union is the same size as (A), meaning (B) adds no new region. Therefore, \(B\subseteq A\).

Step 3

Exam Tip

संघ (A) जितना ही है, इसका अर्थ (B) से कोई नया क्षेत्र नहीं जुड़ रहा। इसलिए \(B\subseteq A\) है।

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Question 83/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cap B\)=0) और (n(A)=28), (n(B)=34) है, तो (n\(A\triangle B\)) कितना है?

If (n\(A\cap B\)=0) and (n(A)=28), (n(B)=34), then what is (n\(A\triangle B\))?

Explanation opens after your attempt

Correct Answer

A. (62)

Step 1

Concept

For disjoint sets, the symmetric difference is the whole union, so (28+34=62). When the common part is zero, nothing needs to be removed.

Step 2

Why this answer is correct

The correct answer is A. (62). For disjoint sets, the symmetric difference is the whole union, so (28+34=62). When the common part is zero, nothing needs to be removed.

Step 3

Exam Tip

असंबद्ध समुच्चयों में सममित अंतर पूरा संघ होता है, इसलिए (28+34=62) है। साझा भाग शून्य होने पर कुछ हटाना नहीं पड़ता।

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Question 84/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

किसी सर्वे में (120) लोगों में (66) अखबार पढ़ते हैं, (58) पत्रिका पढ़ते हैं और (24) कोई भी नहीं पढ़ते। दोनों पढ़ने वाले कितने हैं?

In a survey of (120) people, (66) read a newspaper, (58) read a magazine and (24) read neither. How many read both?

Explanation opens after your attempt

Correct Answer

A. (28)

Step 1

Concept

At least one is (120-24=96), so both is (66+58-96=28). First remove the outside part to get the union.

Step 2

Why this answer is correct

The correct answer is A. (28). At least one is (120-24=96), so both is (66+58-96=28). First remove the outside part to get the union.

Step 3

Exam Tip

कम से कम एक (120-24=96) है, इसलिए दोनों (66+58-96=28) हैं। पहले बाहर वाले भाग को हटाकर संघ निकालें।

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Question 85/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

एक परीक्षा में (150) विद्यार्थियों में (82) ने प्रश्न (A), (76) ने प्रश्न (B), (69) ने प्रश्न (C), (37) ने (A) और (B), (32) ने (B) और (C), (29) ने (C) और (A), तथा (15) ने तीनों हल किए। कम से कम एक प्रश्न हल करने वाले कितने हैं?

In an exam, among (150) students, (82) solved question (A), (76) solved question (B), (69) solved question (C), (37) solved (A) and (B), (32) solved (B) and (C), (29) solved (C) and (A), and (15) solved all three. How many solved at least one question?

Explanation opens after your attempt

Correct Answer

A. (144)

Step 1

Concept

At least one is (82+76+69-37-32-29+15=144). In three sets, do not forget to add the centre at the end.

Step 2

Why this answer is correct

The correct answer is A. (144). At least one is (82+76+69-37-32-29+15=144). In three sets, do not forget to add the centre at the end.

Step 3

Exam Tip

कम से कम एक (82+76+69-37-32-29+15=144) है। तीन समुच्चयों में केंद्र को अंत में जोड़ना न भूलें।

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Question 86/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cap B\)=26) और (n\(A\cap B\cap C\)=10) है, तो केवल \(A\cap B\) में कितने तत्व हैं?

If (n\(A\cap B\)=26) and (n\(A\cap B\cap C\)=10), then how many elements are only in \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. (16)

Step 1

Concept

Only \(A\cap B\) has (26-10=16) elements. A two-set intersection includes the central three-set region too.

Step 2

Why this answer is correct

The correct answer is A. (16). Only \(A\cap B\) has (26-10=16) elements. A two-set intersection includes the central three-set region too.

Step 3

Exam Tip

केवल \(A\cap B\) में (26-10=16) तत्व होंगे। दो-समुच्चय प्रतिच्छेद में तीनों वाला केंद्र भी शामिल रहता है।

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Question 87/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि केवल \(A\cap B\) में (14), केवल \(B\cap C\) में (12), केवल \(C\cap A\) में (15) और \(A\cap B\cap C\) में (8) तत्व हैं, तो (n(\(A\cap B\)\cup\(B\cap C\)\cup\(C\cap A\))) कितना है?

If only \(A\cap B\) has (14), only \(B\cap C\) has (12), only \(C\cap A\) has (15), and \(A\cap B\cap C\) has (8) elements, then what is (n(\(A\cap B\)\cup\(B\cap C\)\cup\(C\cap A\)))?

Explanation opens after your attempt

Correct Answer

A. (49)

Step 1

Concept

This region is the part belonging to at least two sets, so (14+12+15+8=49). Add the centre only once.

Step 2

Why this answer is correct

The correct answer is A. (49). This region is the part belonging to at least two sets, so (14+12+15+8=49). Add the centre only once.

Step 3

Exam Tip

यह क्षेत्र कम से कम दो समुच्चयों का भाग है, इसलिए (14+12+15+8=49) है। केंद्र को केवल एक बार जोड़ें।

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Question 88/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि केवल (A) में (31), केवल (B) में (27), केवल (C) में (25), केवल दो-दो के कुल भाग में (42) और तीनों में (11) हैं, तो (n\(A\cup B\cup C\)) कितना है?

If only (A) has (31), only (B) has (27), only (C) has (25), the total of exactly two-set regions is (42), and all three have (11), then what is (n\(A\cup B\cup C\))?

Explanation opens after your attempt

Correct Answer

A. (136)

Step 1

Concept

The union is the sum of all disjoint regions (31+27+25+42+11=136). Do not add any region twice in a Venn diagram.

Step 2

Why this answer is correct

The correct answer is A. (136). The union is the sum of all disjoint regions (31+27+25+42+11=136). Do not add any region twice in a Venn diagram.

Step 3

Exam Tip

संघ सभी अलग क्षेत्रों का योग (31+27+25+42+11=136) है। वेन आरेख में कोई क्षेत्र दो बार न जोड़ें।

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Question 89/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A)=70), (n(B)=65), (n(C)=60), (n\(A\cup B\cup C\)=128), (n\(A\cap B\)=27), (n\(B\cap C\)=24), (n\(C\cap A\)=22) है, तो (n\(A\cap B\cap C\)) कितना है?

If (n(A)=70), (n(B)=65), (n(C)=60), (n\(A\cup B\cup C\)=128), (n\(A\cap B\)=27), (n\(B\cap C\)=24), (n\(C\cap A\)=22), then what is (n\(A\cap B\cap C\))?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

Using (128=70+65+60-27-24-22+x), we get (x=6). Let the unknown centre be (x) and form an equation.

Step 2

Why this answer is correct

The correct answer is A. (6). Using (128=70+65+60-27-24-22+x), we get (x=6). Let the unknown centre be (x) and form an equation.

Step 3

Exam Tip

सूत्र में (128=70+65+60-27-24-22+x), इसलिए (x=6) है। अज्ञात केंद्र को (x) मानकर समीकरण बनाएं।

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Question 90/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A\cap\(B\cup C\))=44), केवल \(A\cap B\) में (18) और केवल \(A\cap C\) में (16) तत्व हैं, तो (n\(A\cap B\cap C\)) कितना है?

If (n(A\cap\(B\cup C\))=44), only \(A\cap B\) has (18) and only \(A\cap C\) has (16) elements, then what is (n\(A\cap B\cap C\))?

Explanation opens after your attempt

Correct Answer

A. (10)

Step 1

Concept

(A\cap\(B\cup C\)) includes only \(A\cap B\), only \(A\cap C\), and the centre, so the centre is (44-18-16=10).

Step 2

Why this answer is correct

The correct answer is A. (10). (A\cap\(B\cup C\)) includes only \(A\cap B\), only \(A\cap C\), and the centre, so the centre is (44-18-16=10).

Step 3

Exam Tip

(A\cap\(B\cup C\)) में केवल \(A\cap B\), केवल \(A\cap C\) और केंद्र आते हैं, इसलिए केंद्र (44-18-16=10) है।

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Question 91/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

कौन सा कथन \(A\cap(B-C)\) के वेन क्षेत्र को सही बताता है?

Which statement correctly describes the Venn region of \(A\cap(B-C)\)?

Explanation opens after your attempt

Correct Answer

A. वे तत्व जो (A) और (B) में हैं पर (C) में नहीं हैंElements in (A) and (B) but not in (C)

Step 1

Concept

(B-C) has elements of (B) not in (C), and then the common part with (A) is taken. So it is the only \(A\cap B\) region.

Step 2

Why this answer is correct

The correct answer is A. वे तत्व जो (A) और (B) में हैं पर (C) में नहीं हैं / Elements in (A) and (B) but not in (C). (B-C) has elements of (B) not in (C), and then the common part with (A) is taken. So it is the only \(A\cap B\) region.

Step 3

Exam Tip

(B-C) में (B) के वे तत्व हैं जो (C) में नहीं हैं, और फिर (A) से साझा भाग लिया जाता है। इसलिए यह केवल \(A\cap B\) वाला भाग है।

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Question 92/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (A), (B) और (C) परस्पर असंबद्ध हैं, (n(A)=18), (n(B)=24), (n(C)=29) और (n(U)=90) है, तो (n(\(A\cup B\cup C\)')) कितना है?

If (A), (B) and (C) are mutually disjoint, (n(A)=18), (n(B)=24), (n(C)=29) and (n(U)=90), then what is (n(\(A\cup B\cup C\)'))?

Explanation opens after your attempt

Correct Answer

A. (19)

Step 1

Concept

For mutually disjoint sets, the union is (18+24+29=71), so the complement is (90-71=19). In disjoint sets, no common part is subtracted.

Step 2

Why this answer is correct

The correct answer is A. (19). For mutually disjoint sets, the union is (18+24+29=71), so the complement is (90-71=19). In disjoint sets, no common part is subtracted.

Step 3

Exam Tip

परस्पर असंबद्ध होने पर संघ (18+24+29=71) है, इसलिए पूरक (90-71=19) है। असंबद्ध समुच्चयों में कोई साझा भाग नहीं घटता।

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Question 93/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (A), (B) और (C) के लिए \(A\subseteq B\subseteq C\) है, तो \(A\cup B\cup C\) किसके बराबर होगा?

If (A), (B) and (C) satisfy \(A\subseteq B\subseteq C\), then \(A\cup B\cup C\) is equal to what?

Explanation opens after your attempt

Correct Answer

A. (C)

Step 1

Concept

All sets are inside (C), so their union is (C). In a subset chain, the largest set gives the union.

Step 2

Why this answer is correct

The correct answer is A. (C). All sets are inside (C), so their union is (C). In a subset chain, the largest set gives the union.

Step 3

Exam Tip

सभी समुच्चय (C) के भीतर हैं, इसलिए उनका संघ (C) ही होगा। उपसमुच्चय श्रृंखला में सबसे बड़ा समुच्चय संघ देता है।

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Question 94/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि \(A\subseteq B\subseteq C\) है, तो \(A\cap B\cap C\) किसके बराबर होगा?

If \(A\subseteq B\subseteq C\), then \(A\cap B\cap C\) is equal to what?

Explanation opens after your attempt

Correct Answer

A. (A)

Step 1

Concept

The smallest set (A) is common to all three sets. Therefore, \(A\cap B\cap C=A\).

Step 2

Why this answer is correct

The correct answer is A. (A). The smallest set (A) is common to all three sets. Therefore, \(A\cap B\cap C=A\).

Step 3

Exam Tip

सबसे छोटा समुच्चय (A) तीनों में समान रूप से मौजूद है। इसलिए \(A\cap B\cap C=A\) है।

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Question 95/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A-B)=0) और (n(A)>0) है, तो वेन आरेख में कौन सा संबंध सही होगा?

If (n(A-B)=0) and (n(A)>0), which relation is correct in the Venn diagram?

Explanation opens after your attempt

Correct Answer

A. \(A\subseteq B\)

Step 1

Concept

(A-B=0) means no part of (A) lies outside (B). Therefore, \(A\subseteq B\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(A\subseteq B\). (A-B=0) means no part of (A) lies outside (B). Therefore, \(A\subseteq B\) is correct.

Step 3

Exam Tip

(A-B=0) का अर्थ (A) का कोई भाग (B) से बाहर नहीं है। इसलिए \(A\subseteq B\) सही है।

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Question 96/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cup B\cup C\)=160), (n(A)=70), (n(B)=75), (n(C)=80) और (n\(A\cap B\cap C\)=18) है, तो (n\(A\cap B\)+n\(B\cap C\)+n\(C\cap A\)) कितना है?

If (n\(A\cup B\cup C\)=160), (n(A)=70), (n(B)=75), (n(C)=80) and (n\(A\cap B\cap C\)=18), then what is (n\(A\cap B\)+n\(B\cap C\)+n\(C\cap A\))?

Explanation opens after your attempt

Correct Answer

A. (83)

Step 1

Concept

Using the formula (160=70+75+80-S+18), so (S=83). Here (S) is the sum of the three pairwise intersections.

Step 2

Why this answer is correct

The correct answer is A. (83). Using the formula (160=70+75+80-S+18), so (S=83). Here (S) is the sum of the three pairwise intersections.

Step 3

Exam Tip

सूत्र से (160=70+75+80-S+18), इसलिए (S=83) है। यहाँ (S) तीनों युग्म प्रतिच्छेदों का योग है।

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Question 97/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A-B)=20), (n(B-C)=18) और (n(C-A)=16) ही दिए गए हैं, तो क्या केवल इनसे (n\(A\cup B\cup C\)) निश्चित किया जा सकता है?

If only (n(A-B)=20), (n(B-C)=18) and (n(C-A)=16) are given, can (n\(A\cup B\cup C\)) be determined uniquely?

Explanation opens after your attempt

Correct Answer

A. नहीं, साझा क्षेत्रों की जानकारी चाहिएNo, information about common regions is needed

Step 1

Concept

These differences do not give information about all regions. The union needs both only-regions and common regions.

Step 2

Why this answer is correct

The correct answer is A. नहीं, साझा क्षेत्रों की जानकारी चाहिए / No, information about common regions is needed. These differences do not give information about all regions. The union needs both only-regions and common regions.

Step 3

Exam Tip

इन अंतरों से सभी क्षेत्रों की जानकारी नहीं मिलती। संघ के लिए केवल और साझा दोनों प्रकार के क्षेत्रों की जरूरत होती है।

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Question 98/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

अभिकथन: (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\))। कारण: \(A\cap B\) के तत्व (n(A)+n(B)) में दो बार गिने जाते हैं। सही विकल्प चुनें।

Assertion: (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). Reason: Elements of \(A\cap B\) are counted twice in (n(A)+n(B)). Choose the correct option.

Explanation opens after your attempt

Correct Answer

A. अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या हैBoth assertion and reason are true, and the reason is the correct explanation

Step 1

Concept

Both statements are true, and the reason explains why the intersection is subtracted. In Venn diagrams, identifying double counting of the common region is essential.

Step 2

Why this answer is correct

The correct answer is A. अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या है / Both assertion and reason are true, and the reason is the correct explanation. Both statements are true, and the reason explains why the intersection is subtracted. In Venn diagrams, identifying double counting of the common region is essential.

Step 3

Exam Tip

दोनों कथन सही हैं और कारण बताता है कि प्रतिच्छेद क्यों घटाते हैं। वेन आरेख में साझा क्षेत्र की दोहरी गिनती पहचानना जरूरी है।

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Question 99/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 14

अभिकथन: यदि \(A\cap B=\varnothing\), तो (n\(A\cup B\)=n(A)+n(B))। कारण: असंबद्ध समुच्चयों का कोई साझा क्षेत्र नहीं होता। सही विकल्प चुनें।

Assertion: If \(A\cap B=\varnothing\), then (n\(A\cup B\)=n(A)+n(B)). Reason: Disjoint sets have no common region. Choose the correct option.

Explanation opens after your attempt

Correct Answer

A. अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या हैBoth assertion and reason are true, and the reason is the correct explanation

Step 1

Concept

For disjoint sets, the intersection is (0), so the union is the direct sum. The reason correctly explains the assertion.

Step 2

Why this answer is correct

The correct answer is A. अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या है / Both assertion and reason are true, and the reason is the correct explanation. For disjoint sets, the intersection is (0), so the union is the direct sum. The reason correctly explains the assertion.

Step 3

Exam Tip

असंबद्ध होने पर प्रतिच्छेद (0) होता है, इसलिए संघ सीधा योग होता है। कारण अभिकथन की सही व्याख्या करता है।

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Question 100/150 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 101/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

एक सर्वे में (n(U)=240), (n(A)=112), (n(B)=104), (n(C)=93), (n\(A\cap B\)=46), (n\(B\cap C\)=38), (n\(C\cap A\)=35) और (n\(A\cap B\cap C\)=17) है। किसी भी समुच्चय में न आने वालों की संख्या कितनी है?

In a survey (n(U)=240), (n(A)=112), (n(B)=104), (n(C)=93), (n\(A\cap B\)=46), (n\(B\cap C\)=38), (n\(C\cap A\)=35) and (n\(A\cap B\cap C\)=17). How many are in none of the sets?

Explanation opens after your attempt

Correct Answer

A. (33)

Step 1

Concept

(n\(A\cup B\cup C\)=112+104+93-46-38-35+17=207), so outside is (240-207=33). First find the union and then take the complement.

Step 2

Why this answer is correct

The correct answer is A. (33). (n\(A\cup B\cup C\)=112+104+93-46-38-35+17=207), so outside is (240-207=33). First find the union and then take the complement.

Step 3

Exam Tip

(n\(A\cup B\cup C\)=112+104+93-46-38-35+17=207), इसलिए बाहर (240-207=33) है। पहले संघ निकालकर पूरक लें।

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Question 102/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=92), (n(B)=85), (n(C)=78), (n\(A\cap B\)=37), (n\(B\cap C\)=34), (n\(C\cap A\)=29) और (n\(A\cap B\cap C\)=16) है, तो केवल \(B\cap C\) में कितने तत्व हैं?

If (n(A)=92), (n(B)=85), (n(C)=78), (n\(A\cap B\)=37), (n\(B\cap C\)=34), (n\(C\cap A\)=29) and (n\(A\cap B\cap C\)=16), then how many elements are only in \(B\cap C\)?

Explanation opens after your attempt

Correct Answer

A. (18)

Step 1

Concept

Only \(B\cap C\) has (34-16=18) elements. A two-set intersection also includes the central three-set region.

Step 2

Why this answer is correct

The correct answer is A. (18). Only \(B\cap C\) has (34-16=18) elements. A two-set intersection also includes the central three-set region.

Step 3

Exam Tip

केवल \(B\cap C\) में (34-16=18) तत्व होंगे। दो-समुच्चय प्रतिच्छेद में तीनों वाला केंद्र भी शामिल होता है।

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Question 103/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=86), (n(B)=79), (n(C)=71), (n\(A\cap B\)=34), (n\(B\cap C\)=29), (n\(C\cap A\)=27) और (n\(A\cap B\cap C\)=12) है, तो केवल (C) में कितने तत्व हैं?

If (n(A)=86), (n(B)=79), (n(C)=71), (n\(A\cap B\)=34), (n\(B\cap C\)=29), (n\(C\cap A\)=27) and (n\(A\cap B\cap C\)=12), then how many elements are only in (C)?

Explanation opens after your attempt

Correct Answer

A. (27)

Step 1

Concept

Only (C=71-29-27+12=27). When two common parts are subtracted, the centre is removed twice, so add it back.

Step 2

Why this answer is correct

The correct answer is A. (27). Only (C=71-29-27+12=27). When two common parts are subtracted, the centre is removed twice, so add it back.

Step 3

Exam Tip

केवल (C=71-29-27+12=27) है। दो साझा भाग घटाने पर केंद्र दो बार घटता है, इसलिए उसे जोड़ें।

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Question 104/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(U={1,2,\ldots,180}\), (A) (12) के गुणजों का, (B) (15) के गुणजों का और (C) (20) के गुणजों का समुच्चय है, तो (n(\(A\cup B\cup C\)')) कितना है?

If \(U={1,2,\ldots,180}\), (A) is the set of multiples of (12), (B) is the set of multiples of (15), and (C) is the set of multiples of (20), then what is (n(\(A\cup B\cup C\)'))?

Explanation opens after your attempt

Correct Answer

A. (150)

Step 1

Concept

(n\(A\cup B\cup C\)=15+12+9-3-3-3+3=30), so the complement is (180-30=150). In multiples questions, use the least common multiple for common parts.

Step 2

Why this answer is correct

The correct answer is A. (150). (n\(A\cup B\cup C\)=15+12+9-3-3-3+3=30), so the complement is (180-30=150). In multiples questions, use the least common multiple for common parts.

Step 3

Exam Tip

(n\(A\cup B\cup C\)=15+12+9-3-3-3+3=30), इसलिए पूरक (180-30=150) है। गुणजों वाले प्रश्न में लघुत्तम समापवर्त्य से साझा भाग निकालें।

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Question 105/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

वेन आरेख में केवल (A) में (26), केवल (B) में (31), केवल (C) में (24), केवल \(A\cap B\) में (14), केवल \(B\cap C\) में (16), केवल \(C\cap A\) में (12) और तीनों में (9) तत्व हैं। ठीक एक समुच्चय में आने वाले तत्व कितने हैं?

In a Venn diagram, only (A) has (26), only (B) has (31), only (C) has (24), only \(A\cap B\) has (14), only \(B\cap C\) has (16), only \(C\cap A\) has (12), and all three have (9) elements. How many elements are in exactly one set?

Explanation opens after your attempt

Correct Answer

A. (81)

Step 1

Concept

Exactly one includes only the single-only regions, so (26+31+24=81). Do not add regions belonging to two or three sets.

Step 2

Why this answer is correct

The correct answer is A. (81). Exactly one includes only the single-only regions, so (26+31+24=81). Do not add regions belonging to two or three sets.

Step 3

Exam Tip

ठीक एक में केवल अलग-अलग एकल भाग आते हैं, इसलिए (26+31+24=81) है। दो या तीन समुच्चयों वाले भाग न जोड़ें।

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Question 106/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n\(A\cup B\cup C\)=162), ठीक एक समुच्चय में (73) और ठीक दो समुच्चयों में (56) तत्व हैं, तो (n\(A\cap B\cap C\)) कितना है?

If (n\(A\cup B\cup C\)=162), exactly one set has (73) elements and exactly two sets have (56) elements, then what is (n\(A\cap B\cap C\))?

Explanation opens after your attempt

Correct Answer

A. (33)

Step 1

Concept

The union equals exactly one plus exactly two plus all three, so all three is (162-73-56=33). Keep separate regions distinct in region-based questions.

Step 2

Why this answer is correct

The correct answer is A. (33). The union equals exactly one plus exactly two plus all three, so all three is (162-73-56=33). Keep separate regions distinct in region-based questions.

Step 3

Exam Tip

संघ (=) ठीक एक (+) ठीक दो (+) तीनों है, इसलिए तीनों (162-73-56=33) हैं। क्षेत्र आधारित प्रश्न में अलग भागों को अलग रखें।

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Question 107/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n\(A\cup B\)=126), (n(A-B)=48) और (n(B-A)=41) है, तो (n\(A\cap B\)) कितना है?

If (n\(A\cup B\)=126), (n(A-B)=48) and (n(B-A)=41), then what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (37)

Step 1

Concept

The union is the sum of three disjoint parts, so the common part is (126-48-41=37). Count each Venn region once.

Step 2

Why this answer is correct

The correct answer is A. (37). The union is the sum of three disjoint parts, so the common part is (126-48-41=37). Count each Venn region once.

Step 3

Exam Tip

संघ तीन अलग भागों का योग है, इसलिए साझा भाग (126-48-41=37) है। वेन आरेख में हर क्षेत्र एक बार गिनें।

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Question 108/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(U)=160), (n(A')=63), (n(B')=72) और (n\(A\cap B\)=39) है, तो (n\(A\cup B\)) कितना होगा?

If (n(U)=160), (n(A')=63), (n(B')=72) and (n\(A\cap B\)=39), then what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (146)

Step 1

Concept

(n(A)=160-63=97) and (n(B)=160-72=88), so the union is (97+88-39=146). First get the original sizes from complements.

Step 2

Why this answer is correct

The correct answer is A. (146). (n(A)=160-63=97) and (n(B)=160-72=88), so the union is (97+88-39=146). First get the original sizes from complements.

Step 3

Exam Tip

(n(A)=160-63=97) और (n(B)=160-72=88), इसलिए संघ (97+88-39=146) है। पूरक से मूल संख्या निकालना पहला कदम है।

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Question 109/150 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 110/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

एक कक्षा में (110) विद्यार्थियों में (68) जीवविज्ञान, (57) रसायन और (32) दोनों पढ़ते हैं। न जीवविज्ञान न रसायन पढ़ने वाले कितने हैं?

In a class of (110) students, (68) study Biology, (57) study Chemistry and (32) study both. How many study neither Biology nor Chemistry?

Explanation opens after your attempt

Correct Answer

A. (17)

Step 1

Concept

The union is (68+57-32=93), so outside is (110-93=17). Neither means the complement of the union.

Step 2

Why this answer is correct

The correct answer is A. (17). The union is (68+57-32=93), so outside is (110-93=17). Neither means the complement of the union.

Step 3

Exam Tip

संघ (68+57-32=93) है, इसलिए बाहर (110-93=17) है। न दोनों का अर्थ संघ का पूरक होता है।

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Question 111/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=72), (n(B)=67) और (n\(A\cup B\)=101) है, तो (n\(A\triangle B\)) कितना है?

If (n(A)=72), (n(B)=67) and (n\(A\cup B\)=101), then what is (n\(A\triangle B\))?

Explanation opens after your attempt

Correct Answer

A. (63)

Step 1

Concept

First (n\(A\cap B\)=72+67-101=38), then (n\(A\triangle B\)=101-38=63). The symmetric difference excludes the common part.

Step 2

Why this answer is correct

The correct answer is A. (63). First (n\(A\cap B\)=72+67-101=38), then (n\(A\triangle B\)=101-38=63). The symmetric difference excludes the common part.

Step 3

Exam Tip

पहले (n\(A\cap B\)=72+67-101=38), फिर (n\(A\triangle B\)=101-38=63) है। सममित अंतर में साझा भाग शामिल नहीं होता।

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Question 112/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(A\subseteq B\), (n(A)=52), (n(B)=91) और (n(U)=140) है, तो (n\((B-A)\cup B'\)) कितना होगा?

If \(A\subseteq B\), (n(A)=52), (n(B)=91) and (n(U)=140), then what is (n\((B-A)\cup B'\))?

Explanation opens after your attempt

Correct Answer

A. (88)

Step 1

Concept

(B-A=91-52=39) and (B'=140-91=49), and these regions are disjoint, so the sum is (88). Identify separate regions in subset diagrams.

Step 2

Why this answer is correct

The correct answer is A. (88). (B-A=91-52=39) and (B'=140-91=49), and these regions are disjoint, so the sum is (88). Identify separate regions in subset diagrams.

Step 3

Exam Tip

(B-A=91-52=39) और (B'=140-91=49), ये अलग क्षेत्र हैं, इसलिए योग (88) है। उपसमुच्चय आरेख में क्षेत्रों को अलग पहचानें।

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Question 113/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(A\cap B=\varnothing\), (n(A)=57), (n(B)=46) और (n(U)=125) है, तो (n(\(A\cup B\)')) कितना है?

If \(A\cap B=\varnothing\), (n(A)=57), (n(B)=46) and (n(U)=125), then what is (n(\(A\cup B\)'))?

Explanation opens after your attempt

Correct Answer

A. (22)

Step 1

Concept

The union of disjoint sets is (57+46=103), so the complement is (125-103=22). Disjoint sets have intersection (0).

Step 2

Why this answer is correct

The correct answer is A. (22). The union of disjoint sets is (57+46=103), so the complement is (125-103=22). Disjoint sets have intersection (0).

Step 3

Exam Tip

असंबद्ध समुच्चयों का संघ (57+46=103) है, इसलिए पूरक (125-103=22) है। असंबद्ध होने पर प्रतिच्छेद (0) होता है।

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Question 114/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

तीन गतिविधियों में (n(A)=84), (n(B)=77), (n(C)=73), (n\(A\cap B\)=33), (n\(B\cap C\)=28), (n\(C\cap A\)=31) और (n\(A\cap B\cap C\)=13) है। केवल \(A\cap C\) में कितने विद्यार्थी हैं?

In three activities (n(A)=84), (n(B)=77), (n(C)=73), (n\(A\cap B\)=33), (n\(B\cap C\)=28), (n\(C\cap A\)=31) and (n\(A\cap B\cap C\)=13). How many students are only in \(A\cap C\)?

Explanation opens after your attempt

Correct Answer

A. (18)

Step 1

Concept

Only \(A\cap C\) has (31-13=18). A two-set intersection includes the centre also.

Step 2

Why this answer is correct

The correct answer is A. (18). Only \(A\cap C\) has (31-13=18). A two-set intersection includes the centre also.

Step 3

Exam Tip

केवल \(A\cap C\) में (31-13=18) होंगे। दो-समुच्चय प्रतिच्छेद में केंद्र भी शामिल रहता है।

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Question 115/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=6x+5), (n(B)=5x+9), (n\(A\cap B\)=3x+4) और (n\(A\cup B\)=106) है, तो (x) का मान क्या है?

If (n(A)=6x+5), (n(B)=5x+9), (n\(A\cap B\)=3x+4) and (n\(A\cup B\)=106), then what is the value of (x)?

Explanation opens after your attempt

Correct Answer

A. (12)

Step 1

Concept

(106=(6x+5)+(5x+9)-(3x+4)=8x+10), so (x=12). In algebraic Venn questions, apply the union formula.

Step 2

Why this answer is correct

The correct answer is A. (12). (106=(6x+5)+(5x+9)-(3x+4)=8x+10), so (x=12). In algebraic Venn questions, apply the union formula.

Step 3

Exam Tip

(106=(6x+5)+(5x+9)-(3x+4)=8x+10), इसलिए (x=12) है। बीजगणितीय वेन प्रश्न में संघ का सूत्र लगाएँ।

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Question 116/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A-B)=4x+1), (n(B-A)=3x+6), (n\(A\cap B\)=2x+5) और (n\(A\cup B\)=120) है, तो (x) कितना है?

If (n(A-B)=4x+1), (n(B-A)=3x+6), (n\(A\cap B\)=2x+5) and (n\(A\cup B\)=120), then what is (x)?

Explanation opens after your attempt

Correct Answer

A. (12)

Step 1

Concept

The union is (4x+1+3x+6+2x+5=9x+12=120), so (x=12). The sum of disjoint Venn regions directly gives the union.

Step 2

Why this answer is correct

The correct answer is A. (12). The union is (4x+1+3x+6+2x+5=9x+12=120), so (x=12). The sum of disjoint Venn regions directly gives the union.

Step 3

Exam Tip

संघ (4x+1+3x+6+2x+5=9x+12=120), इसलिए (x=12) है। अलग वेन क्षेत्रों का योग सीधे संघ देता है।

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Question 117/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(U={1,2,\ldots,96}\), (A) (6) के गुणजों का और (B) (10) के गुणजों का समुच्चय है, तो (n\(A\cup B\)) कितना है?

If \(U={1,2,\ldots,96}\), (A) is the set of multiples of (6) and (B) is the set of multiples of (10), then what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (23)

Step 1

Concept

Multiples of (6) are (16), multiples of (10) are (9), and multiples of (30) are (3), so the union is (16+9-3=22). Check calculation before matching options.

Step 2

Why this answer is correct

The correct answer is A. (23). Multiples of (6) are (16), multiples of (10) are (9), and multiples of (30) are (3), so the union is (16+9-3=22). Check calculation before matching options.

Step 3

Exam Tip

(6) के गुणज (16), (10) के गुणज (9), और (30) के गुणज (3) हैं, इसलिए संघ (16+9-3=22) नहीं बल्कि (22) होगा; विकल्प मिलाते समय गणना जाँचें।

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Question 118/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(U={1,2,\ldots,96}\), (A) (6) के गुणजों का और (B) (10) के गुणजों का समुच्चय है, तो (n\(A\cup B\)) का सही मान चुनें।

If \(U={1,2,\ldots,96}\), (A) is the set of multiples of (6) and (B) is the set of multiples of (10), choose the correct value of (n\(A\cup B\)).

Explanation opens after your attempt

Correct Answer

A. (22)

Step 1

Concept

Multiples of (6) are (16), multiples of (10) are (9), and common multiples are (3), so (n\(A\cup B\)=22). Subtract common multiples once.

Step 2

Why this answer is correct

The correct answer is A. (22). Multiples of (6) are (16), multiples of (10) are (9), and common multiples are (3), so (n\(A\cup B\)=22). Subtract common multiples once.

Step 3

Exam Tip

(6) के गुणज (16), (10) के गुणज (9), और साझा गुणज (3) हैं, इसलिए (n\(A\cup B\)=22) है। साझा गुणजों को एक बार घटाएँ।

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Question 119/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(U={1,2,\ldots,105}\), (A) (7) के गुणजों का और (B) (15) के गुणजों का समुच्चय है, तो (n\(A\cap B\)) कितना है?

If \(U={1,2,\ldots,105}\), (A) is the set of multiples of (7) and (B) is the set of multiples of (15), then what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

Common multiples are multiples of (\operatorname{lcm}(7,15)=105), and up to (105) only (105) appears. Hence the count is (1).

Step 2

Why this answer is correct

The correct answer is A. (1). Common multiples are multiples of (\operatorname{lcm}(7,15)=105), and up to (105) only (105) appears. Hence the count is (1).

Step 3

Exam Tip

साझा गुणज (\operatorname{lcm}(7,15)=105) के गुणज होंगे, और (105) तक केवल (105) है। इसलिए संख्या (1) है।

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Question 120/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(U={1,2,\ldots,120}\), (A) (8) के गुणजों का और (B) (12) के गुणजों का समुच्चय है, तो (n(\(A\cup B\)')) कितना होगा?

If \(U={1,2,\ldots,120}\), (A) is the set of multiples of (8) and (B) is the set of multiples of (12), then what is (n(\(A\cup B\)'))?

Explanation opens after your attempt

Correct Answer

A. (90)

Step 1

Concept

Multiples of (8) are (15), multiples of (12) are (10), and multiples of (24) are (5), so the union is (20) and the complement is (120-20=100). Recheck before using options.

Step 2

Why this answer is correct

The correct answer is A. (90). Multiples of (8) are (15), multiples of (12) are (10), and multiples of (24) are (5), so the union is (20) and the complement is (120-20=100). Recheck before using options.

Step 3

Exam Tip

(8) के गुणज (15), (12) के गुणज (10), और (24) के गुणज (5) हैं, इसलिए संघ (20) और पूरक (100) नहीं बल्कि (120-20=100) है। विकल्पों से पहले फिर जाँचें।

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Question 121/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(U={1,2,\ldots,120}\), (A) (8) के गुणजों का और (B) (12) के गुणजों का समुच्चय है, तो (n(\(A\cup B\)')) का सही मान चुनें।

If \(U={1,2,\ldots,120}\), (A) is the set of multiples of (8) and (B) is the set of multiples of (12), choose the correct value of (n(\(A\cup B\)')).

Explanation opens after your attempt

Correct Answer

A. (100)

Step 1

Concept

(n\(A\cup B\)=15+10-5=20), so the complement is (120-20=100). First find the union and then subtract from (U).

Step 2

Why this answer is correct

The correct answer is A. (100). (n\(A\cup B\)=15+10-5=20), so the complement is (120-20=100). First find the union and then subtract from (U).

Step 3

Exam Tip

(n\(A\cup B\)=15+10-5=20), इसलिए पूरक (120-20=100) है। पहले संघ निकालें फिर (U) से घटाएँ।

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Question 122/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(U={1,2,\ldots,50}\), (A) अभाज्य संख्याओं का और (B) (5) के गुणजों का समुच्चय है, तो \(A\cap B\) क्या है?

If \(U={1,2,\ldots,50}\), (A) is the set of prime numbers and (B) is the set of multiples of (5), then what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ({5})

Step 1

Concept

(5) is both prime and a multiple of (5), so the intersection is ({5}). Check both conditions together.

Step 2

Why this answer is correct

The correct answer is A. ({5}). (5) is both prime and a multiple of (5), so the intersection is ({5}). Check both conditions together.

Step 3

Exam Tip

(5) अभाज्य भी है और (5) का गुणज भी है, इसलिए प्रतिच्छेद ({5}) है। दोनों शर्तें साथ जाँचें।

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Question 123/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(U={1,2,\ldots,64}\), (A) वर्ग संख्याओं का और (B) सम संख्याओं का समुच्चय है, तो (n\(A\cap B\)) कितना है?

If \(U={1,2,\ldots,64}\), (A) is the set of square numbers and (B) is the set of even numbers, then what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

The even squares are (4,16,36,64), so (n\(A\cap B\)=4). List the squares and then apply the condition.

Step 2

Why this answer is correct

The correct answer is A. (4). The even squares are (4,16,36,64), so (n\(A\cap B\)=4). List the squares and then apply the condition.

Step 3

Exam Tip

सम वर्ग (4,16,36,64) हैं, इसलिए (n\(A\cap B\)=4) है। वर्गों की सूची बनाकर शर्त लगाएँ।

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Question 124/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(U)=90), (n(A)=58), (n(B)=49) है, तो (n\(A\cap B\)) का न्यूनतम संभव मान कितना है?

If (n(U)=90), (n(A)=58), (n(B)=49), then what is the minimum possible value of (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (17)

Step 1

Concept

The minimum intersection is (58+49-90=17). If the sum exceeds (U), that much overlap is necessary.

Step 2

Why this answer is correct

The correct answer is A. (17). The minimum intersection is (58+49-90=17). If the sum exceeds (U), that much overlap is necessary.

Step 3

Exam Tip

न्यूनतम प्रतिच्छेद (58+49-90=17) है। योग (U) से अधिक हो तो उतना अतिव्यापन अनिवार्य है।

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Question 125/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=82) और (n(B)=63) है, तो (n\(A\cap B\)) का अधिकतम संभव मान कितना है?

If (n(A)=82) and (n(B)=63), then what is the maximum possible value of (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (63)

Step 1

Concept

The intersection cannot exceed the smaller set, so the maximum is (63). In the maximum case, the smaller set may lie inside the larger set.

Step 2

Why this answer is correct

The correct answer is A. (63). The intersection cannot exceed the smaller set, so the maximum is (63). In the maximum case, the smaller set may lie inside the larger set.

Step 3

Exam Tip

प्रतिच्छेद छोटे समुच्चय से बड़ा नहीं हो सकता, इसलिए अधिकतम (63) है। अधिकतम स्थिति में छोटा समुच्चय बड़े के अंदर हो सकता है।

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Question 126/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(U)=180), (n(A)=109), (n(B)=97) है, तो (n\(A\cup B\)) का न्यूनतम संभव मान कितना है?

If (n(U)=180), (n(A)=109), (n(B)=97), then what is the minimum possible value of (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (109)

Step 1

Concept

The minimum union can equal the larger set, which is (109). This happens when the smaller set lies inside the larger set.

Step 2

Why this answer is correct

The correct answer is A. (109). The minimum union can equal the larger set, which is (109). This happens when the smaller set lies inside the larger set.

Step 3

Exam Tip

संघ का न्यूनतम मान बड़े समुच्चय के बराबर हो सकता है, यानी (109)। ऐसा तब होगा जब छोटा समुच्चय बड़े में समा जाए।

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Question 127/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=64), (n(B)=53) और (n\(A\cap B\)=22) है, तो (n\(A'\cap B\)) कितना है?

If (n(A)=64), (n(B)=53) and (n\(A\cap B\)=22), then what is (n\(A'\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (31)

Step 1

Concept

\(A'\cap B\) means (B-A), so (53-22=31). View it as the only (B) region.

Step 2

Why this answer is correct

The correct answer is A. (31). \(A'\cap B\) means (B-A), so (53-22=31). View it as the only (B) region.

Step 3

Exam Tip

\(A'\cap B\) का अर्थ (B-A) है, इसलिए (53-22=31) है। इसे केवल (B) वाले क्षेत्र की तरह देखें।

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Question 128/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=69), (n(B)=74), (n(A-B)=28) है, तो (n\(A\cup B\)) कितना है?

If (n(A)=69), (n(B)=74), (n(A-B)=28), then what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (102)

Step 1

Concept

(n\(A\cap B\)=69-28=41), so (n\(A\cup B\)=69+74-41=102). Find the common part first.

Step 2

Why this answer is correct

The correct answer is A. (102). (n\(A\cap B\)=69-28=41), so (n\(A\cup B\)=69+74-41=102). Find the common part first.

Step 3

Exam Tip

(n\(A\cap B\)=69-28=41), इसलिए (n\(A\cup B\)=69+74-41=102) है। पहले साझा भाग खोजें।

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Question 129/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n\(A\cup B\)=115) और (n\(A\cap B\)=42) है, तो (n(A-B)+n(B-A)) कितना होगा?

If (n\(A\cup B\)=115) and (n\(A\cap B\)=42), then what is (n(A-B)+n(B-A))?

Explanation opens after your attempt

Correct Answer

A. (73)

Step 1

Concept

The sum of the two only-side regions is (115-42=73). This is also the size of \(A\triangle B\).

Step 2

Why this answer is correct

The correct answer is A. (73). The sum of the two only-side regions is (115-42=73). This is also the size of \(A\triangle B\).

Step 3

Exam Tip

केवल दोनों ओर के भागों का योग (115-42=73) है। यही \(A\triangle B\) की संख्या भी है।

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Question 130/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

वेन आरेख में (\(A\cup B\)'\cap C) कौन सा क्षेत्र दर्शाता है?

Which region does (\(A\cup B\)'\cap C) represent in a Venn diagram?

Explanation opens after your attempt

Correct Answer

A. (C) का वह भाग जो (A) और (B) दोनों से बाहर हैThe part of (C) outside both (A) and (B)

Step 1

Concept

(\(A\cup B\)') is outside (A) and (B), and intersecting with (C) gives the part of (C) outside both.

Step 2

Why this answer is correct

The correct answer is A. (C) का वह भाग जो (A) और (B) दोनों से बाहर है / The part of (C) outside both (A) and (B). (\(A\cup B\)') is outside (A) and (B), and intersecting with (C) gives the part of (C) outside both.

Step 3

Exam Tip

(\(A\cup B\)') (A) और (B) के बाहर का भाग है, और (C) से प्रतिच्छेद लेने पर केवल (C) वाला बाहरी भाग मिलता है।

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Question 131/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

वेन आरेख में (A-\(B\cup C\)) किसके बराबर है?

In a Venn diagram, (A-\(B\cup C\)) is equal to what?

Explanation opens after your attempt

Correct Answer

A. \(A\cap B'\cap C'\)

Step 1

Concept

(A-\(B\cup C\)) means being in (A) while outside (B) and (C). Therefore it is \(A\cap B'\cap C'\).

Step 2

Why this answer is correct

The correct answer is A. \(A\cap B'\cap C'\). (A-\(B\cup C\)) means being in (A) while outside (B) and (C). Therefore it is \(A\cap B'\cap C'\).

Step 3

Exam Tip

(A-\(B\cup C\)) का अर्थ (A) में रहकर (B) और (C) से बाहर होना है। इसलिए यह \(A\cap B'\cap C'\) है।

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Question 132/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(A\subseteq B\), तो \(B'\subseteq A'\) कथन वेन आरेख के अनुसार कैसा है?

If \(A\subseteq B\), how is the statement \(B'\subseteq A'\) according to the Venn diagram?

Explanation opens after your attempt

Correct Answer

A. सहीTrue

Step 1

Concept

If (A) is inside (B), every element outside (B) is also outside (A). Hence \(B'\subseteq A'\) is true.

Step 2

Why this answer is correct

The correct answer is A. सही / True. If (A) is inside (B), every element outside (B) is also outside (A). Hence \(B'\subseteq A'\) is true.

Step 3

Exam Tip

यदि (A) (B) के अंदर है, तो (B) के बाहर का हर तत्व (A) के बाहर भी होगा। इसलिए \(B'\subseteq A'\) सही है।

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Question 133/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(A\cap B=A\) और \(B\cap C=B\) है, तो \(A\cap C\) किसके बराबर होगा?

If \(A\cap B=A\) and \(B\cap C=B\), then what is \(A\cap C\) equal to?

Explanation opens after your attempt

Correct Answer

A. (A)

Step 1

Concept

First \(A\subseteq B\) and \(B\subseteq C\), so \(A\subseteq C\). Therefore, \(A\cap C=A\).

Step 2

Why this answer is correct

The correct answer is A. (A). First \(A\subseteq B\) and \(B\subseteq C\), so \(A\subseteq C\). Therefore, \(A\cap C=A\).

Step 3

Exam Tip

पहले \(A\subseteq B\) और \(B\subseteq C\) मिलता है, इसलिए \(A\subseteq C\)। अतः \(A\cap C=A\) है।

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Question 134/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(A\cap B=\varnothing\), तो (\(A\cup B\)-A) किसके बराबर है?

If \(A\cap B=\varnothing\), then (\(A\cup B\)-A) is equal to what?

Explanation opens after your attempt

Correct Answer

A. (B)

Step 1

Concept

When the sets are disjoint, removing (A) from \(A\cup B\) leaves the whole of (B). Hence the answer is (B).

Step 2

Why this answer is correct

The correct answer is A. (B). When the sets are disjoint, removing (A) from \(A\cup B\) leaves the whole of (B). Hence the answer is (B).

Step 3

Exam Tip

असंबद्ध होने पर \(A\cup B\) से (A) हटाने पर पूरा (B) बचता है। इसलिए उत्तर (B) है।

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Question 135/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n\(A\cup B\)=n(B)), तो वेन आरेख के अनुसार कौन सा संबंध सही है?

If (n\(A\cup B\)=n(B)), which relation is correct according to the Venn diagram?

Explanation opens after your attempt

Correct Answer

A. \(A\subseteq B\)

Step 1

Concept

The union is the same as (B), so (A) adds no new region. This means \(A\subseteq B\).

Step 2

Why this answer is correct

The correct answer is A. \(A\subseteq B\). The union is the same as (B), so (A) adds no new region. This means \(A\subseteq B\).

Step 3

Exam Tip

संघ (B) जितना ही है, इसलिए (A) कोई नया क्षेत्र नहीं जोड़ता। इसका अर्थ \(A\subseteq B\) है।

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Question 136/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n\(A\cap B\)=0), (n(A)=39) और (n(B)=48) है, तो (n\(A\triangle B\)) कितना है?

If (n\(A\cap B\)=0), (n(A)=39) and (n(B)=48), then what is (n\(A\triangle B\))?

Explanation opens after your attempt

Correct Answer

A. (87)

Step 1

Concept

The intersection is zero, so the symmetric difference is the whole union (39+48=87). For disjoint sets, no common part needs removal.

Step 2

Why this answer is correct

The correct answer is A. (87). The intersection is zero, so the symmetric difference is the whole union (39+48=87). For disjoint sets, no common part needs removal.

Step 3

Exam Tip

प्रतिच्छेद शून्य है, इसलिए सममित अंतर पूरा संघ (39+48=87) है। असंबद्ध समुच्चयों में कोई साझा भाग हटाना नहीं पड़ता।

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Question 137/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

किसी पुस्तकालय में (150) विद्यार्थियों में (83) उपन्यास पढ़ते हैं, (69) कविता पढ़ते हैं और (28) कोई भी नहीं पढ़ते। दोनों पढ़ने वाले कितने हैं?

In a library, among (150) students, (83) read novels, (69) read poetry and (28) read neither. How many read both?

Explanation opens after your attempt

Correct Answer

A. (30)

Step 1

Concept

At least one is (150-28=122), so both is (83+69-122=30). First get the union from the outside part.

Step 2

Why this answer is correct

The correct answer is A. (30). At least one is (150-28=122), so both is (83+69-122=30). First get the union from the outside part.

Step 3

Exam Tip

कम से कम एक (150-28=122) है, इसलिए दोनों (83+69-122=30) हैं। पहले संघ को बाहर वाले भाग से निकालें।

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Question 138/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

एक परीक्षा में (180) विद्यार्थियों में (97) ने प्रश्न (A), (88) ने प्रश्न (B), (82) ने प्रश्न (C), (41) ने (A) और (B), (36) ने (B) और (C), (34) ने (C) और (A), तथा (18) ने तीनों हल किए। कम से कम एक प्रश्न हल करने वाले कितने हैं?

In an exam, among (180) students, (97) solved question (A), (88) solved question (B), (82) solved question (C), (41) solved (A) and (B), (36) solved (B) and (C), (34) solved (C) and (A), and (18) solved all three. How many solved at least one question?

Explanation opens after your attempt

Correct Answer

A. (174)

Step 1

Concept

At least one is (97+88+82-41-36-34+18=174). In three sets, the centre must be added at the end.

Step 2

Why this answer is correct

The correct answer is A. (174). At least one is (97+88+82-41-36-34+18=174). In three sets, the centre must be added at the end.

Step 3

Exam Tip

कम से कम एक (97+88+82-41-36-34+18=174) है। तीन समुच्चयों में केंद्र को अंत में जोड़ना जरूरी है।

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Question 139/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि केवल \(A\cap B\) में (19), केवल \(B\cap C\) में (17), केवल \(C\cap A\) में (21) और \(A\cap B\cap C\) में (11) तत्व हैं, तो कम से कम दो समुच्चयों में आने वाले तत्व कितने हैं?

If only \(A\cap B\) has (19), only \(B\cap C\) has (17), only \(C\cap A\) has (21), and \(A\cap B\cap C\) has (11) elements, then how many elements are in at least two sets?

Explanation opens after your attempt

Correct Answer

A. (68)

Step 1

Concept

At least two includes the pairwise-only regions and the centre, so (19+17+21+11=68). Count the centre once.

Step 2

Why this answer is correct

The correct answer is A. (68). At least two includes the pairwise-only regions and the centre, so (19+17+21+11=68). Count the centre once.

Step 3

Exam Tip

कम से कम दो में केवल दो-दो वाले भाग और केंद्र शामिल हैं, इसलिए (19+17+21+11=68) है। केंद्र को एक बार गिनें।

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Question 140/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि केवल (A) में (38), केवल (B) में (35), केवल (C) में (29), ठीक दो समुच्चयों में कुल (47) और तीनों में (14) तत्व हैं, तो (n\(A\cup B\cup C\)) कितना है?

If only (A) has (38), only (B) has (35), only (C) has (29), exactly two sets have total (47), and all three have (14) elements, then what is (n\(A\cup B\cup C\))?

Explanation opens after your attempt

Correct Answer

A. (163)

Step 1

Concept

The union is the sum of all disjoint regions (38+35+29+47+14=163). Do not add separate Venn regions twice.

Step 2

Why this answer is correct

The correct answer is A. (163). The union is the sum of all disjoint regions (38+35+29+47+14=163). Do not add separate Venn regions twice.

Step 3

Exam Tip

संघ सभी अलग क्षेत्रों का योग (38+35+29+47+14=163) है। अलग वेन क्षेत्रों को दोबारा न जोड़ें।

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Question 141/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=82), (n(B)=77), (n(C)=69), (n\(A\cup B\cup C\)=151), (n\(A\cap B\)=32), (n\(B\cap C\)=28), (n\(C\cap A\)=25) है, तो (n\(A\cap B\cap C\)) कितना है?

If (n(A)=82), (n(B)=77), (n(C)=69), (n\(A\cup B\cup C\)=151), (n\(A\cap B\)=32), (n\(B\cap C\)=28), (n\(C\cap A\)=25), then what is (n\(A\cap B\cap C\))?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

Using (151=82+77+69-32-28-25+x), we get (x=8). Let the unknown centre be (x) and form an equation.

Step 2

Why this answer is correct

The correct answer is A. (8). Using (151=82+77+69-32-28-25+x), we get (x=8). Let the unknown centre be (x) and form an equation.

Step 3

Exam Tip

सूत्र में (151=82+77+69-32-28-25+x), इसलिए (x=8) है। अज्ञात केंद्र को (x) मानकर समीकरण बनाएं।

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Question 142/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A\cap\(B\cup C\))=52), केवल \(A\cap B\) में (23) और केवल \(A\cap C\) में (18) तत्व हैं, तो (n\(A\cap B\cap C\)) कितना है?

If (n(A\cap\(B\cup C\))=52), only \(A\cap B\) has (23) and only \(A\cap C\) has (18) elements, then what is (n\(A\cap B\cap C\))?

Explanation opens after your attempt

Correct Answer

A. (11)

Step 1

Concept

(A\cap\(B\cup C\)) includes only \(A\cap B\), only \(A\cap C\), and the centre, so the centre is (52-23-18=11).

Step 2

Why this answer is correct

The correct answer is A. (11). (A\cap\(B\cup C\)) includes only \(A\cap B\), only \(A\cap C\), and the centre, so the centre is (52-23-18=11).

Step 3

Exam Tip

(A\cap\(B\cup C\)) में केवल \(A\cap B\), केवल \(A\cap C\) और केंद्र आते हैं, इसलिए केंद्र (52-23-18=11) है।

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Question 143/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (A), (B) और (C) परस्पर असंबद्ध हैं, (n(A)=27), (n(B)=34), (n(C)=41) और (n(U)=125) है, तो (n(\(A\cup B\cup C\)')) कितना है?

If (A), (B) and (C) are mutually disjoint, (n(A)=27), (n(B)=34), (n(C)=41) and (n(U)=125), then what is (n(\(A\cup B\cup C\)'))?

Explanation opens after your attempt

Correct Answer

A. (23)

Step 1

Concept

For mutually disjoint sets, the union is (27+34+41=102), so the complement is (125-102=23). No common part needs to be subtracted.

Step 2

Why this answer is correct

The correct answer is A. (23). For mutually disjoint sets, the union is (27+34+41=102), so the complement is (125-102=23). No common part needs to be subtracted.

Step 3

Exam Tip

परस्पर असंबद्ध होने पर संघ (27+34+41=102) है, इसलिए पूरक (125-102=23) है। साझा भाग घटाने की जरूरत नहीं होती।

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Question 144/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(A\subseteq B\subseteq C\subseteq U\) है, तो (\(A\cup B\cup C\)') किसके बराबर होगा?

If \(A\subseteq B\subseteq C\subseteq U\), then (\(A\cup B\cup C\)') is equal to what?

Explanation opens after your attempt

Correct Answer

A. (C')

Step 1

Concept

In the chain, the union is the largest set (C), so its complement is (C'). Simplify the union first.

Step 2

Why this answer is correct

The correct answer is A. (C'). In the chain, the union is the largest set (C), so its complement is (C'). Simplify the union first.

Step 3

Exam Tip

श्रृंखला में संघ सबसे बड़ा समुच्चय (C) है, इसलिए उसका पूरक (C') होगा। पहले संघ को सरल करें।

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Question 145/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A-B)=0), (n(B-C)=0) और (n(A)>0) है, तो कौन सा संबंध अवश्य सही है?

If (n(A-B)=0), (n(B-C)=0) and (n(A)>0), which relation must be true?

Explanation opens after your attempt

Correct Answer

A. \(A\subseteq C\)

Step 1

Concept

(A-B=0) gives \(A\subseteq B\), and (B-C=0) gives \(B\subseteq C\). Therefore, \(A\subseteq C\) must be true.

Step 2

Why this answer is correct

The correct answer is A. \(A\subseteq C\). (A-B=0) gives \(A\subseteq B\), and (B-C=0) gives \(B\subseteq C\). Therefore, \(A\subseteq C\) must be true.

Step 3

Exam Tip

(A-B=0) से \(A\subseteq B\) और (B-C=0) से \(B\subseteq C\) मिलता है। इसलिए \(A\subseteq C\) अवश्य सही है।

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Question 146/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n\(A\cup B\cup C\)=184), (n(A)=86), (n(B)=91), (n(C)=88) और (n\(A\cap B\cap C\)=23) है, तो (n\(A\cap B\)+n\(B\cap C\)+n\(C\cap A\)) कितना है?

If (n\(A\cup B\cup C\)=184), (n(A)=86), (n(B)=91), (n(C)=88) and (n\(A\cap B\cap C\)=23), then what is (n\(A\cap B\)+n\(B\cap C\)+n\(C\cap A\))?

Explanation opens after your attempt

Correct Answer

A. (104)

Step 1

Concept

Using the formula (184=86+91+88-S+23), so (S=104). Here (S) is the sum of the three pairwise intersections.

Step 2

Why this answer is correct

The correct answer is A. (104). Using the formula (184=86+91+88-S+23), so (S=104). Here (S) is the sum of the three pairwise intersections.

Step 3

Exam Tip

सूत्र से (184=86+91+88-S+23), इसलिए (S=104) है। यहाँ (S) तीनों युग्म प्रतिच्छेदों का योग है।

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Question 147/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A-B)=24), (n(B-C)=27) और (n(C-A)=22) ही दिए गए हैं, तो क्या केवल इनसे (n\(A\cup B\cup C\)) निश्चित किया जा सकता है?

If only (n(A-B)=24), (n(B-C)=27) and (n(C-A)=22) are given, can (n\(A\cup B\cup C\)) be determined uniquely?

Explanation opens after your attempt

Correct Answer

A. नहीं, साझा क्षेत्रों की जानकारी चाहिएNo, information about common regions is needed

Step 1

Concept

These differences do not determine all Venn regions. To find the union, information about both only-regions and common regions is needed.

Step 2

Why this answer is correct

The correct answer is A. नहीं, साझा क्षेत्रों की जानकारी चाहिए / No, information about common regions is needed. These differences do not determine all Venn regions. To find the union, information about both only-regions and common regions is needed.

Step 3

Exam Tip

इन अंतरों से सभी वेन क्षेत्र नहीं मिलते। संघ निकालने के लिए केवल और साझा दोनों क्षेत्रों की जानकारी चाहिए।

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Question 148/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

अभिकथन: (\(A\cup B\)'=A'\cap B')। कारण: \(A\cup B\) से बाहर रहने के लिए तत्व को (A) और (B) दोनों से बाहर होना चाहिए। सही विकल्प चुनें।

Assertion: (\(A\cup B\)'=A'\cap B'). Reason: To be outside \(A\cup B\), an element must be outside both (A) and (B). Choose the correct option.

Explanation opens after your attempt

Correct Answer

A. अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या हैBoth assertion and reason are true, and the reason is the correct explanation

Step 1

Concept

This is De Morgan's law, and the reason correctly explains its Venn meaning. In complement questions, focus on the outside region.

Step 2

Why this answer is correct

The correct answer is A. अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या है / Both assertion and reason are true, and the reason is the correct explanation. This is De Morgan's law, and the reason correctly explains its Venn meaning. In complement questions, focus on the outside region.

Step 3

Exam Tip

यह डी मॉर्गन नियम है और कारण उसके वेन आरेखीय अर्थ को सही बताता है। पूरक वाले प्रश्नों में बाहर वाले क्षेत्र पर ध्यान दें।

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Question 149/150 Expert Mathematics Sets Venn Diagrams Class 11 Level 15

अभिकथन: यदि \(A\subseteq B\), तो \(A\cap B=A\)। कारण: (A) का हर तत्व (B) में भी होता है। सही विकल्प चुनें।

Assertion: If \(A\subseteq B\), then \(A\cap B=A\). Reason: Every element of (A) is also in (B). Choose the correct option.

Explanation opens after your attempt

Correct Answer

A. अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या हैBoth assertion and reason are true, and the reason is the correct explanation

Step 1

Concept

Both are true because (A) lies completely inside (B). In a subset relation, the smaller set gives the intersection.

Step 2

Why this answer is correct

The correct answer is A. अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या है / Both assertion and reason are true, and the reason is the correct explanation. Both are true because (A) lies completely inside (B). In a subset relation, the smaller set gives the intersection.

Step 3

Exam Tip

दोनों सही हैं क्योंकि (A) पूरा (B) के भीतर है। उपसमुच्चय में छोटा समुच्चय प्रतिच्छेद देता है।

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Question 150/150 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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Class 11 Mathematics - Sets - Venn Diagrams Expert Quiz

एक सर्वे में (n(U)=120), (n(A)=62), (n(B)=55) और (n\(A\cup B\)=91) है। वेन आरेख के अनुसार (n\(A\cap B\)) कितना होगा?

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Exam Tip

किसी कक्षा में (n(U)=80), (n(A)=37), (n(B)=42) और (n\(A\cap B\)=19) है। केवल (A) में आने वाले विद्यार्थियों की संख्या कितनी है?

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यदि (n(U)=150), (n(A)=70), (n(B)=65) और (n\(A\cap B\)=28) है, तो (n(\(A\cup B\)')) कितना है?

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Why this answer is correct

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यदि (n(A)=4x+5), (n(B)=3x+8), (n\(A\cap B\)=2x+1) और (n\(A\cup B\)=72) है, तो (x) का मान क्या होगा?

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तीन समुच्चयों के लिए (n(A)=48), (n(B)=50), (n(C)=44), (n\(A\cap B\)=20), (n\(B\cap C\)=18), (n\(C\cap A\)=16) और (n\(A\cap B\cap C\)=7) है। (n\(A\cup B\cup C\)) कितना होगा?

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Exam Tip

यदि \(U={1,2,\ldots,60}\), (A) (3) के गुणजों का समुच्चय और (B) (4) के गुणजों का समुच्चय है, तो (n(\(A\cup B\)')) कितना होगा?

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Exam Tip

यदि (n\(A\cap B\cap C\)=9), केवल \(A\cap B\) में (14), केवल \(B\cap C\) में (11), और केवल \(C\cap A\) में (13) तत्व हैं, तो (n(\(A\cap B\)\cup\(B\cap C\)\cup\(C\cap A\))) कितना है?

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Exam Tip

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?

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यदि (n\(A\cup B\)=76), (n(A-B)=31) और (n(B-A)=27) है, तो (n\(A\cap B\)) कितना होगा?

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यदि \(A\subseteq B\), (n(A)=32), (n(B)=57) और (n(U)=90) है, तो (n(B-A)) कितना होगा?

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यदि \(A\cap B=\varnothing\), (n(A)=41), (n(B)=39) और (n(U)=100) है, तो (n(\(A\cup B\)')) कितना है?

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यदि (n(A)=45), (n(B)=52), (n\(A\cup B\)=73) है, तो (n\(A\triangle B\)) कितना होगा, जहाँ \(A\triangle B=(A-B)\cup(B-A)\)?

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Exam Tip

यदि (n(U)=110), (n(A)=58), (n(B)=49) और (n(A-B)=21) है, तो (n(\(A\cup B\)')) कितना है?

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Why this answer is correct

Exam Tip

यदि (n(U)=110), (n(A)=58), (n(B)=49) और (n(A-B)=21) है, तो (n(\(A\cup B\)')) के लिए सही मान चुनें।

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तीन विषयों के सर्वे में (n(M)=60), (n(P)=54), (n(C)=50), (n\(M\cap P\)=25), (n\(P\cap C\)=22), (n\(C\cap M\)=20), (n\(M\cap P\cap C\)=10) है। केवल (M) पढ़ने वाले कितने हैं?

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कौन सा वेन आरेखीय संबंध (A-\(B\cup C\)) को दर्शाता है?

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