एक कक्षा में (n(U)=50), (n(A)=28), (n(B)=22) और (n\(A\cap B\)=10) हैं। वेन आरेख के अनुसार (n\(A\cup B\)) कितना होगा?
In a class (n(U)=50), (n(A)=28), (n(B)=22), and (n\(A\cap B\)=10). According to the Venn diagram, what is (n\(A\cup B\))?
#sets
#venn diagrams
#union
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A (40)
B (38)
C (60)
D (12)
Explanation opens after your attempt
Step 1
Concept
Use (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). In exams, do not count the common part twice.
Step 2
Why this answer is correct
The correct answer is A. (40). Use (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). In exams, do not count the common part twice.
Step 3
Exam Tip
सूत्र (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)) लगाएं। परीक्षा में साझा भाग को दो बार गिनने की गलती न करें।
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एक सर्वे में (n(U)=95), (n(A)=48), (n(B)=39) और (n(\(A\cup B\)^c)=20) है। वेन आरेख के अनुसार (n\(A\cap B\)) कितना होगा?
In a survey (n(U)=95), (n(A)=48), (n(B)=39), and (n(\(A\cup B\)^c)=20). According to the Venn diagram, what is (n\(A\cap B\))?
#sets
#venn diagrams
#intersection from complement
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A (12)
B (15)
C (20)
D (27)
Explanation opens after your attempt
Step 1
Concept
First (n\(A\cup B\)=95-20=75), then (n\(A\cap B\)=48+39-75=12). In such questions, if the outside part is given, find the union first.
Step 2
Why this answer is correct
The correct answer is A. (12). First (n\(A\cup B\)=95-20=75), then (n\(A\cap B\)=48+39-75=12). In such questions, if the outside part is given, find the union first.
Step 3
Exam Tip
पहले (n\(A\cup B\)=95-20=75), फिर (n\(A\cap B\)=48+39-75=12)। ऐसे प्रश्नों में बाहर का भाग दिया हो तो पहले संघ निकालें।
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यदि (n(A)=35), (n(B)=30) और (n\(A\cup B\)=50) है, तो वेन आरेख में (n\(A\cap B\)) कितना है?
If (n(A)=35), (n(B)=30), and (n\(A\cup B\)=50), then what is (n\(A\cap B\)) in the Venn diagram?
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#venn diagrams
#intersection
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A (15)
B (20)
C (25)
D (10)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cap B\)=n(A)+n(B)-n\(A\cup B\)=35+30-50=15). The fourth value can be found directly from the three given values.
Step 2
Why this answer is correct
The correct answer is A. (15). (n\(A\cap B\)=n(A)+n(B)-n\(A\cup B\)=35+30-50=15). The fourth value can be found directly from the three given values.
Step 3
Exam Tip
(n\(A\cap B\)=n(A)+n(B)-n\(A\cup B\)=35+30-50=15)। दिए गए तीन मानों से चौथा मान सीधे निकाला जा सकता है।
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एक सर्वे में (n(U)=80), (n(A)=45), (n(B)=37) और (n\(A\cap B\)=18) हैं। कितने विद्यार्थी किसी भी समूह में नहीं हैं?
In a survey (n(U)=80), (n(A)=45), (n(B)=37), and (n\(A\cap B\)=18). How many students are in neither group?
#sets
#venn diagrams
#complement
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A (16)
B (18)
C (20)
D (64)
Explanation opens after your attempt
Step 1
Concept
First (n\(A\cup B\)=45+37-18=64), so outside is (80-64=16). In a Venn diagram, the outside region is (U-\(A\cup B\)).
Step 2
Why this answer is correct
The correct answer is A. (16). First (n\(A\cup B\)=45+37-18=64), so outside is (80-64=16). In a Venn diagram, the outside region is (U-\(A\cup B\)).
Step 3
Exam Tip
पहले (n\(A\cup B\)=45+37-18=64), इसलिए बाहर (80-64=16)। वेन आरेख में बाहर का क्षेत्र (U-\(A\cup B\)) होता है।
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यदि (n(A)=32) और (n\(A\cap B\)=14) है, तो वेन आरेख में केवल (A) वाले तत्व कितने होंगे?
If (n(A)=32) and (n\(A\cap B\)=14), then how many elements are only in (A) in the Venn diagram?
#sets
#venn diagrams
#only a
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A (18)
B (46)
C (14)
D (32)
Explanation opens after your attempt
Step 1
Concept
Only (A) is (n(A)-n\(A\cap B\)=32-14=18). Drawing the diagram and subtracting the middle part is the safest method.
Step 2
Why this answer is correct
The correct answer is A. (18). Only (A) is (n(A)-n\(A\cap B\)=32-14=18). Drawing the diagram and subtracting the middle part is the safest method.
Step 3
Exam Tip
केवल (A) का भाग (n(A)-n\(A\cap B\)=32-14=18) है। आरेख बनाकर मध्य भाग घटाना सबसे सुरक्षित तरीका है।
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यदि (n(B)=41) और (n\(A\cap B\)=17) है, तो वेन आरेख में केवल (B) वाला क्षेत्र कितना होगा?
If (n(B)=41) and (n\(A\cap B\)=17), then what is the only (B) region in the Venn diagram?
#sets
#venn diagrams
#only b
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A (24)
B (58)
C (17)
D (41)
Explanation opens after your attempt
Step 1
Concept
Only (B) is (41-17=24). Always subtract the common part from total (B).
Step 2
Why this answer is correct
The correct answer is A. (24). Only (B) is (41-17=24). Always subtract the common part from total (B).
Step 3
Exam Tip
केवल (B) के लिए (41-17=24) होगा। हमेशा कुल (B) में से साझा भाग घटाएं।
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दो समुच्चयों के वेन आरेख में (n(A-B)=12), (n(B-A)=9) और (n\(A\cap B\)=6) है। (n\(A\cup B\)) कितना होगा?
In a Venn diagram of two sets, (n(A-B)=12), (n(B-A)=9), and (n\(A\cap B\)=6). What is (n\(A\cup B\))?
#sets
#venn diagrams
#regions
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A (27)
B (21)
C (18)
D (33)
Explanation opens after your attempt
Step 1
Concept
The union is the sum of three separate regions, so (12+9+6=27). In Venn diagrams, add non-overlapping regions directly.
Step 2
Why this answer is correct
The correct answer is A. (27). The union is the sum of three separate regions, so (12+9+6=27). In Venn diagrams, add non-overlapping regions directly.
Step 3
Exam Tip
संघ में तीन अलग-अलग क्षेत्र जुड़ते हैं, इसलिए (12+9+6=27)। वेन आरेख में अलग क्षेत्रों को सीधे जोड़ें।
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यदि \(A\subseteq B\), (n(A)=18) और (n(B)=45) है, तो (n(B-A)) कितना होगा?
If \(A\subseteq B\), (n(A)=18), and (n(B)=45), what is (n(B-A))?
#sets
#venn diagrams
#subset
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A (27)
B (63)
C (18)
D (45)
Explanation opens after your attempt
Step 1
Concept
When \(A\subseteq B\), all of (A) lies inside (B), so (45-18=27). In a subset Venn diagram, the smaller circle is inside the larger one.
Step 2
Why this answer is correct
The correct answer is A. (27). When \(A\subseteq B\), all of (A) lies inside (B), so (45-18=27). In a subset Venn diagram, the smaller circle is inside the larger one.
Step 3
Exam Tip
जब \(A\subseteq B\), तब (A) पूरा (B) के अंदर होता है, इसलिए (45-18=27)। उपसमुच्चय वाले वेन आरेख में छोटा वृत्त बड़े के अंदर बनता है।
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यदि \(A\cap B=\varnothing\), (n(A)=26) और (n(B)=19) है, तो (n\(A\cup B\)) क्या होगा?
If \(A\cap B=\varnothing\), (n(A)=26), and (n(B)=19), what is (n\(A\cup B\))?
#sets
#venn diagrams
#disjoint sets
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A (45)
B (7)
C (26)
D (19)
Explanation opens after your attempt
Step 1
Concept
Disjoint sets have common part (0), so (26+19=45). When \(A\cap B=\varnothing\), take the subtracted part as zero.
Step 2
Why this answer is correct
The correct answer is A. (45). Disjoint sets have common part (0), so (26+19=45). When \(A\cap B=\varnothing\), take the subtracted part as zero.
Step 3
Exam Tip
असंबद्ध समुच्चयों में साझा भाग (0) होता है, इसलिए (26+19=45)। \(A\cap B=\varnothing\) दिखे तो घटाने वाला भाग शून्य मानें।
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वेन आरेख में \(A\cap B\) किस भाग को दिखाता है?
Which part does \(A\cap B\) show in a Venn diagram?
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#intersection concept
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A दोनों (A) और (B) में आने वाला साझा भाग / Common part in both (A) and (B)
B केवल (A) का भाग / Only (A) part
C केवल (B) का भाग / Only (B) part
D (U) के बाहर का भाग / Part outside (U)
Explanation opens after your attempt
Correct Answer
A. दोनों (A) और (B) में आने वाला साझा भाग / Common part in both (A) and (B)
Step 1
Concept
\(A\cap B\) contains elements that are in both sets together. In a Venn diagram, it is the overlap region.
Step 2
Why this answer is correct
The correct answer is A. दोनों (A) और (B) में आने वाला साझा भाग / Common part in both (A) and (B). \(A\cap B\) contains elements that are in both sets together. In a Venn diagram, it is the overlap region.
Step 3
Exam Tip
\(A\cap B\) वे तत्व हैं जो दोनों समुच्चयों में साथ-साथ होते हैं। वेन आरेख में यह ओवरलैप क्षेत्र होता है।
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किसी वेन आरेख में (n(U)=100), (n(A)=52), (n(B)=44) और (n\(A\cap B\)=21) हैं। (n(\(A\cup B\)^c)) कितना है?
In a Venn diagram, (n(U)=100), (n(A)=52), (n(B)=44), and (n\(A\cap B\)=21). What is (n(\(A\cup B\)^c))?
#sets
#venn diagrams
#complement of union
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A (25)
B (75)
C (21)
D (17)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cup B\)=52+44-21=75), so the complement is (100-75=25). For complement, subtract from the universal set.
Step 2
Why this answer is correct
The correct answer is A. (25). (n\(A\cup B\)=52+44-21=75), so the complement is (100-75=25). For complement, subtract from the universal set.
Step 3
Exam Tip
(n\(A\cup B\)=52+44-21=75), इसलिए पूरक (100-75=25)। पूरक के लिए सार्वत्रिक समुच्चय से घटाएं।
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यदि (n(U)=70), (n(A)=38) और (n\(A^c\)=32) है, तो कौन सा कथन सही है?
If (n(U)=70), (n(A)=38), and (n\(A^c\)=32), which statement is correct?
#sets
#venn diagrams
#complement property
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A (n(A)+n\(A^c\)=n(U))
B (n(A)-n\(A^c\)=n(U))
C (n\(A^c\)=n(A))
D (n(U)=n\(A^c\))
Explanation opens after your attempt
Correct Answer
A. (n(A)+n\(A^c\)=n(U))
Step 1
Concept
A set and its complement together equal (U). In a Venn diagram, the circle and the outside part together form the whole rectangle.
Step 2
Why this answer is correct
The correct answer is A. (n(A)+n\(A^c\)=n(U)). A set and its complement together equal (U). In a Venn diagram, the circle and the outside part together form the whole rectangle.
Step 3
Exam Tip
किसी समुच्चय और उसके पूरक का योग (U) के बराबर होता है। वेन आरेख में वृत्त और उसके बाहर का भाग मिलकर पूरा आयत बनाते हैं।
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यदि (n(U)=60), (n(A)=25), (n(B)=30) और कोई भी (5) विद्यार्थी दोनों में नहीं बल्कि किसी में भी नहीं हैं, तो (n\(A\cap B\)) कितना होगा?
If (n(U)=60), (n(A)=25), (n(B)=30), and (5) students are in neither set, what is (n\(A\cap B\))?
#sets
#venn diagrams
#survey
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A (0)
B (5)
C (10)
D (15)
Explanation opens after your attempt
Step 1
Concept
Neither is (5), so (n\(A\cup B\)=55). Then (n\(A\cap B\)=25+30-55=0).
Step 2
Why this answer is correct
The correct answer is A. (0). Neither is (5), so (n\(A\cup B\)=55). Then (n\(A\cap B\)=25+30-55=0).
Step 3
Exam Tip
किसी में भी नहीं (5) हैं, इसलिए (n\(A\cup B\)=55)। तब (n\(A\cap B\)=25+30-55=0)।
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एक समूह में (40) लोग चाय पसंद करते हैं, (32) लोग कॉफी पसंद करते हैं और (18) दोनों पसंद करते हैं। कम से कम एक पेय पसंद करने वाले कितने हैं?
In a group, (40) people like tea, (32) like coffee, and (18) like both. How many like at least one drink?
#sets
#venn diagrams
#at least one
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A (54)
B (90)
C (72)
D (50)
Explanation opens after your attempt
Step 1
Concept
At least one means \(A\cup B\), so (40+32-18=54). In such questions, count those who like both only once.
Step 2
Why this answer is correct
The correct answer is A. (54). At least one means \(A\cup B\), so (40+32-18=54). In such questions, count those who like both only once.
Step 3
Exam Tip
कम से कम एक का अर्थ \(A\cup B\) है, इसलिए (40+32-18=54)। ऐसे प्रश्नों में दोनों पसंद करते हैं को एक बार ही गिनें।
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एक सर्वे में (27) विद्यार्थी गणित, (34) विद्यार्थी विज्ञान और (12) दोनों पढ़ते हैं। केवल गणित पढ़ने वाले कितने हैं?
In a survey, (27) students study Mathematics, (34) study Science, and (12) study both. How many study only Mathematics?
#sets
#venn diagrams
#only one set
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A (15)
B (22)
C (39)
D (46)
Explanation opens after your attempt
Step 1
Concept
Only Mathematics is (27-12=15). In a Venn diagram, write the middle part first and then find the remaining parts.
Step 2
Why this answer is correct
The correct answer is A. (15). Only Mathematics is (27-12=15). In a Venn diagram, write the middle part first and then find the remaining parts.
Step 3
Exam Tip
केवल गणित (27-12=15) है। वेन आरेख में पहले बीच का भाग लिखें और फिर बचे हुए भाग निकालें।
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(n(A-B)=16) और (n\(A\cap B\)=11) है। (n(A)) कितना होगा?
(n(A-B)=16) and (n\(A\cap B\)=11). What is (n(A))?
#sets
#venn diagrams
#set difference
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A (27)
B (5)
C (16)
D (11)
Explanation opens after your attempt
Step 1
Concept
Whole (A) is made of two parts (A-B) and \(A\cap B\). Hence (n(A)=16+11=27).
Step 2
Why this answer is correct
The correct answer is A. (27). Whole (A) is made of two parts (A-B) and \(A\cap B\). Hence (n(A)=16+11=27).
Step 3
Exam Tip
पूरा (A) दो भागों (A-B) और \(A\cap B\) से बनता है। इसलिए (n(A)=16+11=27)।
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यदि (n\(A\cup B\)=48), (n(A-B)=20) और (n(B-A)=13) है, तो (n\(A\cap B\)) कितना होगा?
If (n\(A\cup B\)=48), (n(A-B)=20), and (n(B-A)=13), what is (n\(A\cap B\))?
#sets
#venn diagrams
#intersection from regions
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A (15)
B (33)
C (35)
D (28)
Explanation opens after your attempt
Step 1
Concept
The union has three separate parts, so the common part is (48-20-13=15). Combining separate regions is the main rule of Venn diagrams.
Step 2
Why this answer is correct
The correct answer is A. (15). The union has three separate parts, so the common part is (48-20-13=15). Combining separate regions is the main rule of Venn diagrams.
Step 3
Exam Tip
संघ के तीन अलग भाग हैं, इसलिए साझा भाग (48-20-13=15) होगा। अलग-अलग क्षेत्रों को मिलाना वेन आरेख का मुख्य नियम है।
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तीन समुच्चयों के लिए \(A\cap B\cap C\) वेन आरेख में कौन सा भाग है?
For three sets, which part is \(A\cap B\cap C\) in a Venn diagram?
#sets
#venn diagrams
#three sets
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A तीनों वृत्तों का साझा केंद्रीय भाग / Common central part of all three circles
B केवल (A) का भाग / Only (A) part
C (A) और (B) का वह भाग जो (C) में नहीं है / Part of (A) and (B) not in (C)
D सार्वत्रिक समुच्चय के बाहर का भाग / Part outside the universal set
Explanation opens after your attempt
Correct Answer
A. तीनों वृत्तों का साझा केंद्रीय भाग / Common central part of all three circles
Step 1
Concept
\(A\cap B\cap C\) contains elements present in all three sets. In three circles, it is the central common region.
Step 2
Why this answer is correct
The correct answer is A. तीनों वृत्तों का साझा केंद्रीय भाग / Common central part of all three circles. \(A\cap B\cap C\) contains elements present in all three sets. In three circles, it is the central common region.
Step 3
Exam Tip
\(A\cap B\cap C\) में वे तत्व होते हैं जो तीनों में मौजूद हों। तीन वृत्तों में यह सबसे बीच का साझा क्षेत्र है।
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यदि (n(A)=30), (n(B)=28), (n(C)=24), (n\(A\cap B\)=10), (n\(B\cap C\)=8), (n\(C\cap A\)=6) और (n\(A\cap B\cap C\)=4) है, तो (n\(A\cup B\cup C\)) कितना होगा?
If (n(A)=30), (n(B)=28), (n(C)=24), (n\(A\cap B\)=10), (n\(B\cap C\)=8), (n\(C\cap A\)=6), and (n\(A\cap B\cap C\)=4), what is (n\(A\cup B\cup C\))?
#sets
#venn diagrams
#three set union
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A (62)
B (58)
C (70)
D (54)
Explanation opens after your attempt
Step 1
Concept
The formula gives (30+28+24-10-8-6+4=62). For three sets, remember to add back the final common part.
Step 2
Why this answer is correct
The correct answer is A. (62). The formula gives (30+28+24-10-8-6+4=62). For three sets, remember to add back the final common part.
Step 3
Exam Tip
सूत्र (30+28+24-10-8-6+4=62) देता है। तीन समुच्चयों में अंतिम साझा भाग वापस जोड़ना याद रखें।
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तीन समुच्चयों में केवल (A) का भाग किससे मिलेगा?
In three sets, how do we get the only (A) region?
#sets
#venn diagrams
#only a three sets
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A (n(A)-n\(A\cap B\)-n\(A\cap C\)+n\(A\cap B\cap C\))
B (n(A)+n\(A\cap B\)+n\(A\cap C\))
C (n\(A\cup B\)-n(C))
D (n(U)-n(A))
Explanation opens after your attempt
Correct Answer
A. (n(A)-n\(A\cap B\)-n\(A\cap C\)+n\(A\cap B\cap C\))
Step 1
Concept
While finding only (A), subtract \(A\cap B\) and \(A\cap C\), but the central part is subtracted twice, so add it once. This is inclusion-exclusion in use.
Step 2
Why this answer is correct
The correct answer is A. (n(A)-n\(A\cap B\)-n\(A\cap C\)+n\(A\cap B\cap C\)). While finding only (A), subtract \(A\cap B\) and \(A\cap C\), but the central part is subtracted twice, so add it once. This is inclusion-exclusion in use.
Step 3
Exam Tip
केवल (A) निकालते समय \(A\cap B\) और \(A\cap C\) घटते हैं, लेकिन केंद्रीय भाग दो बार घट जाता है इसलिए एक बार जोड़ते हैं। यही समावेशन-बहिष्करण का प्रयोग है।
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यदि (n(A)=42), (n\(A\cap B\)=15), (n\(A\cap C\)=18) और (n\(A\cap B\cap C\)=7) है, तो केवल (A) कितने हैं?
If (n(A)=42), (n\(A\cap B\)=15), (n\(A\cap C\)=18), and (n\(A\cap B\cap C\)=7), how many are only in (A)?
#sets
#venn diagrams
#only a calculation
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A (16)
B (9)
C (22)
D (28)
Explanation opens after your attempt
Step 1
Concept
Only (A=42-15-18+7=16). In three circles, adjustment of the central part is necessary.
Step 2
Why this answer is correct
The correct answer is A. (16). Only (A=42-15-18+7=16). In three circles, adjustment of the central part is necessary.
Step 3
Exam Tip
केवल (A=42-15-18+7=16)। तीन वृत्तों में केंद्रीय भाग का समायोजन जरूरी है।
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यदि (n\(A\cap B\)=14) और (n\(A\cap B\cap C\)=5) है, तो केवल (A) और (B) में लेकिन (C) में नहीं कितने हैं?
If (n\(A\cap B\)=14) and (n\(A\cap B\cap C\)=5), then how many are in only (A) and (B) but not in (C)?
#sets
#venn diagrams
#pair only
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A (9)
B (19)
C (5)
D (14)
Explanation opens after your attempt
Step 1
Concept
For only (A) and (B), subtract the central part, (14-5=9). A pairwise intersection includes the common part of all three.
Step 2
Why this answer is correct
The correct answer is A. (9). For only (A) and (B), subtract the central part, (14-5=9). A pairwise intersection includes the common part of all three.
Step 3
Exam Tip
केवल (A) और (B) के लिए केंद्रीय भाग घटाएं, (14-5=9)। जोड़ी वाले क्षेत्र में तीनों का साझा भाग शामिल होता है।
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(n(U)=90) और (n\(A\cup B\cup C\)=76) है। तीन समुच्चयों के वेन आरेख में किसी भी समुच्चय में नहीं आने वाले कितने हैं?
(n(U)=90) and (n\(A\cup B\cup C\)=76). In a three-set Venn diagram, how many are in none of the sets?
#sets
#venn diagrams
#none three sets
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A (14)
B (166)
C (76)
D (90)
Explanation opens after your attempt
Step 1
Concept
None is (n(U)-n\(A\cup B\cup C\)=90-76=14). The outside part is always found by subtracting the union from the universal set.
Step 2
Why this answer is correct
The correct answer is A. (14). None is (n(U)-n\(A\cup B\cup C\)=90-76=14). The outside part is always found by subtracting the union from the universal set.
Step 3
Exam Tip
किसी में नहीं (n(U)-n\(A\cup B\cup C\)=90-76=14) है। बाहर का भाग हमेशा सार्वत्रिक समुच्चय से संघ घटाकर मिलता है।
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यदि (A) और (B) वेन आरेख में दो ओवरलैपिंग वृत्त हैं, तो (A-B) कौन सा भाग है?
If (A) and (B) are two overlapping circles in a Venn diagram, which part is (A-B)?
#sets
#venn diagrams
#difference concept
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A (A) का वह भाग जो (B) में नहीं है / Part of (A) that is not in (B)
B (B) का वह भाग जो (A) में नहीं है / Part of (B) that is not in (A)
C दोनों का साझा भाग / Common part of both
D पूरा \(A\cup B\) / Whole \(A\cup B\)
Explanation opens after your attempt
Correct Answer
A. (A) का वह भाग जो (B) में नहीं है / Part of (A) that is not in (B)
Step 1
Concept
(A-B) means elements present in (A) but absent in (B). In a Venn diagram, it is the only (A) region.
Step 2
Why this answer is correct
The correct answer is A. (A) का वह भाग जो (B) में नहीं है / Part of (A) that is not in (B). (A-B) means elements present in (A) but absent in (B). In a Venn diagram, it is the only (A) region.
Step 3
Exam Tip
(A-B) का अर्थ (A) में मौजूद लेकिन (B) में अनुपस्थित तत्व हैं। वेन आरेख में यह केवल (A) वाला क्षेत्र है।
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\(A\triangle B\) वेन आरेख में किस क्षेत्र को दर्शाता है?
What region does \(A\triangle B\) represent in a Venn diagram?
#sets
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#symmetric difference
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A (A-B) और (B-A) का संयुक्त क्षेत्र / Combined region of (A-B) and (B-A)
B केवल \(A\cap B\) / Only \(A\cap B\)
C केवल (\(A\cup B\)^c) / Only (\(A\cup B\)^c)
D पूरा (U) / Whole (U)
Explanation opens after your attempt
Correct Answer
A. (A-B) और (B-A) का संयुक्त क्षेत्र / Combined region of (A-B) and (B-A)
Step 1
Concept
\(A\triangle B\) contains elements that are in exactly one set. So the common part is not included.
Step 2
Why this answer is correct
The correct answer is A. (A-B) और (B-A) का संयुक्त क्षेत्र / Combined region of (A-B) and (B-A). \(A\triangle B\) contains elements that are in exactly one set. So the common part is not included.
Step 3
Exam Tip
\(A\triangle B\) में वे तत्व होते हैं जो ठीक एक समुच्चय में हों। इसलिए साझा भाग शामिल नहीं होता।
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यदि (n(A-B)=23) और (n(B-A)=31) है, तो (n\(A\triangle B\)) कितना होगा?
If (n(A-B)=23) and (n(B-A)=31), what is (n\(A\triangle B\))?
#sets
#venn diagrams
#symmetric difference count
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A (54)
B (8)
C (23)
D (31)
Explanation opens after your attempt
Step 1
Concept
The symmetric difference \(A\triangle B\) is the sum of the two separate regions (A-B) and (B-A). Hence (23+31=54).
Step 2
Why this answer is correct
The correct answer is A. (54). The symmetric difference \(A\triangle B\) is the sum of the two separate regions (A-B) and (B-A). Hence (23+31=54).
Step 3
Exam Tip
सममित अंतर \(A\triangle B\) दो अलग क्षेत्रों (A-B) और (B-A) का योग है। इसलिए (23+31=54)।
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एक वेन आरेख में (n\(A\cup B\)=63) और (n\(A\cap B\)=17) है। ठीक एक समुच्चय में आने वाले तत्व कितने हैं?
In a Venn diagram, (n\(A\cup B\)=63) and (n\(A\cap B\)=17). How many elements are in exactly one set?
#sets
#venn diagrams
#exactly one
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A (46)
B (80)
C (17)
D (29)
Explanation opens after your attempt
Step 1
Concept
Exactly one set is (n\(A\cup B\)-n\(A\cap B\)=63-17=46). The union includes the common part, so remove it.
Step 2
Why this answer is correct
The correct answer is A. (46). Exactly one set is (n\(A\cup B\)-n\(A\cap B\)=63-17=46). The union includes the common part, so remove it.
Step 3
Exam Tip
ठीक एक समुच्चय (n\(A\cup B\)-n\(A\cap B\)=63-17=46) है। संघ में साझा भाग भी शामिल होता है, इसलिए उसे हटाएं।
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\(A\subseteq B\) होने पर वेन आरेख में \(A\cup B\) किसके बराबर होगा?
When \(A\subseteq B\), what is \(A\cup B\) equal to in a Venn diagram?
#sets
#venn diagrams
#subset union
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A (B)
B (A)
C \(\varnothing\)
D \(A\cap B^c\)
Explanation opens after your attempt
Step 1
Concept
If \(A\subseteq B\), then (B) already contains (A). Hence the union is just (B).
Step 2
Why this answer is correct
The correct answer is A. (B). If \(A\subseteq B\), then (B) already contains (A). Hence the union is just (B).
Step 3
Exam Tip
यदि \(A\subseteq B\), तो (B) में (A) पहले से शामिल है। इसलिए संघ केवल (B) बनता है।
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\(A\subseteq B\) होने पर \(A\cap B\) किसके बराबर होता है?
When \(A\subseteq B\), what is \(A\cap B\) equal to?
#sets
#venn diagrams
#subset intersection
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A (A)
B (B)
C \(A^c\)
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
When (A) is fully inside (B), the common part is (A) itself. Recognizing subset relation can give the answer without formula.
Step 2
Why this answer is correct
The correct answer is A. (A). When (A) is fully inside (B), the common part is (A) itself. Recognizing subset relation can give the answer without formula.
Step 3
Exam Tip
जब (A) पूरी तरह (B) में है, तो साझा भाग (A) ही होता है। उपसमुच्चय पहचानकर सूत्र के बिना उत्तर मिल सकता है।
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(A) और (B) असंबद्ध हैं। इनमें से कौन सा कथन सही है?
(A) and (B) are disjoint. Which statement is correct?
#sets
#venn diagrams
#disjoint concept
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A \(A\cap B=\varnothing\)
B \(A\cup B=\varnothing\)
C (A=B)
D \(A\subseteq B\)
Explanation opens after your attempt
Correct Answer
A. \(A\cap B=\varnothing\)
Step 1
Concept
Disjoint sets have no common element, so \(A\cap B=\varnothing\). In a Venn diagram, their circles are separate.
Step 2
Why this answer is correct
The correct answer is A. \(A\cap B=\varnothing\). Disjoint sets have no common element, so \(A\cap B=\varnothing\). In a Venn diagram, their circles are separate.
Step 3
Exam Tip
असंबद्ध समुच्चयों में कोई साझा तत्व नहीं होता, इसलिए \(A\cap B=\varnothing\)। वेन आरेख में उनके वृत्त अलग-अलग बनते हैं।
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यदि (n(A)=20), (n(B)=25) और \(A\cap B=\varnothing\), तो ठीक एक समुच्चय में कितने तत्व हैं?
If (n(A)=20), (n(B)=25), and \(A\cap B=\varnothing\), how many elements are in exactly one set?
#sets
#venn diagrams
#disjoint counting
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A (45)
B (5)
C (0)
D (25)
Explanation opens after your attempt
Step 1
Concept
In disjoint sets, every element is in exactly one of the sets, so (20+25=45). Here the common part is zero.
Step 2
Why this answer is correct
The correct answer is A. (45). In disjoint sets, every element is in exactly one of the sets, so (20+25=45). Here the common part is zero.
Step 3
Exam Tip
असंबद्ध समुच्चयों में हर तत्व ठीक एक ही समुच्चय में होता है, इसलिए (20+25=45)। यहां साझा भाग शून्य है।
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\(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{2,4,6,8,10\}\) और \(B=\{1,2,3,5,7\}\) हैं। \(A\cap B\) क्या है?
\(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{2,4,6,8,10\}\), and \(B=\{1,2,3,5,7\}\). What is \(A\cap B\)?
#sets
#venn diagrams
#set listing
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A ({2})
B ({1,3,5,7})
C ({4,6,8,10})
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
Only (2) is common to both sets. In intersection, write only the elements that are in both.
Step 2
Why this answer is correct
The correct answer is A. ({2}). Only (2) is common to both sets. In intersection, write only the elements that are in both.
Step 3
Exam Tip
दोनों समुच्चयों में केवल (2) समान है। प्रतिच्छेद में वही तत्व लिखें जो दोनों में हों।
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\(U=\{a,b,c,d,e,f\}\), \(A=\{a,c,e\}\) और \(B=\{b,c,d\}\) हैं। \(A\cup B\) क्या है?
\(U=\{a,b,c,d,e,f\}\), \(A=\{a,c,e\}\), and \(B=\{b,c,d\}\). What is \(A\cup B\)?
#sets
#venn diagrams
#union listing
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A ({a,b,c,d,e})
B ({c})
C ({f})
D ({a,e})
Explanation opens after your attempt
Correct Answer
A. ({a,b,c,d,e})
Step 1
Concept
The union contains all distinct elements of (A) and (B). Write the repeated (c) only once.
Step 2
Why this answer is correct
The correct answer is A. ({a,b,c,d,e}). The union contains all distinct elements of (A) and (B). Write the repeated (c) only once.
Step 3
Exam Tip
संघ में (A) और (B) के सभी अलग तत्व आते हैं। दोहराए गए (c) को केवल एक बार लिखें।
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\(U=\{1,2,3,4,5,6,7\}\) और \(A=\{1,3,5,7\}\) है। वेन आरेख में \(A^c\) क्या होगा?
\(U=\{1,2,3,4,5,6,7\}\) and \(A=\{1,3,5,7\}\). What is \(A^c\) in the Venn diagram?
#sets
#venn diagrams
#complement listing
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A ({2,4,6})
B ({1,3,5,7})
C ({1,2,3,4,5,6,7})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({2,4,6})
Step 1
Concept
The complement \(A^c\) contains elements of (U) that are not in (A). Hence the answer is ({2,4,6}).
Step 2
Why this answer is correct
The correct answer is A. ({2,4,6}). The complement \(A^c\) contains elements of (U) that are not in (A). Hence the answer is ({2,4,6}).
Step 3
Exam Tip
पूरक \(A^c\) में (U) के वे तत्व हैं जो (A) में नहीं हैं। इसलिए उत्तर ({2,4,6}) है।
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\(A=\{1,2,3,4,5\}\) और \(B=\{4,5,6,7\}\) हैं। (A-B) क्या है?
\(A=\{1,2,3,4,5\}\) and \(B=\{4,5,6,7\}\). What is (A-B)?
#sets
#venn diagrams
#difference listing
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A ({1,2,3})
B ({4,5})
C ({6,7})
D ({1,2,3,4,5,6,7})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3})
Step 1
Concept
(A-B) contains elements of (A) that are not in (B). (4) and (5) are common, so they are removed.
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3}). (A-B) contains elements of (A) that are not in (B). (4) and (5) are common, so they are removed.
Step 3
Exam Tip
(A-B) में (A) के वे तत्व होते हैं जो (B) में नहीं हैं। (4) और (5) साझा हैं, इसलिए हट जाते हैं।
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\(A=\{p,q,r,s\}\) और \(B=\{r,s,t\}\) हैं। (B-A) क्या है?
\(A=\{p,q,r,s\}\) and \(B=\{r,s,t\}\). What is (B-A)?
#sets
#venn diagrams
#difference listing
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A ({t})
B ({r,s})
C ({p,q})
D ({p,q,r,s,t})
Explanation opens after your attempt
Step 1
Concept
(B-A) contains elements of (B) that are not in (A). Here only (t) is such an element.
Step 2
Why this answer is correct
The correct answer is A. ({t}). (B-A) contains elements of (B) that are not in (A). Here only (t) is such an element.
Step 3
Exam Tip
(B-A) में (B) के वे तत्व हैं जो (A) में नहीं हैं। यहां केवल (t) ऐसा तत्व है।
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वेन आरेख में (\(A\cap B\)^c) किस क्षेत्र को दर्शाता है?
What region does (\(A\cap B\)^c) represent in a Venn diagram?
#sets
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#de morgan idea
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A \(A\cap B\) को छोड़कर (U) का बाकी भाग / All of (U) except \(A\cap B\)
B केवल \(A\cap B\) / Only \(A\cap B\)
C केवल (A-B) / Only (A-B)
D केवल (B-A) / Only (B-A)
Explanation opens after your attempt
Correct Answer
A. \(A\cap B\) को छोड़कर (U) का बाकी भाग / All of (U) except \(A\cap B\)
Step 1
Concept
(\(A\cap B\)^c) means the complement of the common part. So it includes everything in (U) except the common part.
Step 2
Why this answer is correct
The correct answer is A. \(A\cap B\) को छोड़कर (U) का बाकी भाग / All of (U) except \(A\cap B\). (\(A\cap B\)^c) means the complement of the common part. So it includes everything in (U) except the common part.
Step 3
Exam Tip
(\(A\cap B\)^c) का अर्थ साझा भाग का पूरक है। इसलिए (U) में साझा भाग को छोड़कर सब शामिल होगा।
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डी मॉर्गन नियम के अनुसार (\(A\cup B\)^c) किसके बराबर है?
According to De Morgan's law, what is (\(A\cup B\)^c) equal to?
#sets
#venn diagrams
#de morgan law
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A \(A^c\cap B^c\)
B \(A^c\cup B^c\)
C \(A\cap B\)
D \(A\cup B\)
Explanation opens after your attempt
Correct Answer
A. \(A^c\cap B^c\)
Step 1
Concept
The complement of a union is the region outside both sets, so (\(A\cup B\)^c=A^c\cap B^c). This rule is easy to see from a Venn diagram.
Step 2
Why this answer is correct
The correct answer is A. \(A^c\cap B^c\). The complement of a union is the region outside both sets, so (\(A\cup B\)^c=A^c\cap B^c). This rule is easy to see from a Venn diagram.
Step 3
Exam Tip
संघ के पूरक में दोनों से बाहर का भाग आता है, इसलिए (\(A\cup B\)^c=A^c\cap B^c)। वेन आरेख से यह नियम आसानी से दिखता है।
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डी मॉर्गन नियम के अनुसार (\(A\cap B\)^c) किसके बराबर है?
According to De Morgan's law, what is (\(A\cap B\)^c) equal to?
#sets
#venn diagrams
#de morgan law
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A \(A^c\cup B^c\)
B \(A^c\cap B^c\)
C (A-B)
D (B-A)
Explanation opens after your attempt
Correct Answer
A. \(A^c\cup B^c\)
Step 1
Concept
The region outside the common part is \(A^c\cup B^c\). While taking complements, union and intersection interchange.
Step 2
Why this answer is correct
The correct answer is A. \(A^c\cup B^c\). The region outside the common part is \(A^c\cup B^c\). While taking complements, union and intersection interchange.
Step 3
Exam Tip
साझा भाग के बाहर का क्षेत्र \(A^c\cup B^c\) होता है। पूरक लेते समय संघ और प्रतिच्छेद आपस में बदल जाते हैं।
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यदि (n(U)=120), (n(A)=65), (n(B)=58) और (n\(A\cap B\)=29) है, तो (n\(A^c\cap B^c\)) कितना है?
If (n(U)=120), (n(A)=65), (n(B)=58), and (n\(A\cap B\)=29), what is (n\(A^c\cap B^c\))?
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#de morgan counting
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A (26)
B (94)
C (29)
D (55)
Explanation opens after your attempt
Step 1
Concept
(A^c\cap B^c=\(A\cup B\)^c). (n\(A\cup B\)=65+58-29=94), so the answer is (120-94=26).
Step 2
Why this answer is correct
The correct answer is A. (26). (A^c\cap B^c=\(A\cup B\)^c). (n\(A\cup B\)=65+58-29=94), so the answer is (120-94=26).
Step 3
Exam Tip
(A^c\cap B^c=\(A\cup B\)^c) है। (n\(A\cup B\)=65+58-29=94), इसलिए उत्तर (120-94=26)।
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यदि (n(U)=75), (n\(A\cap B\)=18) है, तो (n(\(A\cap B\)^c)) कितना होगा?
If (n(U)=75) and (n\(A\cap B\)=18), what is (n(\(A\cap B\)^c))?
#sets
#venn diagrams
#complement of intersection
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A (57)
B (93)
C (18)
D (75)
Explanation opens after your attempt
Step 1
Concept
The complement is found by subtracting from (U), so (75-18=57). Here the complement of only the common part is asked.
Step 2
Why this answer is correct
The correct answer is A. (57). The complement is found by subtracting from (U), so (75-18=57). Here the complement of only the common part is asked.
Step 3
Exam Tip
पूरक (U) से घटाकर मिलता है, इसलिए (75-18=57)। यहां केवल साझा भाग का पूरक पूछा गया है।
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एक परीक्षा में (36) विद्यार्थियों ने हिंदी, (42) ने अंग्रेजी और (20) ने दोनों विषय चुने। केवल एक विषय चुनने वाले कितने विद्यार्थी हैं?
In an exam, (36) students chose Hindi, (42) chose English, and (20) chose both subjects. How many students chose exactly one subject?
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#exactly one survey
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A (38)
B (58)
C (78)
D (20)
Explanation opens after your attempt
Step 1
Concept
Exactly one (=(36-20)+(42-20)=38). You can also use (n(A)+n(B)-2n\(A\cap B\)).
Step 2
Why this answer is correct
The correct answer is A. (38). Exactly one (=(36-20)+(42-20)=38). You can also use (n(A)+n(B)-2n\(A\cap B\)).
Step 3
Exam Tip
केवल एक (=(36-20)+(42-20)=38)। सीधे (n(A)+n(B)-2n\(A\cap B\)) भी लगा सकते हैं।
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यदि (65) लोगों में (31) क्रिकेट, (29) फुटबॉल और (11) दोनों खेल पसंद करते हैं, तो कोई भी खेल पसंद न करने वाले कितने हैं?
Among (65) people, (31) like cricket, (29) like football, and (11) like both. How many like neither sport?
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#venn diagrams
#neither survey
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A (16)
B (49)
C (54)
D (5)
Explanation opens after your attempt
Step 1
Concept
At least one is (31+29-11=49), so neither is (65-49=16). In survey questions, finding the union first is useful.
Step 2
Why this answer is correct
The correct answer is A. (16). At least one is (31+29-11=49), so neither is (65-49=16). In survey questions, finding the union first is useful.
Step 3
Exam Tip
कम से कम एक (31+29-11=49) है, इसलिए कोई नहीं (65-49=16)। सर्वे प्रश्नों में पहले संघ निकालना उपयोगी है।
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(n\(A\cup B\)=72), (n(A)=46) और (n(B-A)=26) है। (n\(A\cap B\)) कितना होगा?
(n\(A\cup B\)=72), (n(A)=46), and (n(B-A)=26). What is (n\(A\cap B\))?
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#region relation
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A (0)
B (20)
C (26)
D (46)
Explanation opens after your attempt
Step 1
Concept
\(A\cup B\) contains all of (A) and (B-A), so (46+26=72). Thus the common part is already inside (A), and the extra value is (0).
Step 2
Why this answer is correct
The correct answer is A. (0). \(A\cup B\) contains all of (A) and (B-A), so (46+26=72). Thus the common part is already inside (A), and the extra value is (0).
Step 3
Exam Tip
\(A\cup B\) में पूरा (A) और (B-A) शामिल है, इसलिए (46+26=72)। अतः साझा भाग पहले से (A) में है और अतिरिक्त मान (0) निकलता है।
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एक वेन आरेख में (n(A-B)=18), (n\(A\cap B\)=12), (n(B-A)=22) और बाहर (8) तत्व हैं। (n(U)) कितना है?
In a Venn diagram, (n(A-B)=18), (n\(A\cap B\)=12), (n(B-A)=22), and (8) elements are outside. What is (n(U))?
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#total universal
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A (60)
B (52)
C (48)
D (40)
Explanation opens after your attempt
Step 1
Concept
The universal set is the sum of all regions, so (18+12+22+8=60). In a Venn diagram, no region should be missed.
Step 2
Why this answer is correct
The correct answer is A. (60). The universal set is the sum of all regions, so (18+12+22+8=60). In a Venn diagram, no region should be missed.
Step 3
Exam Tip
सार्वत्रिक समुच्चय सभी क्षेत्रों का योग है, इसलिए (18+12+22+8=60)। वेन आरेख में कोई क्षेत्र छोड़ना नहीं चाहिए।
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यदि (n(U)=55), (n(A-B)=14), (n\(A\cap B\)=9) और (n(B-A)=17) है, तो बाहर का क्षेत्र कितना है?
If (n(U)=55), (n(A-B)=14), (n\(A\cap B\)=9), and (n(B-A)=17), what is the outside region?
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#venn diagrams
#outside region
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A (15)
B (40)
C (23)
D (32)
Explanation opens after your attempt
Step 1
Concept
The union is (14+9+17=40), so outside is (55-40=15). The outside region is the complement of the union.
Step 2
Why this answer is correct
The correct answer is A. (15). The union is (14+9+17=40), so outside is (55-40=15). The outside region is the complement of the union.
Step 3
Exam Tip
संघ (14+9+17=40) है, इसलिए बाहर (55-40=15)। बाहर का क्षेत्र संघ का पूरक होता है।
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तीन समुच्चयों के वेन आरेख में (n\(A\cap B\)=12), (n\(B\cap C\)=13), (n\(C\cap A\)=10) और (n\(A\cap B\cap C\)=4) है। ठीक दो समुच्चयों में आने वाले तत्व कितने हैं?
In a three-set Venn diagram, (n\(A\cap B\)=12), (n\(B\cap C\)=13), (n\(C\cap A\)=10), and (n\(A\cap B\cap C\)=4). How many elements are in exactly two sets?
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#venn diagrams
#exactly two
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A (23)
B (35)
C (31)
D (12)
Explanation opens after your attempt
Step 1
Concept
Exactly two (=(12-4)+(13-4)+(10-4)=23). The central part must be subtracted from each pair.
Step 2
Why this answer is correct
The correct answer is A. (23). Exactly two (=(12-4)+(13-4)+(10-4)=23). The central part must be subtracted from each pair.
Step 3
Exam Tip
ठीक दो (=(12-4)+(13-4)+(10-4)=23)। हर जोड़ी से केंद्रीय भाग घटाना जरूरी है।
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यदि (n(A)=25), (n(B)=22), (n(C)=19), (n\(A\cap B\)=7), (n\(B\cap C\)=6), (n\(C\cap A\)=5), (n\(A\cap B\cap C\)=2) और (n(U)=60) है, तो किसी भी समुच्चय में नहीं आने वाले कितने हैं?
If (n(A)=25), (n(B)=22), (n(C)=19), (n\(A\cap B\)=7), (n\(B\cap C\)=6), (n\(C\cap A\)=5), (n\(A\cap B\cap C\)=2), and (n(U)=60), how many are in none of the sets?
#sets
#venn diagrams
#three set none
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A (10)
B (50)
C (12)
D (8)
Explanation opens after your attempt
Step 1
Concept
The union is (25+22+19-7-6-5+2=50), so none is (60-50=10). In three sets, add back the final common part.
Step 2
Why this answer is correct
The correct answer is A. (10). The union is (25+22+19-7-6-5+2=50), so none is (60-50=10). In three sets, add back the final common part.
Step 3
Exam Tip
संघ (25+22+19-7-6-5+2=50) है, इसलिए कोई नहीं (60-50=10)। तीन समुच्चयों में अंतिम साझा भाग वापस जोड़ें।
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यदि केवल (A=11), केवल (B=13), केवल (C=9), केवल \(A\cap B=5\), केवल \(B\cap C=4\), केवल \(C\cap A=6\) और \(A\cap B\cap C=3\) हैं, तो (n\(A\cup B\cup C\)) कितना है?
If only (A=11), only (B=13), only (C=9), only \(A\cap B=5\), only \(B\cap C=4\), only \(C\cap A=6\), and \(A\cap B\cap C=3\), what is (n\(A\cup B\cup C\))?
#sets
#venn diagrams
#three set regions
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A (51)
B (48)
C (41)
D (54)
Explanation opens after your attempt
Step 1
Concept
The union is the sum of all seven inside regions, (11+13+9+5+4+6+3=51). Add each separate region only once.
Step 2
Why this answer is correct
The correct answer is A. (51). The union is the sum of all seven inside regions, (11+13+9+5+4+6+3=51). Add each separate region only once.
Step 3
Exam Tip
संघ सभी सात अंदरूनी क्षेत्रों का योग है, (11+13+9+5+4+6+3=51)। अलग-अलग क्षेत्रों को केवल एक बार जोड़ें।
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वेन आरेख में छायांकित भाग \(A\cap B^c\) है। यह किसके बराबर है?
In a Venn diagram, the shaded region is \(A\cap B^c\). What is it equal to?
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#shaded region
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A (A-B)
B (B-A)
C \(A\cap B\)
D \(A\cup B\)
Explanation opens after your attempt
Step 1
Concept
\(A\cap B^c\) means inside (A) and outside (B), so it is (A-B). Notice the complement sign to identify the outside part.
Step 2
Why this answer is correct
The correct answer is A. (A-B). \(A\cap B^c\) means inside (A) and outside (B), so it is (A-B). Notice the complement sign to identify the outside part.
Step 3
Exam Tip
\(A\cap B^c\) का अर्थ (A) में और (B) के बाहर है, इसलिए यह (A-B) है। पूरक चिन्ह देखकर बाहर वाले भाग को पहचानें।
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