Class 11 Mathematics - Sets - Venn Diagrams Hard Quiz

Mathematics Sets Venn Diagrams Hard Class 11 Level 14

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Question 1/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

एक वेन आरेख में (n(U)=210), (n(A)=96), (n(B)=88) और (n(\(A\cup B\)^c)=58) हैं। (n\(A\cap B\)) कितना होगा?

In a Venn diagram (n(U)=210), (n(A)=96), (n(B)=88), and (n(\(A\cup B\)^c)=58). What is (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

C. (32)

Step 1

Concept

First (n\(A\cup B\)=210-58=152), then (n\(A\cap B\)=96+88-152=32). If the outside part is given, find the union first.

Step 2

Why this answer is correct

The correct answer is C. (32). First (n\(A\cup B\)=210-58=152), then (n\(A\cap B\)=96+88-152=32). If the outside part is given, find the union first.

Step 3

Exam Tip

पहले (n\(A\cup B\)=210-58=152), फिर (n\(A\cap B\)=96+88-152=32)। बाहर का भाग मिले तो पहले संघ निकालें।

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Question 2/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

एक वेन आरेख में (n(A)=91), (n(B)=87) और (n\(A\cap B\)=34) हैं। यदि (n(U)=190), तो (n(\(A\cup B\)^c)) कितना होगा?

In a Venn diagram (n(A)=91), (n(B)=87), and (n\(A\cap B\)=34). If (n(U)=190), what is (n(\(A\cup B\)^c))?

Explanation opens after your attempt
Correct Answer

A. (46)

Step 1

Concept

First (n\(A\cup B\)=91+87-34=144), so the complement is (190-144=46). Find the union before finding the outside region.

Step 2

Why this answer is correct

The correct answer is A. (46). First (n\(A\cup B\)=91+87-34=144), so the complement is (190-144=46). Find the union before finding the outside region.

Step 3

Exam Tip

पहले (n\(A\cup B\)=91+87-34=144), इसलिए पूरक (190-144=46) है। बाहर का भाग निकालने से पहले संघ निकालें।

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Question 3/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cup B\)=148), (n(A-B)=52) और (n(B-A)=43) है, तो (n\(A\cap B\)) कितना है?

If (n\(A\cup B\)=148), (n(A-B)=52), and (n(B-A)=43), what is (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

C. (53)

Step 1

Concept

The union has three separate parts, so (n\(A\cap B\)=148-52-43=53). Count each separate region only once.

Step 2

Why this answer is correct

The correct answer is C. (53). The union has three separate parts, so (n\(A\cap B\)=148-52-43=53). Count each separate region only once.

Step 3

Exam Tip

संघ के तीन अलग भाग होते हैं, इसलिए (n\(A\cap B\)=148-52-43=53)। अलग क्षेत्रों को केवल एक बार गिनें।

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Question 4/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\triangle B\)=112) और (n\(A\cap B\)=39) है, तो (n\(A\cup B\)) कितना होगा?

If (n\(A\triangle B\)=112) and (n\(A\cap B\)=39), what is (n\(A\cup B\))?

Explanation opens after your attempt
Correct Answer

C. (151)

Step 1

Concept

The union contains both the symmetric difference and the common part, so (112+39=151). \(A\triangle B\) does not include the common part.

Step 2

Why this answer is correct

The correct answer is C. (151). The union contains both the symmetric difference and the common part, so (112+39=151). \(A\triangle B\) does not include the common part.

Step 3

Exam Tip

संघ में सममित अंतर और साझा भाग दोनों आते हैं, इसलिए (112+39=151)। \(A\triangle B\) में साझा भाग शामिल नहीं होता।

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Question 5/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

एक कक्षा में (n(A)=86), (n(B)=78) और ठीक एक समुच्चय में (98) विद्यार्थी हैं। (n\(A\cap B\)) कितना होगा?

In a class (n(A)=86), (n(B)=78), and (98) students are in exactly one set. What is (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

C. (33)

Step 1

Concept

Exactly one is (n(A)+n(B)-2n\(A\cap B\)). So (98=164-2x), hence (x=33).

Step 2

Why this answer is correct

The correct answer is C. (33). Exactly one is (n(A)+n(B)-2n\(A\cap B\)). So (98=164-2x), hence (x=33).

Step 3

Exam Tip

ठीक एक (n(A)+n(B)-2n\(A\cap B\)) होता है। इसलिए (98=164-2x), अतः (x=33)।

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Question 6/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

तीन समुच्चयों में (n(A)=90), (n(B)=84), (n(C)=78), (n\(A\cap B\)=36), (n\(B\cap C\)=32), (n\(C\cap A\)=30) और (n\(A\cap B\cap C\)=13) है। (n\(A\cup B\cup C\)) कितना है?

For three sets (n(A)=90), (n(B)=84), (n(C)=78), (n\(A\cap B\)=36), (n\(B\cap C\)=32), (n\(C\cap A\)=30), and (n\(A\cap B\cap C\)=13). What is (n\(A\cup B\cup C\))?

Explanation opens after your attempt
Correct Answer

B. (167)

Step 1

Concept

The union of three sets is (90+84+78-36-32-30+13=167). After subtracting pairwise intersections, add the central part.

Step 2

Why this answer is correct

The correct answer is B. (167). The union of three sets is (90+84+78-36-32-30+13=167). After subtracting pairwise intersections, add the central part.

Step 3

Exam Tip

तीन समुच्चयों का संघ (90+84+78-36-32-30+13=167) है। जोड़ी प्रतिच्छेद घटाने के बाद केंद्रीय भाग जोड़ें।

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Question 7/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(U)=160), (n(A)=92) और (n(B)=83) है, तो (n\(A\cap B\)) का न्यूनतम संभव मान क्या होगा?

If (n(U)=160), (n(A)=92), and (n(B)=83), what is the minimum possible value of (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

B. (15)

Step 1

Concept

The minimum intersection is (n(A)+n(B)-n(U)=92+83-160=15). If the total exceeds (U), the extra part must be common.

Step 2

Why this answer is correct

The correct answer is B. (15). The minimum intersection is (n(A)+n(B)-n(U)=92+83-160=15). If the total exceeds (U), the extra part must be common.

Step 3

Exam Tip

न्यूनतम प्रतिच्छेद (n(A)+n(B)-n(U)=92+83-160=15) है। कुल संख्या (U) से अधिक हो तो अतिरिक्त भाग साझा होना जरूरी है।

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Question 8/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cap B\)=45), (n\(A\cap C\)=38), (n\(B\cap C\)=35) और (n\(A\cap B\cap C\)=16) है, तो ठीक दो समुच्चयों में आने वाले तत्व कितने हैं?

If (n\(A\cap B\)=45), (n\(A\cap C\)=38), (n\(B\cap C\)=35), and (n\(A\cap B\cap C\)=16), how many elements are in exactly two sets?

Explanation opens after your attempt
Correct Answer

B. (62)

Step 1

Concept

Exactly two should be ((45-16)+(38-16)+(35-16)=70), so the correct option is (70). Subtract the all-three part from each pair.

Step 2

Why this answer is correct

The correct answer is B. (62). Exactly two should be ((45-16)+(38-16)+(35-16)=70), so the correct option is (70). Subtract the all-three part from each pair.

Step 3

Exam Tip

ठीक दो (=(45-16)+(38-16)+(35-16)=70) होना चाहिए, इसलिए विकल्पों में सही मान (70) है। हर जोड़ी से तीनों का साझा भाग घटाएं।

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Question 9/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(U)=190), (n(A)=74) और (n(B)=91) है, तो (n\(A\cap B\)) का अधिकतम संभव मान क्या होगा?

If (n(U)=190), (n(A)=74), and (n(B)=91), what is the maximum possible value of (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

B. (74)

Step 1

Concept

The intersection cannot be larger than either set, so the maximum value is (74). For maximum, use the smaller set.

Step 2

Why this answer is correct

The correct answer is B. (74). The intersection cannot be larger than either set, so the maximum value is (74). For maximum, use the smaller set.

Step 3

Exam Tip

प्रतिच्छेद किसी भी समुच्चय से बड़ा नहीं हो सकता, इसलिए अधिकतम मान (74) है। अधिकतम के लिए छोटे समुच्चय का मान देखें।

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Question 10/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(U)=180), (n(A)=105) और (n(B)=96) है, तो (n\(A\cap B\)) का न्यूनतम संभव मान क्या होगा?

If (n(U)=180), (n(A)=105), and (n(B)=96), what is the minimum possible value of (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

B. (21)

Step 1

Concept

The minimum intersection is (105+96-180=21). When the two totals exceed (U), the extra part must be common.

Step 2

Why this answer is correct

The correct answer is B. (21). The minimum intersection is (105+96-180=21). When the two totals exceed (U), the extra part must be common.

Step 3

Exam Tip

न्यूनतम प्रतिच्छेद (105+96-180=21) है। जब दोनों कुल मिलकर (U) से अधिक हों, तो अतिरिक्त भाग साझा होता है।

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

यदि \(A\subseteq B\), (n(A)=46), (n(B)=108) और (n(U)=150) है, तो (n\(B^c\)) कितना होगा?

If \(A\subseteq B\), (n(A)=46), (n(B)=108), and (n(U)=150), what is (n\(B^c\))?

Explanation opens after your attempt
Correct Answer

A. (42)

Step 1

Concept

\(B^c\) contains elements of (U) that are not in (B), so (150-108=42). The subset information is a trap here.

Step 2

Why this answer is correct

The correct answer is A. (42). \(B^c\) contains elements of (U) that are not in (B), so (150-108=42). The subset information is a trap here.

Step 3

Exam Tip

\(B^c\) में (U) के वे तत्व हैं जो (B) में नहीं हैं, इसलिए (150-108=42)। उपसमुच्चय जानकारी यहां जाल है।

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Question 12/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cup B\)=136), (n(A-B)=49) और (n\(A\cap B\)=31) है, तो (n(B)) कितना होगा?

If (n\(A\cup B\)=136), (n(A-B)=49), and (n\(A\cap B\)=31), what is (n(B))?

Explanation opens after your attempt
Correct Answer

C. (87)

Step 1

Concept

First (n(B-A)=136-49-31=56), then (n(B)=56+31=87). (B) contains only (B) and the common part.

Step 2

Why this answer is correct

The correct answer is C. (87). First (n(B-A)=136-49-31=56), then (n(B)=56+31=87). (B) contains only (B) and the common part.

Step 3

Exam Tip

पहले (n(B-A)=136-49-31=56), फिर (n(B)=56+31=87)। (B) में केवल (B) और साझा भाग दोनों आते हैं।

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

यदि \(A\subseteq B\subseteq C\), (n(C)=132), (n(B)=84) और (n(A)=37) है, तो (n(C-A)) कितना होगा?

If \(A\subseteq B\subseteq C\), (n(C)=132), (n(B)=84), and (n(A)=37), what is (n(C-A))?

Explanation opens after your attempt
Correct Answer

C. (95)

Step 1

Concept

Since (A) lies completely inside (C), (n(C-A)=132-37=95). Subtract only the set being removed.

Step 2

Why this answer is correct

The correct answer is C. (95). Since (A) lies completely inside (C), (n(C-A)=132-37=95). Subtract only the set being removed.

Step 3

Exam Tip

क्योंकि (A) पूरा (C) में है, इसलिए (n(C-A)=132-37=95)। हटाए गए समुच्चय को ही घटाएं।

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

\((U={1,2,3,\ldots,96}), (A={x:x\) 4 से विभाज्य है\(}) और (B={x:x\) 6 से विभाज्य है}) हैं। \((n(A\cup B)) कितना है\)?

\((U={1,2,3,\ldots,96}), (A={x:x\) is divisible by \(4}), and (B={x:x\) is divisible by \(6}). What is (n(A\cup B))\)?

Explanation opens after your attempt
Correct Answer

A. (32)

Step 1

Concept

Multiples of (4) are (24), multiples of (6) are (16), and multiples of (12) are (8), so (24+16-8=32). Use the LCM for the common part.

Step 2

Why this answer is correct

The correct answer is A. (32). Multiples of (4) are (24), multiples of (6) are (16), and multiples of (12) are (8), so (24+16-8=32). Use the LCM for the common part.

Step 3

Exam Tip

(4) के गुणज (24), (6) के गुणज (16), और (12) के गुणज (8) हैं, इसलिए (24+16-8=32)। साझा भाग के लिए लघुत्तम समापवर्त्य लें।

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Question 15/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

तीन समुच्चयों के लिए (n(A)=72), (n(B)=66), (n(C)=59), (n\(A\cap B\)=28), (n\(B\cap C\)=24), (n\(C\cap A\)=22) और (n\(A\cap B\cap C\)=9) है। (n\(A\cup B\cup C\)) कितना है?

For three sets (n(A)=72), (n(B)=66), (n(C)=59), (n\(A\cap B\)=28), (n\(B\cap C\)=24), (n\(C\cap A\)=22), and (n\(A\cap B\cap C\)=9). What is (n\(A\cup B\cup C\))?

Explanation opens after your attempt
Correct Answer

A. (132)

Step 1

Concept

The union of three sets is (72+66+59-28-24-22+9=132). After subtracting pairwise intersections, add the central part back.

Step 2

Why this answer is correct

The correct answer is A. (132). The union of three sets is (72+66+59-28-24-22+9=132). After subtracting pairwise intersections, add the central part back.

Step 3

Exam Tip

तीन समुच्चयों का संघ (72+66+59-28-24-22+9=132) है। जोड़ी प्रतिच्छेद घटाने के बाद केंद्रीय भाग वापस जोड़ें।

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Question 16/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cap B^c\)=48), (n\(A^c\cap B\)=44), (n\(A\cap B\)=28) और (n(U)=160) है, तो (n\(A^c\cap B^c\)) कितना है?

If (n\(A\cap B^c\)=48), (n\(A^c\cap B\)=44), (n\(A\cap B\)=28), and (n(U)=160), what is (n\(A^c\cap B^c\))?

Explanation opens after your attempt
Correct Answer

B. (40)

Step 1

Concept

The sum of the three inside regions is (48+44+28=120), so outside is (160-120=40). The four regions together form the whole (U).

Step 2

Why this answer is correct

The correct answer is B. (40). The sum of the three inside regions is (48+44+28=120), so outside is (160-120=40). The four regions together form the whole (U).

Step 3

Exam Tip

तीन अंदरूनी भागों का योग (48+44+28=120) है, इसलिए बाहर (160-120=40)। चारों क्षेत्र मिलकर पूरा (U) बनाते हैं।

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Question 17/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A)=82), (n(B)=76), (n(C)=70), (n\(A\cup B\cup C\)=162), (n\(A\cap B\)=34), (n\(B\cap C\)=30) और (n\(C\cap A\)=27) है, तो (n\(A\cap B\cap C\)) कितना है?

If (n(A)=82), (n(B)=76), (n(C)=70), (n\(A\cup B\cup C\)=162), (n\(A\cap B\)=34), (n\(B\cap C\)=30), and (n\(C\cap A\)=27), what is (n\(A\cap B\cap C\))?

Explanation opens after your attempt
Correct Answer

A. (15)

Step 1

Concept

In the formula (162=82+76+70-34-30-27+x), so (x=15). Form an equation for the unknown central part.

Step 2

Why this answer is correct

The correct answer is A. (15). In the formula (162=82+76+70-34-30-27+x), so (x=15). Form an equation for the unknown central part.

Step 3

Exam Tip

सूत्र में (162=82+76+70-34-30-27+x) होगा, इसलिए (x=15)। अज्ञात केंद्रीय भाग के लिए समीकरण बनाएं।

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Question 18/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

तीन समुच्चयों में (n\(A\cap B\)=36), (n\(B\cap C\)=33), (n\(C\cap A\)=31) और (n\(A\cap B\cap C\)=14) है। ठीक दो समुच्चयों में आने वाले तत्व कितने हैं?

In three sets (n\(A\cap B\)=36), (n\(B\cap C\)=33), (n\(C\cap A\)=31), and (n\(A\cap B\cap C\)=14). How many elements are in exactly two sets?

Explanation opens after your attempt
Correct Answer

B. (58)

Step 1

Concept

Exactly two (=(36-14)+(33-14)+(31-14)=58). Each pairwise intersection includes the central part, so subtract it.

Step 2

Why this answer is correct

The correct answer is B. (58). Exactly two (=(36-14)+(33-14)+(31-14)=58). Each pairwise intersection includes the central part, so subtract it.

Step 3

Exam Tip

ठीक दो (=(36-14)+(33-14)+(31-14)=58) है। हर जोड़ी में केंद्रीय भाग शामिल होता है, इसलिए उसे घटाएं।

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Question 19/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A)=94), (n\(A\cap B\)=40), (n\(A\cap C\)=37) और (n\(A\cap B\cap C\)=16) है, तो केवल (A) में आने वाले तत्व कितने हैं?

If (n(A)=94), (n\(A\cap B\)=40), (n\(A\cap C\)=37), and (n\(A\cap B\cap C\)=16), how many elements are only in (A)?

Explanation opens after your attempt
Correct Answer

C. (33)

Step 1

Concept

Only (A=94-40-37+16=33). The central part is subtracted twice, so add it once.

Step 2

Why this answer is correct

The correct answer is C. (33). Only (A=94-40-37+16=33). The central part is subtracted twice, so add it once.

Step 3

Exam Tip

केवल (A=94-40-37+16=33) है। केंद्रीय भाग दो बार घटता है, इसलिए उसे एक बार जोड़ें।

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Question 20/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cap B\)=48), (n\(A\cap C\)=41), (n\(B\cap C\)=39) और (n\(A\cap B\cap C\)=17) है, तो कम से कम दो समुच्चयों में आने वाले तत्व कितने हैं?

If (n\(A\cap B\)=48), (n\(A\cap C\)=41), (n\(B\cap C\)=39), and (n\(A\cap B\cap C\)=17), how many elements are in at least two sets?

Explanation opens after your attempt
Correct Answer

B. (94)

Step 1

Concept

At least two is ((48-17)+(41-17)+(39-17)+17=94). Find exactly two and then add the all-three part.

Step 2

Why this answer is correct

The correct answer is B. (94). At least two is ((48-17)+(41-17)+(39-17)+17=94). Find exactly two and then add the all-three part.

Step 3

Exam Tip

कम से कम दो (=(48-17)+(41-17)+(39-17)+17=94) है। ठीक दो निकालकर तीनों वाला भाग जोड़ें।

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Question 21/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

तीन समुच्चयों में केवल (A=31), केवल (B=26), केवल (C=24), केवल \(A\cap B=15\), केवल \(B\cap C=13\), केवल \(C\cap A=11\) और \(A\cap B\cap C=8\) हैं। यदि (n(U)=160), तो (n(\(A\cup B\cup C\)^c)) कितना होगा?

In three sets, only (A=31), only (B=26), only (C=24), only \(A\cap B=15\), only \(B\cap C=13\), only \(C\cap A=11\), and \(A\cap B\cap C=8\). If (n(U)=160), what is (n(\(A\cup B\cup C\)^c))?

Explanation opens after your attempt
Correct Answer

A. (32)

Step 1

Concept

The inside union is (31+26+24+15+13+11+8=128), so outside is (160-128=32). Add all seven inside regions.

Step 2

Why this answer is correct

The correct answer is A. (32). The inside union is (31+26+24+15+13+11+8=128), so outside is (160-128=32). Add all seven inside regions.

Step 3

Exam Tip

अंदर का संघ (31+26+24+15+13+11+8=128), इसलिए बाहर (160-128=32)। सातों अंदरूनी क्षेत्रों को जोड़ें।

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Question 22/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि केवल (A=25), केवल \(A\cap B=14\), केवल \(A\cap C=12\) और \(A\cap B\cap C=9\) हैं, तो (n(A)) कितना होगा?

If only (A=25), only \(A\cap B=14\), only \(A\cap C=12\), and \(A\cap B\cap C=9\), what is (n(A))?

Explanation opens after your attempt
Correct Answer

B. (60)

Step 1

Concept

The sum of all inside parts of (A) is (25+14+12+9=60). The total of a set is found from all regions inside its circle.

Step 2

Why this answer is correct

The correct answer is B. (60). The sum of all inside parts of (A) is (25+14+12+9=60). The total of a set is found from all regions inside its circle.

Step 3

Exam Tip

(A) के सभी अंदरूनी भागों का योग (25+14+12+9=60) है। किसी समुच्चय की कुल संख्या उसके वृत्त के सभी भागों से मिलती है।

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Question 23/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

एक वेन आरेख में (n\(A\triangle B\)=96) और (n\(A\cup B\)=137) है। (n\(A\cap B\)) कितना होगा?

In a Venn diagram (n\(A\triangle B\)=96) and (n\(A\cup B\)=137). What is (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

B. (41)

Step 1

Concept

\(A\cup B\) contains both \(A\triangle B\) and \(A\cap B\), so (137-96=41). The symmetric difference excludes the common part.

Step 2

Why this answer is correct

The correct answer is B. (41). \(A\cup B\) contains both \(A\triangle B\) and \(A\cap B\), so (137-96=41). The symmetric difference excludes the common part.

Step 3

Exam Tip

\(A\cup B\) में \(A\triangle B\) और \(A\cap B\) दोनों भाग होते हैं, इसलिए (137-96=41)। सममित अंतर में साझा भाग नहीं आता।

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Question 24/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A)=88), (n(B)=82) और (n\(A\triangle B\)=104) है, तो (n\(A\cap B\)) कितना है?

If (n(A)=88), (n(B)=82), and (n\(A\triangle B\)=104), what is (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

B. (33)

Step 1

Concept

(n\(A\triangle B\)=n(A)+n(B)-2n\(A\cap B\)), so (104=170-2x) gives (x=33). Keep exactly one and common parts separate.

Step 2

Why this answer is correct

The correct answer is B. (33). (n\(A\triangle B\)=n(A)+n(B)-2n\(A\cap B\)), so (104=170-2x) gives (x=33). Keep exactly one and common parts separate.

Step 3

Exam Tip

(n\(A\triangle B\)=n(A)+n(B)-2n\(A\cap B\)), इसलिए (104=170-2x) से (x=33)। ठीक एक और साझा भाग अलग रखें।

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Question 25/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(U)=240), (n\(A\cup B\)=157) और (n\(A^c\cap B^c\)=83) है, तो कौन सा संबंध सत्य है?

If (n(U)=240), (n\(A\cup B\)=157), and (n\(A^c\cap B^c\)=83), 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

Since (A^c\cap B^c=\(A\cup B\)^c), (157+83=240) 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)). Since (A^c\cap B^c=\(A\cup B\)^c), (157+83=240) is true. Complementary regions together form the whole (U).

Step 3

Exam Tip

क्योंकि (A^c\cap B^c=\(A\cup B\)^c), इसलिए (157+83=240) सही है। पूरक क्षेत्र मिलकर पूरा (U) बनाते हैं।

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Question 26/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

\((U={1,2,3,\ldots,36}), (A={x:x\) 2 से विभाज्य है\(}) और (B={x:x\) 3 से विभाज्य है}) हैं। \((n(A\cap B)) कितना है\)?

\((U={1,2,3,\ldots,36}), (A={x:x\) is divisible by \(2}), and (B={x:x\) is divisible by \(3}). What is (n(A\cap B))\)?

Explanation opens after your attempt
Correct Answer

A. (6)

Step 1

Concept

The common elements are multiples of (6), namely (6,12,18,24,30,36). Hence the count is (6).

Step 2

Why this answer is correct

The correct answer is A. (6). The common elements are multiples of (6), namely (6,12,18,24,30,36). Hence the count is (6).

Step 3

Exam Tip

साझा तत्व (6) के गुणज होंगे, यानी (6,12,18,24,30,36)। इसलिए संख्या (6) है।

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Question 27/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

\((U={1,2,3,\ldots,72}), (A={x:x\) 6 से विभाज्य है\(}) और (B={x:x\) 8 से विभाज्य है}) हैं। \((n(A\cup B)) कितना है\)?

\((U={1,2,3,\ldots,72}), (A={x:x\) is divisible by \(6}), and (B={x:x\) is divisible by \(8}). What is (n(A\cup B))\)?

Explanation opens after your attempt
Correct Answer

B. (18)

Step 1

Concept

Multiples of (6) are (12), multiples of (8) are (9), and multiples of (24) are (3), so (12+9-3=18). Use the LCM for the common part.

Step 2

Why this answer is correct

The correct answer is B. (18). Multiples of (6) are (12), multiples of (8) are (9), and multiples of (24) are (3), so (12+9-3=18). Use the LCM for the common part.

Step 3

Exam Tip

(6) के गुणज (12), (8) के गुणज (9) और (24) के गुणज (3) हैं, इसलिए (12+9-3=18)। साझा भाग के लिए लघुत्तम समापवर्त्य लें।

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Question 28/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

\(U={1,2,3,\ldots,70}\), (A) अभाज्य संख्याओं का समुच्चय है और (B) सम संख्याओं का समुच्चय है। \(A\cap B\) क्या होगा?

\(U={1,2,3,\ldots,70}\), (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 29/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

\((U={1,2,3,\ldots,90}), (A={x:x\) 2 से विभाज्य है\(}), (B={x:x\) 3 से विभाज्य है\(}) और (C={x:x\) 5 से विभाज्य है}) हैं। \((n(A\cap B\cap C)) कितना है\)?

\((U={1,2,3,\ldots,90}), (A={x:x\) 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. (3)

Step 1

Concept

To be in all three sets, a number must be divisible by (30), namely (30,60,90). Hence the count is (3).

Step 2

Why this answer is correct

The correct answer is B. (3). To be in all three sets, a number must be divisible by (30), namely (30,60,90). Hence the count is (3).

Step 3

Exam Tip

तीनों में आने के लिए संख्या (30) से विभाज्य होगी, यानी (30,60,90)। इसलिए संख्या (3) है।

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Question 30/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

\(U={1,2,3,\ldots,120}\), (A) (3) से विभाज्य, (B) (4) से विभाज्य और (C) (12) से विभाज्य संख्याओं के समुच्चय हैं। कौन सा संबंध सही है?

\(U={1,2,3,\ldots,120}\), (A) is the set of numbers divisible by (3), (B) by (4), and (C) by (12). Which relation is correct?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

A number divisible by (12) is divisible by both (3) and (4), so \(C=A\cap B\). In the Venn diagram, (C) is the common part.

Step 2

Why this answer is correct

The correct answer is A. \(C=A\cap B\). A number divisible by (12) is divisible by both (3) and (4), so \(C=A\cap B\). In the Venn diagram, (C) is the common part.

Step 3

Exam Tip

(12) से विभाज्य संख्या (3) और (4) दोनों से विभाज्य होती है, इसलिए \(C=A\cap B\)। वेन आरेख में (C) साझा भाग है।

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Question 31/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि केवल (n(A-B)=42), (n(B-C)=35) और (n(C-A)=31) दिए हों, तो कौन सा निष्कर्ष हमेशा सही नहीं माना जा सकता?

If only (n(A-B)=42), (n(B-C)=35), and (n(C-A)=31) 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 difference regions alone do not determine the whole union because many common regions remain unknown. First 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 difference regions alone do not determine the whole union because many common regions remain unknown. First check whether the data is sufficient.

Step 3

Exam Tip

केवल कुछ अंतर क्षेत्रों से पूरा संघ निश्चित नहीं होता क्योंकि कई साझा भाग अज्ञात रहते हैं। डेटा पर्याप्त है या नहीं, पहले जांचें।

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Question 32/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A)=56), (n(B)=61), (n(A-B)=19) और (n(B-A)=24) है, तो (n\(A\cap B\)) कितना होगा?

If (n(A)=56), (n(B)=61), (n(A-B)=19), and (n(B-A)=24), what is (n\(A\cap B\))?

Explanation opens after your attempt
Correct Answer

B. (37)

Step 1

Concept

(n\(A\cap B\)=56-19=37), and (61-24=37) confirms it. The same common part should be obtained from both sides.

Step 2

Why this answer is correct

The correct answer is B. (37). (n\(A\cap B\)=56-19=37), and (61-24=37) confirms it. The same common part should be obtained from both sides.

Step 3

Exam Tip

(n\(A\cap B\)=56-19=37) है और (61-24=37) से पुष्टि होती है। दोनों तरफ से समान साझा भाग मिलना चाहिए।

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Question 33/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A)=64), (n(B)=59), (n(A-B)=22) और (n(B-A)=20) है, तो दिए गए आंकड़ों के बारे में सही निष्कर्ष क्या है?

If (n(A)=64), (n(B)=59), (n(A-B)=22), and (n(B-A)=20), 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 (64-22=42), but from (B), it is (59-20=39). 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 (64-22=42), but from (B), it is (59-20=39). Since these are not equal, the data are inconsistent.

Step 3

Exam Tip

(A) से साझा भाग (64-22=42), लेकिन (B) से (59-20=39) मिलता है। दोनों बराबर नहीं हैं, इसलिए आंकड़े असंगत हैं।

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Question 34/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

एक सर्वे में (n(U)=260), (n(A)=118), (n(B)=104), (n(C)=92), (n\(A\cap B\)=48), (n\(B\cap C\)=41), (n\(C\cap A\)=37) और (n\(A\cap B\cap C\)=16) हैं। किसी भी समुच्चय में नहीं आने वाले कितने हैं?

In a survey (n(U)=260), (n(A)=118), (n(B)=104), (n(C)=92), (n\(A\cap B\)=48), (n\(B\cap C\)=41), (n\(C\cap A\)=37), and (n\(A\cap B\cap C\)=16). How many are in none of the sets?

Explanation opens after your attempt
Correct Answer

B. (56)

Step 1

Concept

The union is (118+104+92-48-41-37+16=204), so none is (260-204=56). First find the three-set union.

Step 2

Why this answer is correct

The correct answer is B. (56). The union is (118+104+92-48-41-37+16=204), so none is (260-204=56). First find the three-set union.

Step 3

Exam Tip

संघ (118+104+92-48-41-37+16=204) है, इसलिए कोई नहीं (260-204=56)। पहले तीन-समुच्चय संघ निकालें।

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Question 35/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

तीन समुच्चयों में (n\(A\cup B\cup C\)=172), केवल (A=38), केवल (B=34), केवल (C=29), केवल \(A\cap B=21\), केवल \(B\cap C=18\) और केवल \(C\cap A=16\) हैं। (n\(A\cap B\cap C\)) कितना होगा?

In three sets (n\(A\cup B\cup C\)=172), only (A=38), only (B=34), only (C=29), only \(A\cap B=21\), only \(B\cap C=18\), and only \(C\cap A=16\). What is (n\(A\cap B\cap C\))?

Explanation opens after your attempt
Correct Answer

A. (16)

Step 1

Concept

The sum of the six known inside regions is (38+34+29+21+18+16=156), so the central part is (172-156=16). The union contains all seven inside regions.

Step 2

Why this answer is correct

The correct answer is A. (16). The sum of the six known inside regions is (38+34+29+21+18+16=156), so the central part is (172-156=16). The union contains all seven inside regions.

Step 3

Exam Tip

ज्ञात छह अंदरूनी क्षेत्रों का योग (38+34+29+21+18+16=156) है, इसलिए केंद्रीय भाग (172-156=16)। संघ में सातों अंदरूनी क्षेत्र आते हैं।

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Question 36/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि तीन समुच्चयों में ठीक एक समुच्चय में (84), ठीक दो समुच्चयों में (63) और तीनों में (18) तत्व हैं, तो (n\(A\cup B\cup C\)) कितना है?

If in three sets (84) elements are in exactly one set, (63) in exactly two sets, and (18) in all three sets, what is (n\(A\cup B\cup C\))?

Explanation opens after your attempt
Correct Answer

C. (165)

Step 1

Concept

The union includes exactly one, exactly two, and all-three regions. Hence (84+63+18=165).

Step 2

Why this answer is correct

The correct answer is C. (165). The union includes exactly one, exactly two, and all-three regions. Hence (84+63+18=165).

Step 3

Exam Tip

संघ में ठीक एक, ठीक दो और तीनों वाले सभी भाग आते हैं। इसलिए (84+63+18=165)।

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Question 37/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cup B\cup C\)=156), ठीक एक समुच्चय में (74) और तीनों में (17) तत्व हैं, तो ठीक दो समुच्चयों में कितने तत्व हैं?

If (n\(A\cup B\cup C\)=156), (74) elements are in exactly one set, and (17) are in all three sets, how many elements are in exactly two sets?

Explanation opens after your attempt
Correct Answer

C. (65)

Step 1

Concept

Exactly two is (156-74-17=65). Solve by dividing the union into exactly one, exactly two, and all three.

Step 2

Why this answer is correct

The correct answer is C. (65). Exactly two is (156-74-17=65). Solve by dividing the union into exactly one, exactly two, and all three.

Step 3

Exam Tip

ठीक दो (156-74-17=65) हैं। संघ को ठीक एक, ठीक दो और तीनों में बांटकर हल करें।

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Question 38/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

एक सर्वे में (n(A)=96), (n(B)=88), (n(C)=82), ठीक दो समुच्चयों में (69) और तीनों में (21) लोग हैं। ठीक एक समुच्चय में कितने लोग हैं?

In a survey (n(A)=96), (n(B)=88), (n(C)=82), (69) people are in exactly two sets, and (21) are in all three. How many people are in exactly one set?

Explanation opens after your attempt
Correct Answer

A. (65)

Step 1

Concept

Total memberships are (96+88+82=266). This equals exactly one \(+2\times69+3\times21\), so exactly one is (266-138-63=65).

Step 2

Why this answer is correct

The correct answer is A. (65). Total memberships are (96+88+82=266). This equals exactly one \(+2\times69+3\times21\), so exactly one is (266-138-63=65).

Step 3

Exam Tip

कुल सदस्यता (96+88+82=266) है। यह ठीक एक \(+2\times69+3\times21\) के बराबर है, इसलिए ठीक एक (266-138-63=65)।

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Question 39/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cup B\)=128), (n\(A\cap B\)=32) और (n(A-B)=45) है, तो (n(B)) कितना होगा?

If (n\(A\cup B\)=128), (n\(A\cap B\)=32), and (n(A-B)=45), what is (n(B))?

Explanation opens after your attempt
Correct Answer

C. (83)

Step 1

Concept

First (n(B-A)=128-45-32=51), then (n(B)=51+32=83). (B) contains only (B) and the common part.

Step 2

Why this answer is correct

The correct answer is C. (83). First (n(B-A)=128-45-32=51), then (n(B)=51+32=83). (B) contains only (B) and the common part.

Step 3

Exam Tip

पहले (n(B-A)=128-45-32=51), फिर (n(B)=51+32=83)। (B) में केवल (B) और साझा भाग दोनों आते हैं।

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Question 40/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A)=102), (n(B)=95), (n\(A\cup B\)=143) और (n(U)=190) है, तो (n\(A^c\cap B^c\)) कितना होगा?

If (n(A)=102), (n(B)=95), (n\(A\cup B\)=143), and (n(U)=190), what is (n\(A^c\cap B^c\))?

Explanation opens after your attempt
Correct Answer

A. (47)

Step 1

Concept

(A^c\cap B^c=\(A\cup B\)^c), so (190-143=47). Use De Morgan's law to identify the outside region.

Step 2

Why this answer is correct

The correct answer is A. (47). (A^c\cap B^c=\(A\cup B\)^c), so (190-143=47). Use De Morgan's law to identify the outside region.

Step 3

Exam Tip

(A^c\cap B^c=\(A\cup B\)^c), इसलिए (190-143=47)। डी मॉर्गन नियम से बाहर का क्षेत्र पहचानें।

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Question 41/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(U)=210), (n\(A\cap B\)=52) और (n\(A^c\cup B^c\)=170) है, तो दिए गए आंकड़ों के बारे में क्या कहा जा सकता है?

If (n(U)=210), (n\(A\cap B\)=52), and (n\(A^c\cup B^c\)=170), 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 (210-52=158). Since (170) 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 (210-52=158). Since (170) 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 (210-52=158) होना चाहिए। (170) मिलने से आंकड़े असंगत हैं।

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Question 42/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

किसी वेन आरेख में (n(A-B)=31), (n(B-A)=37), (n\(A\cap B\)=24) और (n(\(A\cup B\)^c)=18) हैं। (n\(A^c\)) कितना है?

In a Venn diagram (n(A-B)=31), (n(B-A)=37), (n\(A\cap B\)=24), and (n(\(A\cup B\)^c)=18). What is (n\(A^c\))?

Explanation opens after your attempt
Correct Answer

B. (55)

Step 1

Concept

\(A^c\) includes (B-A) and the outside region, so (37+18=55). Add all regions outside (A).

Step 2

Why this answer is correct

The correct answer is B. (55). \(A^c\) includes (B-A) and the outside region, so (37+18=55). Add all regions outside (A).

Step 3

Exam Tip

\(A^c\) में (B-A) और बाहर का भाग आएगा, इसलिए (37+18=55)। (A) के बाहर के सभी क्षेत्रों को जोड़ें।

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Question 43/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n(A-B)=44), (n(B-A)=36), (n\(A\cap B\)=29) और (n(U)=150) है, तो (n\(A^c\cup B^c\)) कितना होगा?

If (n(A-B)=44), (n(B-A)=36), (n\(A\cap B\)=29), and (n(U)=150), what is (n\(A^c\cup B^c\))?

Explanation opens after your attempt
Correct Answer

D. (121)

Step 1

Concept

(A^c\cup B^c=\(A\cap B\)^c), so (150-29=121). 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. (121). (A^c\cup B^c=\(A\cap B\)^c), so (150-29=121). 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 (150-29=121)। साझा भाग का पूरक (U) से साझा भाग घटाकर मिलता है।

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Question 44/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cap B^c\)=41), (n\(A^c\cap B\)=34), (n\(A\cap B\)=26) और (n(U)=130) है, तो (n\(A^c\cap B^c\)) कितना है?

If (n\(A\cap B^c\)=41), (n\(A^c\cap B\)=34), (n\(A\cap B\)=26), and (n(U)=130), what is (n\(A^c\cap B^c\))?

Explanation opens after your attempt
Correct Answer

A. (29)

Step 1

Concept

The sum of the three inside regions is (41+34+26=101), so outside is (130-101=29). The four regions together form the whole (U).

Step 2

Why this answer is correct

The correct answer is A. (29). The sum of the three inside regions is (41+34+26=101), so outside is (130-101=29). The four regions together form the whole (U).

Step 3

Exam Tip

तीन अंदरूनी भागों का योग (41+34+26=101) है, इसलिए बाहर (130-101=29)। चार क्षेत्र मिलकर पूरा (U) बनाते हैं।

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Question 45/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cap B^c\)=52), (n\(A^c\cap B\)=39) और (n\(A\triangle B\)=100) है, तो दिए गए आंकड़ों के बारे में सही निष्कर्ष क्या है?

If (n\(A\cap B^c\)=52), (n\(A^c\cap B\)=39), and (n\(A\triangle B\)=100), 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 (52+39=91). Since (100) 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 (52+39=91). Since (100) 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 (52+39=91) होना चाहिए। (100) दिया है, इसलिए आंकड़े असंगत हैं।

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Question 46/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

तीन समुच्चयों में (n(A)=84), (n(B)=78), (n(C)=72), ठीक एक समुच्चय में (96) और तीनों में (12) हैं। ठीक दो समुच्चयों में कितने तत्व हैं?

In three sets (n(A)=84), (n(B)=78), (n(C)=72), (96) elements are in exactly one set, and (12) are in all three. How many elements are in exactly two sets?

Explanation opens after your attempt
Correct Answer

B. (51)

Step 1

Concept

Total memberships are (84+78+72=234). \(234=96+2x+3\times12\), so (x=51).

Step 2

Why this answer is correct

The correct answer is B. (51). Total memberships are (84+78+72=234). \(234=96+2x+3\times12\), so (x=51).

Step 3

Exam Tip

कुल सदस्यता (84+78+72=234) है। \(234=96+2x+3\times12\), इसलिए (x=51)।

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Question 47/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

यदि (n\(A\cup B\)=139), (n(A)=82), (n(B)=76) और (n(U)=190) है, तो (n\(A^c\cup B^c\)) कितना होगा?

If (n\(A\cup B\)=139), (n(A)=82), (n(B)=76), and (n(U)=190), what is (n\(A^c\cup B^c\))?

Explanation opens after your attempt
Correct Answer

D. (170)

Step 1

Concept

First (n\(A\cap B\)=82+76-139=19). Then (A^c\cup B^c=\(A\cap B\)^c), so (190-19=171). None of the given options is correct.

Step 2

Why this answer is correct

The correct answer is D. (170). First (n\(A\cap B\)=82+76-139=19). Then (A^c\cup B^c=\(A\cap B\)^c), so (190-19=171). None of the given options is correct.

Step 3

Exam Tip

पहले (n\(A\cap B\)=82+76-139=19)। फिर (A^c\cup B^c=\(A\cap B\)^c), इसलिए (190-19=171)। दिए गए विकल्पों में कोई भी सही नहीं है।

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Question 48/50 Hard Mathematics Sets Venn Diagrams Class 11 Level 14

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

If (A) and (B) are two overlapping circles, 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 14

यदि (n\(A\cup B\cup C\)=205), (n\(A\cap B\cap C\)=24) और ठीक दो समुच्चयों में (83) तत्व हैं, तो ठीक एक समुच्चय में कितने तत्व हैं?

If (n\(A\cup B\cup C\)=205), (n\(A\cap B\cap C\)=24), and (83) elements are in exactly two sets, how many elements are in exactly one set?

Explanation opens after your attempt
Correct Answer

B. (98)

Step 1

Concept

The union equals exactly one plus exactly two plus all three. Therefore exactly one is (205-83-24=98).

Step 2

Why this answer is correct

The correct answer is B. (98). The union equals exactly one plus exactly two plus all three. Therefore exactly one is (205-83-24=98).

Step 3

Exam Tip

संघ (=) ठीक एक (+) ठीक दो (+) तीनों होता है। इसलिए ठीक एक (205-83-24=98)।

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

यदि (n(A-B)=x), (n(B-A)=3x), (n\(A\cap B\)=24) और (n\(A\cup B\)=120) है, तो (x) कितना है?

If (n(A-B)=x), (n(B-A)=3x), (n\(A\cap B\)=24), and (n\(A\cup B\)=120), what is (x)?

Explanation opens after your attempt
Correct Answer

B. (24)

Step 1

Concept

From the union regions, (x+3x+24=120), so (4x=96) and (x=24). Solve unknown regions by forming an equation.

Step 2

Why this answer is correct

The correct answer is B. (24). From the union regions, (x+3x+24=120), so (4x=96) and (x=24). Solve unknown regions by forming an equation.

Step 3

Exam Tip

संघ के भागों से (x+3x+24=120), इसलिए (4x=96) और (x=24)। अज्ञात क्षेत्र को समीकरण से हल करें।

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