Class 11 Mathematics - Sets - Complement of a Set and its properties Hard Quiz

Mathematics Sets Complement of a Set and its properties Hard Class 11 Level 13

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Question 1/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

एक वेन आरेख में (n(U)=180), (n(A)=92), (n(B)=84) और (n(\(A\cup B\)^c)=38) हैं। (n\(A\cap B\)) कितना होगा?

In a Venn diagram (n(U)=180), (n(A)=92), (n(B)=84), and (n(\(A\cup B\)^c)=38). What is (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

B. (34)

Step 1

Concept

First (n\(A\cup B\)=180-38=142), then (n\(A\cap B\)=92+84-142=34). If the outside region is given, find the union first.

Step 2

Why this answer is correct

The correct answer is B. (34). First (n\(A\cup B\)=180-38=142), then (n\(A\cap B\)=92+84-142=34). If the outside region is given, find the union first.

Step 3

Exam Tip

पहले (n\(A\cup B\)=180-38=142), फिर (n\(A\cap B\)=92+84-142=34)। बाहर का भाग दिया हो तो पहले संघ निकालें।

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Question 2/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cup B\)=126), (n(A-B)=47) और (n(B-A)=39) है, तो (n\(A\cap B\)) कितना है?

If (n\(A\cup B\)=126), (n(A-B)=47), and (n(B-A)=39), what is (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

A. (40)

Step 1

Concept

The union is the sum of three separate parts, so (n\(A\cap B\)=126-47-39=40). In region-partition questions, identify separate inside regions.

Step 2

Why this answer is correct

The correct answer is A. (40). The union is the sum of three separate parts, so (n\(A\cap B\)=126-47-39=40). In region-partition questions, identify separate inside regions.

Step 3

Exam Tip

संघ तीन अलग भागों का योग है, इसलिए (n\(A\cap B\)=126-47-39=40)। क्षेत्रीय विभाजन वाले प्रश्नों में अंदर के अलग भाग पहचानें।

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Question 3/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

एक कक्षा में (n(A)=74), (n(B)=68) और ठीक एक समुच्चय में (86) विद्यार्थी हैं। (n\(A\cap B\)) कितना होगा?

In a class (n(A)=74), (n(B)=68), and (86) students are in exactly one set. What is (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

C. (28)

Step 1

Concept

Exactly one is (n(A)+n(B)-2n\(A\cap B\)), so (86=142-2x) gives (x=28). For inverse questions, form an equation.

Step 2

Why this answer is correct

The correct answer is C. (28). Exactly one is (n(A)+n(B)-2n\(A\cap B\)), so (86=142-2x) gives (x=28). For inverse questions, form an equation.

Step 3

Exam Tip

ठीक एक (n(A)+n(B)-2n\(A\cap B\)) होता है, इसलिए (86=142-2x) से (x=28)। इस प्रकार उल्टे प्रश्न में समीकरण बनाएं।

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Question 4/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(U)=120), (n(A)=77) और (n(B)=64) है, तो (n\(A\cap B\)) का न्यूनतम संभव मान क्या होगा?

If (n(U)=120), (n(A)=77), and (n(B)=64), what is the minimum possible value of (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

C. (21)

Step 1

Concept

The minimum intersection is (n(A)+n(B)-n(U)=77+64-120=21). When the total exceeds (U), the extra part must be common.

Step 2

Why this answer is correct

The correct answer is C. (21). The minimum intersection is (n(A)+n(B)-n(U)=77+64-120=21). When the total exceeds (U), the extra part must be common.

Step 3

Exam Tip

न्यूनतम प्रतिच्छेद (n(A)+n(B)-n(U)=77+64-120=21) है। जब कुल (U) से अधिक हो जाए तो अतिरिक्त भाग अनिवार्य साझा होता है।

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Question 5/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(U)=150), (n(A)=66) और (n(B)=59) है, तो (n\(A\cap B\)) का अधिकतम संभव मान क्या होगा?

If (n(U)=150), (n(A)=66), and (n(B)=59), what is the maximum possible value of (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

B. (59)

Step 1

Concept

The maximum intersection cannot exceed the smaller set, so the value is (59). For maximum, check (\min(n(A),n(B))).

Step 2

Why this answer is correct

The correct answer is B. (59). The maximum intersection cannot exceed the smaller set, so the value is (59). For maximum, check (\min(n(A),n(B))).

Step 3

Exam Tip

अधिकतम प्रतिच्छेद छोटे समुच्चय से अधिक नहीं हो सकता, इसलिए मान (59) है। अधिकतम के लिए (\min(n(A),n(B))) देखें।

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Question 6/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि \(A\subseteq B\), (n(A)=38), (n(B)=91) और (n(U)=130) है, तो (n\(B^c\)) कितना होगा?

If \(A\subseteq B\), (n(A)=38), (n(B)=91), and (n(U)=130), what is (n\(B^c\))?

Explanation opens after your attempt
Correct Answer

A. (39)

Step 1

Concept

\(B^c\) contains elements of (U) not in (B), so (130-91=39). The subset information is not needed here and can be a trap.

Step 2

Why this answer is correct

The correct answer is A. (39). \(B^c\) contains elements of (U) not in (B), so (130-91=39). The subset information is not needed here and can be a trap.

Step 3

Exam Tip

\(B^c\) में (U) के वे तत्व हैं जो (B) में नहीं हैं, इसलिए (130-91=39)। उपसमुच्चय जानकारी यहां जरूरी नहीं है, यह जाल हो सकता है।

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Question 7/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि \(A\subseteq B\subseteq C\), (n(C)=118), (n(B)=73) और (n(A)=29) है, तो (n(C-A)) कितना होगा?

If \(A\subseteq B\subseteq C\), (n(C)=118), (n(B)=73), and (n(A)=29), what is (n(C-A))?

Explanation opens after your attempt
Correct Answer

C. (89)

Step 1

Concept

Since (A) lies fully inside (C), (n(C-A)=118-29=89). In a nested Venn diagram, subtract only the set being removed.

Step 2

Why this answer is correct

The correct answer is C. (89). Since (A) lies fully inside (C), (n(C-A)=118-29=89). In a nested Venn diagram, subtract only the set being removed.

Step 3

Exam Tip

क्योंकि (A) पूरा (C) में है, इसलिए (n(C-A)=118-29=89)। nested वेन आरेख में जिस समुच्चय को हटाना हो केवल वही घटाएं।

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Question 8/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

तीन समुच्चयों के लिए (n(A)=64), (n(B)=58), (n(C)=52), (n\(A\cap B\)=24), (n\(B\cap C\)=21), (n\(C\cap A\)=19) और (n\(A\cap B\cap C\)=8) है। (n\(A\cup B\cup C\)) कितना है?

For three sets (n(A)=64), (n(B)=58), (n(C)=52), (n\(A\cap B\)=24), (n\(B\cap C\)=21), (n\(C\cap A\)=19), and (n\(A\cap B\cap C\)=8). What is (n\(A\cup B\cup C\))?

Explanation opens after your attempt
Correct Answer

B. (118)

Step 1

Concept

The union of three sets is (64+58+52-24-21-19+8=118). After subtracting pairwise intersections, add the central part back.

Step 2

Why this answer is correct

The correct answer is B. (118). The union of three sets is (64+58+52-24-21-19+8=118). After subtracting pairwise intersections, add the central part back.

Step 3

Exam Tip

तीन समुच्चयों का संघ (64+58+52-24-21-19+8=118) है। जोड़ी प्रतिच्छेद घटाने के बाद केंद्रीय भाग वापस जोड़ें।

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Question 9/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(A)=70), (n(B)=65), (n(C)=60), (n\(A\cup B\cup C\)=140), (n\(A\cap B\)=28), (n\(B\cap C\)=24) और (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\(A\cup B\cup C\)=140), (n\(A\cap B\)=28), (n\(B\cap C\)=24), and (n\(C\cap A\)=22), what is (n\(A\cap B\cap C\))?

Explanation opens after your attempt
Correct Answer

C. (19)

Step 1

Concept

In the formula (140=70+65+60-28-24-22+x), so (x=19). For the central part, write inclusion-exclusion as an equation.

Step 2

Why this answer is correct

The correct answer is C. (19). In the formula (140=70+65+60-28-24-22+x), so (x=19). For the central part, write inclusion-exclusion as an equation.

Step 3

Exam Tip

सूत्र में (140=70+65+60-28-24-22+x) होगा, इसलिए (x=19)। केंद्रीय भाग के लिए समावेशन-बहिष्करण को समीकरण की तरह लिखें।

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Question 10/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

तीन समुच्चयों में (n\(A\cap B\)=31), (n\(B\cap C\)=29), (n\(C\cap A\)=25) और (n\(A\cap B\cap C\)=12) है। ठीक दो समुच्चयों में आने वाले तत्व कितने हैं?

In three sets (n\(A\cap B\)=31), (n\(B\cap C\)=29), (n\(C\cap A\)=25), and (n\(A\cap B\cap C\)=12). How many elements are in exactly two sets?

Explanation opens after your attempt
Correct Answer

A. (49)

Step 1

Concept

Exactly two (=(31-12)+(29-12)+(25-12)=49). Each pairwise intersection includes the central part, so subtract it.

Step 2

Why this answer is correct

The correct answer is A. (49). Exactly two (=(31-12)+(29-12)+(25-12)=49). Each pairwise intersection includes the central part, so subtract it.

Step 3

Exam Tip

ठीक दो (=(31-12)+(29-12)+(25-12)=49) है। प्रत्येक जोड़ी में केंद्रीय भाग शामिल होता है, इसलिए उसे घटाएं।

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Question 11/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(A)=80), (n\(A\cap B\)=35), (n\(A\cap C\)=32) और (n\(A\cap B\cap C\)=14) है, तो केवल (A) में आने वाले तत्व कितने हैं?

If (n(A)=80), (n\(A\cap B\)=35), (n\(A\cap C\)=32), and (n\(A\cap B\cap C\)=14), how many elements are only in (A)?

Explanation opens after your attempt
Correct Answer

C. (27)

Step 1

Concept

Only (A=80-35-32+14=27). The central part is subtracted twice, so add it back once.

Step 2

Why this answer is correct

The correct answer is C. (27). Only (A=80-35-32+14=27). The central part is subtracted twice, so add it back once.

Step 3

Exam Tip

केवल (A=80-35-32+14=27) है। केंद्रीय भाग दो बार घटता है, इसलिए एक बार वापस जोड़ें।

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Question 12/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cap B\)=42), (n\(A\cap C\)=36), (n\(B\cap C\)=34) और (n\(A\cap B\cap C\)=15) है, तो कम से कम दो समुच्चयों में आने वाले तत्व कितने हैं?

If (n\(A\cap B\)=42), (n\(A\cap C\)=36), (n\(B\cap C\)=34), and (n\(A\cap B\cap C\)=15), how many elements are in at least two sets?

Explanation opens after your attempt
Correct Answer

A. (67)

Step 1

Concept

At least two should be ((42-15)+(36-15)+(34-15)+15=82), so the correct value is (82). First find exactly two and then add the all-three part.

Step 2

Why this answer is correct

The correct answer is A. (67). At least two should be ((42-15)+(36-15)+(34-15)+15=82), so the correct value is (82). First find exactly two and then add the all-three part.

Step 3

Exam Tip

कम से कम दो (=(42-15)+(36-15)+(34-15)+15=82) होना चाहिए, इसलिए सही मान (82) है। पहले ठीक दो निकालें और फिर तीनों वाला भाग जोड़ें।

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Question 13/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

तीन समुच्चयों में केवल (A=23), केवल (B=27), केवल (C=21), केवल \(A\cap B=13\), केवल \(B\cap C=11\), केवल \(C\cap A=9\) और \(A\cap B\cap C=7\) हैं। (n(\(A\cup B\cup C\)^c)) कितना होगा यदि (n(U)=130)?

In three sets, only (A=23), only (B=27), only (C=21), only \(A\cap B=13\), only \(B\cap C=11\), only \(C\cap A=9\), and \(A\cap B\cap C=7\). What is (n(\(A\cup B\cup C\)^c)) if (n(U)=130)?

Explanation opens after your attempt
Correct Answer

A. (19)

Step 1

Concept

The inside union is (23+27+21+13+11+9+7=111), so outside is (130-111=19). Add all seven inside regions only once.

Step 2

Why this answer is correct

The correct answer is A. (19). The inside union is (23+27+21+13+11+9+7=111), so outside is (130-111=19). Add all seven inside regions only once.

Step 3

Exam Tip

अंदर का संघ (23+27+21+13+11+9+7=111), इसलिए बाहर (130-111=19)। सातों अंदरूनी क्षेत्रों को केवल एक बार जोड़ें।

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Question 14/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि केवल (A=18), केवल \(A\cap B=12\), केवल \(A\cap C=10\) और \(A\cap B\cap C=6\) हैं, तो (n(A)) कितना होगा?

If only (A=18), only \(A\cap B=12\), only \(A\cap C=10\), and \(A\cap B\cap C=6\), what is (n(A))?

Explanation opens after your attempt
Correct Answer

C. (46)

Step 1

Concept

The sum of all inside parts of (A) is (18+12+10+6=46). The total of a set comes from all regions of its circle.

Step 2

Why this answer is correct

The correct answer is C. (46). The sum of all inside parts of (A) is (18+12+10+6=46). The total of a set comes from all regions of its circle.

Step 3

Exam Tip

(A) के सभी अंदरूनी भागों का योग (18+12+10+6=46) है। किसी समुच्चय की कुल संख्या उसके पूरे वृत्त के भागों से मिलती है।

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Question 15/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

एक वेन आरेख में (n\(A\triangle B\)=82) और (n\(A\cup B\)=119) है। (n\(A\cap B\)) कितना होगा?

In a Venn diagram (n\(A\triangle B\)=82) and (n\(A\cup B\)=119). What is (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

A. (37)

Step 1

Concept

\(A\cup B\) contains both \(A\triangle B\) and \(A\cap B\), so (119-82=37). The symmetric difference does not include the common part.

Step 2

Why this answer is correct

The correct answer is A. (37). \(A\cup B\) contains both \(A\triangle B\) and \(A\cap B\), so (119-82=37). The symmetric difference does not include the common part.

Step 3

Exam Tip

\(A\cup B\) में \(A\triangle B\) और \(A\cap B\) दोनों शामिल हैं, इसलिए (119-82=37)। सममित अंतर में साझा भाग नहीं आता।

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Question 16/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(A)=73), (n(B)=69) और (n\(A\triangle B\)=88) है, तो (n\(A\cap B\)) कितना है?

If (n(A)=73), (n(B)=69), and (n\(A\triangle B\)=88), what is (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

A. (27)

Step 1

Concept

(n\(A\triangle B\)=n(A)+n(B)-2n\(A\cap B\)), so (88=142-2x) gives (x=27). Distinguish exactly one from the common part.

Step 2

Why this answer is correct

The correct answer is A. (27). (n\(A\triangle B\)=n(A)+n(B)-2n\(A\cap B\)), so (88=142-2x) gives (x=27). Distinguish exactly one from the common part.

Step 3

Exam Tip

(n\(A\triangle B\)=n(A)+n(B)-2n\(A\cap B\)), इसलिए (88=142-2x) से (x=27)। ठीक एक और साझा भाग में अंतर करें।

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Question 17/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

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

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

Explanation opens after your attempt
Correct Answer

A. \(A\triangle B\)

Step 1

Concept

Removing the common part from the union leaves the regions belonging to exactly one set. That is \(A\triangle B\).

Step 2

Why this answer is correct

The correct answer is A. \(A\triangle B\). Removing the common part from the union leaves the regions belonging to exactly one set. That is \(A\triangle B\).

Step 3

Exam Tip

संघ से साझा भाग हटाने पर केवल एक-एक समुच्चय वाले भाग बचते हैं। यही \(A\triangle B\) है।

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Question 18/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

डी मॉर्गन नियम से (\(A\cap B\cap C\)^c) किसके बराबर है?

By De Morgan's law, what is (\(A\cap B\cap C\)^c) equal to?

Explanation opens after your attempt
Correct Answer

A. \(A^c\cup B^c\cup C^c\)

Step 1

Concept

The complement of an intersection changes into a union, so (\(A\cap B\cap C\)^c=A^c\cup B^c\cup C^c). Remember that the operation changes under complement.

Step 2

Why this answer is correct

The correct answer is A. \(A^c\cup B^c\cup C^c\). The complement of an intersection changes into a union, so (\(A\cap B\cap C\)^c=A^c\cup B^c\cup C^c). Remember that the operation changes under complement.

Step 3

Exam Tip

प्रतिच्छेद का पूरक संघ में बदलता है, इसलिए (\(A\cap B\cap C\)^c=A^c\cup B^c\cup C^c)। पूरक लेते समय चिन्ह बदलना याद रखें।

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Question 19/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

डी मॉर्गन नियम से (\(A\cup B\cup C\)^c) किसके बराबर है?

By De Morgan's law, what is (\(A\cup B\cup C\)^c) equal to?

Explanation opens after your attempt
Correct Answer

B. \(A^c\cap B^c\cap C^c\)

Step 1

Concept

The complement of a union changes into an intersection, so (\(A\cup B\cup C\)^c=A^c\cap B^c\cap C^c). In a Venn diagram, it is the outside of all three circles.

Step 2

Why this answer is correct

The correct answer is B. \(A^c\cap B^c\cap C^c\). The complement of a union changes into an intersection, so (\(A\cup B\cup C\)^c=A^c\cap B^c\cap C^c). In a Venn diagram, it is the outside of all three circles.

Step 3

Exam Tip

संघ का पूरक प्रतिच्छेद में बदलता है, इसलिए (\(A\cup B\cup C\)^c=A^c\cap B^c\cap C^c)। वेन आरेख में यह तीनों वृत्तों के बाहर का भाग है।

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Question 20/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(U)=200), (n\(A\cup B\)=128), (n\(A\cap B\)=36) और (n\(A^c\cap B^c\)=72) है, तो कौन सा संबंध सत्य है?

If (n(U)=200), (n\(A\cup B\)=128), (n\(A\cap B\)=36), and (n\(A^c\cap B^c\)=72), which relation is true?

Explanation opens after your attempt
Correct Answer

A. (n\(A\cup B\)+n\(A^c\cap B^c\)=n(U))

Step 1

Concept

(\(A\cup B\)^c=A^c\cap B^c), so (128+72=200) is true. Complementary regions together form the whole (U).

Step 2

Why this answer is correct

The correct answer is A. (n\(A\cup B\)+n\(A^c\cap B^c\)=n(U)). (\(A\cup B\)^c=A^c\cap B^c), so (128+72=200) is true. Complementary regions together form the whole (U).

Step 3

Exam Tip

(\(A\cup B\)^c=A^c\cap B^c), इसलिए (128+72=200) सही है। पूरक क्षेत्र मिलकर पूरा (U) बनाते हैं।

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Question 21/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

\((U={1,2,3,\ldots,30}), (A={x:x\) is a multiple of \(2}) और (B={x:x\) is a multiple of 3}) हैं। \((n(A\cap B)) कितना है\)?

\((U={1,2,3,\ldots,30}), (A={x:x\) is a multiple of \(2}), and (B={x:x\) is a multiple of \(3}). What is (n(A\cap B))\)?

Explanation opens after your attempt
Correct Answer

A. (5)

Step 1

Concept

The common elements are multiples of (6), namely (6,12,18,24,30). Hence the count is (5).

Step 2

Why this answer is correct

The correct answer is A. (5). The common elements are multiples of (6), namely (6,12,18,24,30). Hence the count is (5).

Step 3

Exam Tip

साझा तत्व (6) के गुणज होंगे, जो (6,12,18,24,30) हैं। इसलिए संख्या (5) है।

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Question 22/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

\((U={1,2,3,\ldots,40}), (A={x:x\) is divisible by \(4}) और (B={x:x\) is divisible by 5}) हैं। \((n(A\cup B)) कितना है\)?

\((U={1,2,3,\ldots,40}), (A={x:x\) is divisible by \(4}), and (B={x:x\) is divisible by \(5}). What is (n(A\cup B))\)?

Explanation opens after your attempt
Correct Answer

B. (16)

Step 1

Concept

Multiples of (4) are (10), multiples of (5) are (8), and multiples of (20) are (2), so (10+8-2=16). Use the LCM to find the common part.

Step 2

Why this answer is correct

The correct answer is B. (16). Multiples of (4) are (10), multiples of (5) are (8), and multiples of (20) are (2), so (10+8-2=16). Use the LCM to find the common part.

Step 3

Exam Tip

(4) के गुणज (10), (5) के गुणज (8), और (20) के गुणज (2) हैं, इसलिए (10+8-2=16)। लघुत्तम समापवर्त्य से साझा भाग निकालें।

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Question 23/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

\(U={1,2,3,\ldots,50}\), (A) अभाज्य संख्याओं का समुच्चय है और (B) सम संख्याओं का समुच्चय है। \(A\cap B\) क्या होगा?

\(U={1,2,3,\ldots,50}\), (A) is the set of prime numbers and (B) is the set of even numbers. What is \(A\cap B\)?

Explanation opens after your attempt
Correct Answer

A. ({2})

Step 1

Concept

(2) is the only even prime number. Therefore the intersection is ({2}).

Step 2

Why this answer is correct

The correct answer is A. ({2}). (2) is the only even prime number. Therefore the intersection is ({2}).

Step 3

Exam Tip

(2) ही एकमात्र सम अभाज्य संख्या है। इसलिए प्रतिच्छेद ({2}) होगा।

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Question 24/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

\((U={1,2,3,\ldots,60}), (A={x:x\) is divisible by \(2}), (B={x:x\) is divisible by \(3}) और (C={x:x\) is divisible by 5}) हैं। \((n(A\cap B\cap C)) कितना है\)?

\((U={1,2,3,\ldots,60}), (A={x:x\) is divisible by \(2}), (B={x:x\) is divisible by \(3}), and (C={x:x\) is divisible by \(5}). What is (n(A\cap B\cap C))\)?

Explanation opens after your attempt
Correct Answer

B. (2)

Step 1

Concept

To be in all three sets, a number must be divisible by (30), namely (30,60). Hence the count is (2).

Step 2

Why this answer is correct

The correct answer is B. (2). To be in all three sets, a number must be divisible by (30), namely (30,60). Hence the count is (2).

Step 3

Exam Tip

तीनों में आने के लिए संख्या (30) से विभाज्य होगी, यानी (30,60)। इसलिए संख्या (2) है।

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Question 25/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

\(U={1,2,3,\ldots,100}\), (A) (2) से विभाज्य, (B) (5) से विभाज्य और (C) (10) से विभाज्य संख्याओं के समुच्चय हैं। कौन सा संबंध सही है?

\(U={1,2,3,\ldots,100}\), (A) is the set of numbers divisible by (2), (B) by (5), and (C) by (10). Which relation is correct?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

A number divisible by (10) is divisible by both (2) and (5), so \(C=A\cap B\). In the Venn diagram, (C) is the common region.

Step 2

Why this answer is correct

The correct answer is A. \(C=A\cap B\). A number divisible by (10) is divisible by both (2) and (5), so \(C=A\cap B\). In the Venn diagram, (C) is the common region.

Step 3

Exam Tip

(10) से विभाज्य संख्या (2) और (5) दोनों से विभाज्य होती है, इसलिए \(C=A\cap B\)। वेन आरेख में (C) साझा भाग है।

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Question 26/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(A-B)=34), (n(B-C)=41), (n(C-A)=29) दिए हों, तो कौन सा निष्कर्ष हमेशा सही नहीं माना जा सकता?

If (n(A-B)=34), (n(B-C)=41), and (n(C-A)=29) are given, which conclusion cannot always be assumed true?

Explanation opens after your attempt
Correct Answer

A. इनसे (n\(A\cup B\cup C\)) निश्चित हो जाता हैThese determine (n\(A\cup B\cup C\))

Step 1

Concept

A few differences alone do not determine the whole union because intersection information is incomplete. In such questions, check whether the data is sufficient.

Step 2

Why this answer is correct

The correct answer is A. इनसे (n\(A\cup B\cup C\)) निश्चित हो जाता है / These determine (n\(A\cup B\cup C\)). A few differences alone do not determine the whole union because intersection information is incomplete. In such questions, check whether the data is sufficient.

Step 3

Exam Tip

केवल कुछ अंतरों से पूरा संघ निश्चित नहीं होता क्योंकि प्रतिच्छेदों की जानकारी अधूरी है। ऐसे प्रश्नों में पर्याप्त डेटा की जांच करें।

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Question 27/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

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

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

Explanation opens after your attempt
Correct Answer

A. \(A\cap B=\varnothing\)

Step 1

Concept

In the union formula, the subtracted part is (n\(A\cap B\)), which must be (0) here. Hence the sets are disjoint.

Step 2

Why this answer is correct

The correct answer is A. \(A\cap B=\varnothing\). In the union formula, the subtracted part is (n\(A\cap B\)), which must be (0) here. Hence the sets are disjoint.

Step 3

Exam Tip

संघ सूत्र में घटने वाला भाग (n\(A\cap B\)) है, जो यहां (0) होगा। इसलिए समुच्चय असंबद्ध हैं।

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Question 28/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cup B\)=n(A)), तो कौन सा संबंध अवश्य सत्य है?

If (n\(A\cup B\)=n(A)), which relation must be true?

Explanation opens after your attempt
Correct Answer

A. \(B\subseteq A\)

Step 1

Concept

Adding (B) to (A) does not enlarge the region, so (B) is already inside (A). Therefore \(B\subseteq A\).

Step 2

Why this answer is correct

The correct answer is A. \(B\subseteq A\). Adding (B) to (A) does not enlarge the region, so (B) is already inside (A). Therefore \(B\subseteq A\).

Step 3

Exam Tip

संघ में (B) जोड़ने पर (A) से बड़ा क्षेत्र नहीं बन रहा, इसलिए (B) पहले से (A) में है। इसलिए \(B\subseteq A\)।

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Question 29/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cap B\)=n(A)), तो कौन सा संबंध अवश्य सत्य है?

If (n\(A\cap B\)=n(A)), which relation must be true?

Explanation opens after your attempt
Correct Answer

A. \(A\subseteq B\)

Step 1

Concept

All of (A) is appearing in the intersection, so every element of (A) is also in (B). Hence \(A\subseteq B\).

Step 2

Why this answer is correct

The correct answer is A. \(A\subseteq B\). All of (A) is appearing in the intersection, so every element of (A) is also in (B). Hence \(A\subseteq B\).

Step 3

Exam Tip

पूरा (A) प्रतिच्छेद में आ रहा है, इसलिए (A) का हर तत्व (B) में भी है। अतः \(A\subseteq B\)।

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Question 30/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(A)=48), (n(B)=52), (n(A-B)=17) और (n(B-A)=21) है, तो (n\(A\cap B\)) कितना होगा?

If (n(A)=48), (n(B)=52), (n(A-B)=17), and (n(B-A)=21), what is (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

A. (31)

Step 1

Concept

(n\(A\cap B\)=n(A)-n(A-B)=48-17=31). From (B), (52-21=31) should also match.

Step 2

Why this answer is correct

The correct answer is A. (31). (n\(A\cap B\)=n(A)-n(A-B)=48-17=31). From (B), (52-21=31) should also match.

Step 3

Exam Tip

(n\(A\cap B\)=n(A)-n(A-B)=48-17=31)। (B) से भी (52-21=31) मिलना चाहिए।

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Question 31/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(A)=55), (n(B)=50), (n(A-B)=20) और (n(B-A)=18) है, तो दिए गए आंकड़ों के बारे में सही निष्कर्ष क्या है?

If (n(A)=55), (n(B)=50), (n(A-B)=20), and (n(B-A)=18), what is the correct conclusion about the given data?

Explanation opens after your attempt
Correct Answer

A. आंकड़े असंगत हैंThe data are inconsistent

Step 1

Concept

From (A), the common part is (55-20=35), but from (B), it is (50-18=32). Since these are not equal, the data are inconsistent.

Step 2

Why this answer is correct

The correct answer is A. आंकड़े असंगत हैं / The data are inconsistent. From (A), the common part is (55-20=35), but from (B), it is (50-18=32). Since these are not equal, the data are inconsistent.

Step 3

Exam Tip

(A) से साझा भाग (55-20=35), लेकिन (B) से (50-18=32) मिलता है। दोनों बराबर नहीं हैं, इसलिए आंकड़े असंगत हैं।

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Question 32/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

एक सर्वे में (n(U)=200), (n(A)=96), (n(B)=88), (n(C)=74), (n\(A\cap B\)=40), (n\(B\cap C\)=31), (n\(C\cap A\)=29) और (n\(A\cap B\cap C\)=12) हैं। किसी भी समुच्चय में नहीं आने वाले कितने हैं?

In a survey (n(U)=200), (n(A)=96), (n(B)=88), (n(C)=74), (n\(A\cap B\)=40), (n\(B\cap C\)=31), (n\(C\cap A\)=29), and (n\(A\cap B\cap C\)=12). How many are in none of the sets?

Explanation opens after your attempt
Correct Answer

C. (30)

Step 1

Concept

The union is (96+88+74-40-31-29+12=170), so none is (200-170=30). First find the three-set union.

Step 2

Why this answer is correct

The correct answer is C. (30). The union is (96+88+74-40-31-29+12=170), so none is (200-170=30). First find the three-set union.

Step 3

Exam Tip

संघ (96+88+74-40-31-29+12=170) है, इसलिए कोई नहीं (200-170=30)। पहले तीन-समुच्चय संघ निकालें।

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Question 33/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

तीन समुच्चयों में (n\(A\cup B\cup C\)=150), केवल (A=32), केवल (B=28), केवल (C=24), केवल \(A\cap B=18\), केवल \(B\cap C=16\) और केवल \(C\cap A=14\) हैं। (n\(A\cap B\cap C\)) कितना होगा?

In three sets (n\(A\cup B\cup C\)=150), only (A=32), only (B=28), only (C=24), only \(A\cap B=18\), only \(B\cap C=16\), and only \(C\cap A=14\). What is (n\(A\cap B\cap C\))?

Explanation opens after your attempt
Correct Answer

B. (18)

Step 1

Concept

The sum of six known inside regions is (32+28+24+18+16+14=132), so the central part is (150-132=18). The union contains all seven inside regions.

Step 2

Why this answer is correct

The correct answer is B. (18). The sum of six known inside regions is (32+28+24+18+16+14=132), so the central part is (150-132=18). The union contains all seven inside regions.

Step 3

Exam Tip

ज्ञात छह अंदरूनी क्षेत्रों का योग (32+28+24+18+16+14=132) है, इसलिए केंद्रीय भाग (150-132=18)। संघ में सभी सात अंदरूनी क्षेत्र आते हैं।

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Question 34/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि तीन समुच्चयों में ठीक एक समुच्चय में (71), ठीक दो समुच्चयों में (46) और तीनों में (15) तत्व हैं, तो (n\(A\cup B\cup C\)) कितना है?

If in three sets (71) elements are in exactly one set, (46) in exactly two sets, and (15) in all three sets, what is (n\(A\cup B\cup C\))?

Explanation opens after your attempt
Correct Answer

C. (132)

Step 1

Concept

The union includes the regions of exactly one, exactly two, and all three. Hence (71+46+15=132).

Step 2

Why this answer is correct

The correct answer is C. (132). The union includes the regions of exactly one, exactly two, and all three. Hence (71+46+15=132).

Step 3

Exam Tip

संघ में ठीक एक, ठीक दो और तीनों वाले सभी भाग आते हैं। इसलिए (71+46+15=132)।

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Question 35/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cup B\cup C\)=128), ठीक एक समुच्चय में (63) और तीनों में (11) तत्व हैं, तो ठीक दो समुच्चयों में कितने तत्व हैं?

If (n\(A\cup B\cup C\)=128), (63) elements are in exactly one set, and (11) are in all three sets, how many elements are in exactly two sets?

Explanation opens after your attempt
Correct Answer

B. (54)

Step 1

Concept

Exactly two is (128-63-11=54). Solve by dividing the union into three classes.

Step 2

Why this answer is correct

The correct answer is B. (54). Exactly two is (128-63-11=54). Solve by dividing the union into three classes.

Step 3

Exam Tip

ठीक दो (128-63-11=54) हैं। संघ को तीन वर्गों में बांटकर हल करें।

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Question 36/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

एक सर्वे में (n(A)=82), (n(B)=76), (n(C)=70) और ठीक दो समुच्चयों में (54) तथा तीनों में (18) लोग हैं। ठीक एक समुच्चय में कितने लोग हैं?

In a survey (n(A)=82), (n(B)=76), (n(C)=70), and (54) people are in exactly two sets while (18) are in all three. How many people are in exactly one set?

Explanation opens after your attempt
Correct Answer

C. (120)

Step 1

Concept

Total memberships are (82+76+70=228). This equals exactly one \(+2\times54+3\times18\), so exactly one is (228-108-54=66).

Step 2

Why this answer is correct

The correct answer is C. (120). Total memberships are (82+76+70=228). This equals exactly one \(+2\times54+3\times18\), so exactly one is (228-108-54=66).

Step 3

Exam Tip

कुल सदस्यता (82+76+70=228) है। यह ठीक एक \(+2\times54+3\times18\) के बराबर है, इसलिए ठीक एक (228-108-54=66)।

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Question 37/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cup B\)=104), (n\(A\cap B\)=26) और (n(A-B)=37) है, तो (n(B)) कितना होगा?

If (n\(A\cup B\)=104), (n\(A\cap B\)=26), and (n(A-B)=37), what is (n(B))?

Explanation opens after your attempt
Correct Answer

C. (67)

Step 1

Concept

First (n(B-A)=104-37-26=41), then (n(B)=41+26=67). Add only (B) and the common part to get (B).

Step 2

Why this answer is correct

The correct answer is C. (67). First (n(B-A)=104-37-26=41), then (n(B)=41+26=67). Add only (B) and the common part to get (B).

Step 3

Exam Tip

पहले (n(B-A)=104-37-26=41), फिर (n(B)=41+26=67)। (B) में केवल (B) और साझा भाग दोनों जोड़ें।

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Question 38/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(A)=90), (n(B)=85), (n\(A\cup B\)=125) और (n(U)=160) है, तो (n\(A^c\cap B^c\)) कितना होगा?

If (n(A)=90), (n(B)=85), (n\(A\cup B\)=125), and (n(U)=160), what is (n\(A^c\cap B^c\))?

Explanation opens after your attempt
Correct Answer

A. (35)

Step 1

Concept

(A^c\cap B^c=\(A\cup B\)^c), so (160-125=35). Use De Morgan's law to identify the outside region.

Step 2

Why this answer is correct

The correct answer is A. (35). (A^c\cap B^c=\(A\cup B\)^c), so (160-125=35). Use De Morgan's law to identify the outside region.

Step 3

Exam Tip

(A^c\cap B^c=\(A\cup B\)^c), इसलिए (160-125=35)। डी मॉर्गन नियम से बाहर का क्षेत्र पहचानें।

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Question 39/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(U)=170), (n\(A\cap B\)=44) और (n\(A^c\cup B^c\)=146) है, तो दिए गए आंकड़ों के बारे में क्या कहा जा सकता है?

If (n(U)=170), (n\(A\cap B\)=44), and (n\(A^c\cup B^c\)=146), what can be said about the given data?

Explanation opens after your attempt
Correct Answer

A. आंकड़े असंगत हैंThe data are inconsistent

Step 1

Concept

By De Morgan's law, (A^c\cup B^c=\(A\cap B\)^c), so its value should be (170-44=126). Since (146) is given, the data are inconsistent.

Step 2

Why this answer is correct

The correct answer is A. आंकड़े असंगत हैं / The data are inconsistent. By De Morgan's law, (A^c\cup B^c=\(A\cap B\)^c), so its value should be (170-44=126). Since (146) is given, the data are inconsistent.

Step 3

Exam Tip

डी मॉर्गन से (A^c\cup B^c=\(A\cap B\)^c), इसलिए इसका मान (170-44=126) होना चाहिए। (146) मिलने से आंकड़े असंगत हैं।

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Question 40/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

किसी वेन आरेख में (n(A-B)=25), (n(B-A)=30), (n\(A\cap B\)=20) और (n(\(A\cup B\)^c)=15) हैं। (n\(A^c\)) कितना है?

In a Venn diagram (n(A-B)=25), (n(B-A)=30), (n\(A\cap B\)=20), and (n(\(A\cup B\)^c)=15). What is (n\(A^c\))?

Explanation opens after your attempt
Correct Answer

A. (45)

Step 1

Concept

\(A^c\) includes (B-A) and the outside region, so (30+15=45). Add all regions outside (A).

Step 2

Why this answer is correct

The correct answer is A. (45). \(A^c\) includes (B-A) and the outside region, so (30+15=45). Add all regions outside (A).

Step 3

Exam Tip

\(A^c\) में (B-A) और बाहर का भाग आएगा, इसलिए (30+15=45)। (A) के बाहर के सभी क्षेत्रों को जोड़ें।

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Question 41/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(A-B)=36), (n(B-A)=28), (n\(A\cap B\)=22) और (n(U)=120) है, तो (n\(A^c\cup B^c\)) कितना होगा?

If (n(A-B)=36), (n(B-A)=28), (n\(A\cap B\)=22), and (n(U)=120), what is (n\(A^c\cup B^c\))?

Explanation opens after your attempt
Correct Answer

D. (98)

Step 1

Concept

(A^c\cup B^c=\(A\cap B\)^c), so (120-22=98). The complement of the common part is found by subtracting it from (U).

Step 2

Why this answer is correct

The correct answer is D. (98). (A^c\cup B^c=\(A\cap B\)^c), so (120-22=98). The complement of the common part is found by subtracting it from (U).

Step 3

Exam Tip

(A^c\cup B^c=\(A\cap B\)^c), इसलिए (120-22=98)। साझा भाग का पूरक पूरे (U) से साझा भाग घटाकर मिलता है।

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Question 42/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

वेन आरेख में (\(A\cap B\)\cup\(A\cap B^c\)) किसके बराबर है?

In a Venn diagram, what is (\(A\cap B\)\cup\(A\cap B^c\)) equal to?

Explanation opens after your attempt
Correct Answer

A. (A)

Step 1

Concept

(A) splits into two parts, \(A\cap B\) and \(A\cap B^c\). Their union forms the whole of (A).

Step 2

Why this answer is correct

The correct answer is A. (A). (A) splits into two parts, \(A\cap B\) and \(A\cap B^c\). Their union forms the whole of (A).

Step 3

Exam Tip

(A) दो भागों में बंटता है, \(A\cap B\) और \(A\cap B^c\)। दोनों का संघ पूरा (A) बनाता है।

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Question 43/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

वेन आरेख में (\(A\cup B\)\cap\(A\cup B^c\)) किसके बराबर है?

In a Venn diagram, what is (\(A\cup B\)\cap\(A\cup B^c\)) equal to?

Explanation opens after your attempt
Correct Answer

A. (A)

Step 1

Concept

By distributive law, (\(A\cup B\)\cap\(A\cup B^c\)=A\cup\(B\cap B^c\)=A). This is because \(B\cap B^c=\varnothing\).

Step 2

Why this answer is correct

The correct answer is A. (A). By distributive law, (\(A\cup B\)\cap\(A\cup B^c\)=A\cup\(B\cap B^c\)=A). This is because \(B\cap B^c=\varnothing\).

Step 3

Exam Tip

वितरण नियम से (\(A\cup B\)\cap\(A\cup B^c\)=A\cup\(B\cap B^c\)=A)। क्योंकि \(B\cap B^c=\varnothing\)।

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Question 44/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cap B^c\)=33), (n\(A^c\cap B\)=27), (n\(A\cap B\)=18) और (n(U)=110) है, तो (n\(A^c\cap B^c\)) कितना है?

If (n\(A\cap B^c\)=33), (n\(A^c\cap B\)=27), (n\(A\cap B\)=18), and (n(U)=110), what is (n\(A^c\cap B^c\))?

Explanation opens after your attempt
Correct Answer

A. (32)

Step 1

Concept

The sum of the three inside regions is (33+27+18=78), so outside is (110-78=32). The four regions together form the whole (U).

Step 2

Why this answer is correct

The correct answer is A. (32). The sum of the three inside regions is (33+27+18=78), so outside is (110-78=32). The four regions together form the whole (U).

Step 3

Exam Tip

तीन अंदरूनी भागों का योग (33+27+18=78) है, इसलिए बाहर (110-78=32)। चार क्षेत्र मिलकर पूरा (U) बनाते हैं।

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Question 45/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cap B^c\)=44), (n\(A^c\cap B\)=36) और (n\(A\triangle B\)=92) है, तो दिए गए आंकड़ों के बारे में सही निष्कर्ष क्या है?

If (n\(A\cap B^c\)=44), (n\(A^c\cap B\)=36), and (n\(A\triangle B\)=92), what is the correct conclusion about the data?

Explanation opens after your attempt
Correct Answer

A. आंकड़े असंगत हैंThe data are inconsistent

Step 1

Concept

(A\triangle B=\(A\cap B^c\)\cup\(A^c\cap B\)), so its value should be (44+36=80). Since (92) is given, the data are inconsistent.

Step 2

Why this answer is correct

The correct answer is A. आंकड़े असंगत हैं / The data are inconsistent. (A\triangle B=\(A\cap B^c\)\cup\(A^c\cap B\)), so its value should be (44+36=80). Since (92) is given, the data are inconsistent.

Step 3

Exam Tip

(A\triangle B=\(A\cap B^c\)\cup\(A^c\cap B\)), इसलिए इसका मान (44+36=80) होना चाहिए। (92) दिया है, इसलिए आंकड़े असंगत हैं।

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Question 46/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

तीन समुच्चयों में (n(A)=72), (n(B)=66), (n(C)=60), ठीक एक समुच्चय में (84) और तीनों में (10) हैं। ठीक दो समुच्चयों में कितने तत्व हैं?

In three sets (n(A)=72), (n(B)=66), (n(C)=60), (84) elements are in exactly one set, and (10) are in all three. How many elements are in exactly two sets?

Explanation opens after your attempt
Correct Answer

B. (42)

Step 1

Concept

Total memberships are (72+66+60=198). \(198=84+2x+3\times10\), so (x=42).

Step 2

Why this answer is correct

The correct answer is B. (42). Total memberships are (72+66+60=198). \(198=84+2x+3\times10\), so (x=42).

Step 3

Exam Tip

कुल सदस्यता (72+66+60=198) है। \(198=84+2x+3\times10\), इसलिए (x=42)।

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Question 47/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cup B\)=115), (n(A)=73), (n(B)=67) और (n(U)=150) है, तो (n\(A^c\cup B^c\)) कितना होगा?

If (n\(A\cup B\)=115), (n(A)=73), (n(B)=67), and (n(U)=150), what is (n\(A^c\cup B^c\))?

Explanation opens after your attempt
Correct Answer

D. (108)

Step 1

Concept

First (n\(A\cap B\)=73+67-115=25). Then (A^c\cup B^c=\(A\cap B\)^c), so (150-25=125), hence none of the given options is correct.

Step 2

Why this answer is correct

The correct answer is D. (108). First (n\(A\cap B\)=73+67-115=25). Then (A^c\cup B^c=\(A\cap B\)^c), so (150-25=125), hence none of the given options is correct.

Step 3

Exam Tip

पहले (n\(A\cap B\)=73+67-115=25)। फिर (A^c\cup B^c=\(A\cap B\)^c), इसलिए (150-25=125), अतः दिए गए विकल्पों में कोई सही नहीं है।

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Question 48/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (A) और (B) स्वतंत्र चित्र में दो ओवरलैपिंग वृत्त हैं, तो (A-\(A\cap B\)) किसके बराबर है?

If (A) and (B) are two overlapping circles in a Venn diagram, what is (A-\(A\cap B\)) equal to?

Explanation opens after your attempt
Correct Answer

A. (A-B)

Step 1

Concept

Removing the common part from (A) leaves the only (A) region. This is (A-B).

Step 2

Why this answer is correct

The correct answer is A. (A-B). Removing the common part from (A) leaves the only (A) region. This is (A-B).

Step 3

Exam Tip

(A) से साझा भाग हटाने पर केवल (A) का क्षेत्र बचता है। यह (A-B) है।

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Question 49/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n\(A\cup B\cup C\)=180), (n\(A\cap B\cap C\)=20) और ठीक दो समुच्चयों में (70) तत्व हैं, तो ठीक एक समुच्चय में कितने तत्व हैं?

If (n\(A\cup B\cup C\)=180), (n\(A\cap B\cap C\)=20), and (70) elements are in exactly two sets, how many elements are in exactly one set?

Explanation opens after your attempt
Correct Answer

B. (90)

Step 1

Concept

The union equals exactly one plus exactly two plus all three. Therefore exactly one is (180-70-20=90).

Step 2

Why this answer is correct

The correct answer is B. (90). The union equals exactly one plus exactly two plus all three. Therefore exactly one is (180-70-20=90).

Step 3

Exam Tip

संघ (=) ठीक एक (+) ठीक दो (+) तीनों होता है। इसलिए ठीक एक (180-70-20=90)।

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Question 50/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 13

यदि (n(A-B)=x), (n(B-A)=2x), (n\(A\cap B\)=15) और (n\(A\cup B\)=75) है, तो (x) कितना है?

If (n(A-B)=x), (n(B-A)=2x), (n\(A\cap B\)=15), and (n\(A\cup B\)=75), what is (x)?

Explanation opens after your attempt
Correct Answer

B. (20)

Step 1

Concept

From the union regions, (x+2x+15=75), so (3x=60) and (x=20). Solve unknown regions by forming an equation.

Step 2

Why this answer is correct

The correct answer is B. (20). From the union regions, (x+2x+15=75), so (3x=60) and (x=20). Solve unknown regions by forming an equation.

Step 3

Exam Tip

संघ के भागों से (x+2x+15=75), इसलिए (3x=60) और (x=20)। अज्ञात क्षेत्र को समीकरण से हल करें।

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