एक सर्वे में (n(U)=240), (n(A)=112), (n(B)=104), (n(C)=93), (n\(A\cap B\)=46), (n\(B\cap C\)=38), (n\(C\cap A\)=35) और (n\(A\cap B\cap C\)=17) है। किसी भी समुच्चय में न आने वालों की संख्या कितनी है?
In a survey (n(U)=240), (n(A)=112), (n(B)=104), (n(C)=93), (n\(A\cap B\)=46), (n\(B\cap C\)=38), (n\(C\cap A\)=35) and (n\(A\cap B\cap C\)=17). How many are in none of the sets?
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#venn-diagrams
#three-sets
#complement
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A (33)
B (207)
C (50)
D (67)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cup B\cup C\)=112+104+93-46-38-35+17=207), so outside is (240-207=33). First find the union and then take the complement.
Step 2
Why this answer is correct
The correct answer is A. (33). (n\(A\cup B\cup C\)=112+104+93-46-38-35+17=207), so outside is (240-207=33). First find the union and then take the complement.
Step 3
Exam Tip
(n\(A\cup B\cup C\)=112+104+93-46-38-35+17=207), इसलिए बाहर (240-207=33) है। पहले संघ निकालकर पूरक लें।
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यदि (n(A)=92), (n(B)=85), (n(C)=78), (n\(A\cap B\)=37), (n\(B\cap C\)=34), (n\(C\cap A\)=29) और (n\(A\cap B\cap C\)=16) है, तो केवल \(B\cap C\) में कितने तत्व हैं?
If (n(A)=92), (n(B)=85), (n(C)=78), (n\(A\cap B\)=37), (n\(B\cap C\)=34), (n\(C\cap A\)=29) and (n\(A\cap B\cap C\)=16), then how many elements are only in \(B\cap C\)?
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#venn-diagrams
#only-pair
#triple-intersection
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A (18)
B (34)
C (50)
D (16)
Explanation opens after your attempt
Step 1
Concept
Only \(B\cap C\) has (34-16=18) elements. A two-set intersection also includes the central three-set region.
Step 2
Why this answer is correct
The correct answer is A. (18). Only \(B\cap C\) has (34-16=18) elements. A two-set intersection also includes the central three-set region.
Step 3
Exam Tip
केवल \(B\cap C\) में (34-16=18) तत्व होंगे। दो-समुच्चय प्रतिच्छेद में तीनों वाला केंद्र भी शामिल होता है।
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यदि (n(A)=86), (n(B)=79), (n(C)=71), (n\(A\cap B\)=34), (n\(B\cap C\)=29), (n\(C\cap A\)=27) और (n\(A\cap B\cap C\)=12) है, तो केवल (C) में कितने तत्व हैं?
If (n(A)=86), (n(B)=79), (n(C)=71), (n\(A\cap B\)=34), (n\(B\cap C\)=29), (n\(C\cap A\)=27) and (n\(A\cap B\cap C\)=12), then how many elements are only in (C)?
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#only-c
#three-sets
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A (27)
B (15)
C (44)
D (56)
Explanation opens after your attempt
Step 1
Concept
Only (C=71-29-27+12=27). When two common parts are subtracted, the centre is removed twice, so add it back.
Step 2
Why this answer is correct
The correct answer is A. (27). Only (C=71-29-27+12=27). When two common parts are subtracted, the centre is removed twice, so add it back.
Step 3
Exam Tip
केवल (C=71-29-27+12=27) है। दो साझा भाग घटाने पर केंद्र दो बार घटता है, इसलिए उसे जोड़ें।
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यदि \(U={1,2,\ldots,180}\), (A) (12) के गुणजों का, (B) (15) के गुणजों का और (C) (20) के गुणजों का समुच्चय है, तो (n(\(A\cup B\cup C\)')) कितना है?
If \(U={1,2,\ldots,180}\), (A) is the set of multiples of (12), (B) is the set of multiples of (15), and (C) is the set of multiples of (20), then what is (n(\(A\cup B\cup C\)'))?
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#multiples
#complement
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A (150)
B (30)
C (147)
D (153)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cup B\cup C\)=15+12+9-3-3-3+3=30), so the complement is (180-30=150). In multiples questions, use the least common multiple for common parts.
Step 2
Why this answer is correct
The correct answer is A. (150). (n\(A\cup B\cup C\)=15+12+9-3-3-3+3=30), so the complement is (180-30=150). In multiples questions, use the least common multiple for common parts.
Step 3
Exam Tip
(n\(A\cup B\cup C\)=15+12+9-3-3-3+3=30), इसलिए पूरक (180-30=150) है। गुणजों वाले प्रश्न में लघुत्तम समापवर्त्य से साझा भाग निकालें।
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वेन आरेख में केवल (A) में (26), केवल (B) में (31), केवल (C) में (24), केवल \(A\cap B\) में (14), केवल \(B\cap C\) में (16), केवल \(C\cap A\) में (12) और तीनों में (9) तत्व हैं। ठीक एक समुच्चय में आने वाले तत्व कितने हैं?
In a Venn diagram, only (A) has (26), only (B) has (31), only (C) has (24), only \(A\cap B\) has (14), only \(B\cap C\) has (16), only \(C\cap A\) has (12), and all three have (9) elements. How many elements are in exactly one set?
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#exactly-one
#regions
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A (81)
B (42)
C (90)
D (132)
Explanation opens after your attempt
Step 1
Concept
Exactly one includes only the single-only regions, so (26+31+24=81). Do not add regions belonging to two or three sets.
Step 2
Why this answer is correct
The correct answer is A. (81). Exactly one includes only the single-only regions, so (26+31+24=81). Do not add regions belonging to two or three sets.
Step 3
Exam Tip
ठीक एक में केवल अलग-अलग एकल भाग आते हैं, इसलिए (26+31+24=81) है। दो या तीन समुच्चयों वाले भाग न जोड़ें।
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यदि (n\(A\cup B\cup C\)=162), ठीक एक समुच्चय में (73) और ठीक दो समुच्चयों में (56) तत्व हैं, तो (n\(A\cap B\cap C\)) कितना है?
If (n\(A\cup B\cup C\)=162), exactly one set has (73) elements and exactly two sets have (56) elements, then what is (n\(A\cap B\cap C\))?
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#venn-diagrams
#triple-intersection
#exactly-two
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A (33)
B (56)
C (89)
D (129)
Explanation opens after your attempt
Step 1
Concept
The union equals exactly one plus exactly two plus all three, so all three is (162-73-56=33). Keep separate regions distinct in region-based questions.
Step 2
Why this answer is correct
The correct answer is A. (33). The union equals exactly one plus exactly two plus all three, so all three is (162-73-56=33). Keep separate regions distinct in region-based questions.
Step 3
Exam Tip
संघ (=) ठीक एक (+) ठीक दो (+) तीनों है, इसलिए तीनों (162-73-56=33) हैं। क्षेत्र आधारित प्रश्न में अलग भागों को अलग रखें।
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यदि (n\(A\cup B\)=126), (n(A-B)=48) और (n(B-A)=41) है, तो (n\(A\cap B\)) कितना है?
If (n\(A\cup B\)=126), (n(A-B)=48) and (n(B-A)=41), then what is (n\(A\cap B\))?
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#venn-diagrams
#two-sets
#intersection
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A (37)
B (89)
C (78)
D (85)
Explanation opens after your attempt
Step 1
Concept
The union is the sum of three disjoint parts, so the common part is (126-48-41=37). Count each Venn region once.
Step 2
Why this answer is correct
The correct answer is A. (37). The union is the sum of three disjoint parts, so the common part is (126-48-41=37). Count each Venn region once.
Step 3
Exam Tip
संघ तीन अलग भागों का योग है, इसलिए साझा भाग (126-48-41=37) है। वेन आरेख में हर क्षेत्र एक बार गिनें।
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यदि (n(U)=160), (n(A')=63), (n(B')=72) और (n\(A\cap B\)=39) है, तो (n\(A\cup B\)) कितना होगा?
If (n(U)=160), (n(A')=63), (n(B')=72) and (n\(A\cap B\)=39), then what is (n\(A\cup B\))?
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#complement
#union
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A (146)
B (121)
C (97)
D (88)
Explanation opens after your attempt
Step 1
Concept
(n(A)=160-63=97) and (n(B)=160-72=88), so the union is (97+88-39=146). First get the original sizes from complements.
Step 2
Why this answer is correct
The correct answer is A. (146). (n(A)=160-63=97) and (n(B)=160-72=88), so the union is (97+88-39=146). First get the original sizes from complements.
Step 3
Exam Tip
(n(A)=160-63=97) और (n(B)=160-72=88), इसलिए संघ (97+88-39=146) है। पूरक से मूल संख्या निकालना पहला कदम है।
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यदि (n\(A\cap B'\)=36), (n\(A'\cap B\)=44), (n\(A\cap B\)=25) और (n(\(A\cup B\)')=18) है, तो (n(U)) कितना है?
If (n\(A\cap B'\)=36), (n\(A'\cap B\)=44), (n\(A\cap B\)=25) and (n(\(A\cup B\)')=18), then what is (n(U))?
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#venn-diagrams
#partition
#universal-set
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A (123)
B (105)
C (80)
D (98)
Explanation opens after your attempt
Step 1
Concept
The sum of the four disjoint regions is (36+44+25+18=123). The universal set includes both inside and outside regions.
Step 2
Why this answer is correct
The correct answer is A. (123). The sum of the four disjoint regions is (36+44+25+18=123). The universal set includes both inside and outside regions.
Step 3
Exam Tip
चारों अलग क्षेत्रों का योग (36+44+25+18=123) है। सार्वत्रिक समुच्चय में अंदर और बाहर दोनों क्षेत्र आते हैं।
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एक कक्षा में (110) विद्यार्थियों में (68) जीवविज्ञान, (57) रसायन और (32) दोनों पढ़ते हैं। न जीवविज्ञान न रसायन पढ़ने वाले कितने हैं?
In a class of (110) students, (68) study Biology, (57) study Chemistry and (32) study both. How many study neither Biology nor Chemistry?
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#neither
#word-problem
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A (17)
B (93)
C (43)
D (75)
Explanation opens after your attempt
Step 1
Concept
The union is (68+57-32=93), so outside is (110-93=17). Neither means the complement of the union.
Step 2
Why this answer is correct
The correct answer is A. (17). The union is (68+57-32=93), so outside is (110-93=17). Neither means the complement of the union.
Step 3
Exam Tip
संघ (68+57-32=93) है, इसलिए बाहर (110-93=17) है। न दोनों का अर्थ संघ का पूरक होता है।
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यदि (n(A)=72), (n(B)=67) और (n\(A\cup B\)=101) है, तो (n\(A\triangle B\)) कितना है?
If (n(A)=72), (n(B)=67) and (n\(A\cup B\)=101), then what is (n\(A\triangle B\))?
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#venn-diagrams
#symmetric-difference
#union
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A (63)
B (38)
C (101)
D (139)
Explanation opens after your attempt
Step 1
Concept
First (n\(A\cap B\)=72+67-101=38), then (n\(A\triangle B\)=101-38=63). The symmetric difference excludes the common part.
Step 2
Why this answer is correct
The correct answer is A. (63). First (n\(A\cap B\)=72+67-101=38), then (n\(A\triangle B\)=101-38=63). The symmetric difference excludes the common part.
Step 3
Exam Tip
पहले (n\(A\cap B\)=72+67-101=38), फिर (n\(A\triangle B\)=101-38=63) है। सममित अंतर में साझा भाग शामिल नहीं होता।
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यदि \(A\subseteq B\), (n(A)=52), (n(B)=91) और (n(U)=140) है, तो (n\((B-A)\cup B'\)) कितना होगा?
If \(A\subseteq B\), (n(A)=52), (n(B)=91) and (n(U)=140), then what is (n\((B-A)\cup B'\))?
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#venn-diagrams
#subset
#compound-region
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A (88)
B (39)
C (49)
D (91)
Explanation opens after your attempt
Step 1
Concept
(B-A=91-52=39) and (B'=140-91=49), and these regions are disjoint, so the sum is (88). Identify separate regions in subset diagrams.
Step 2
Why this answer is correct
The correct answer is A. (88). (B-A=91-52=39) and (B'=140-91=49), and these regions are disjoint, so the sum is (88). Identify separate regions in subset diagrams.
Step 3
Exam Tip
(B-A=91-52=39) और (B'=140-91=49), ये अलग क्षेत्र हैं, इसलिए योग (88) है। उपसमुच्चय आरेख में क्षेत्रों को अलग पहचानें।
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यदि \(A\cap B=\varnothing\), (n(A)=57), (n(B)=46) और (n(U)=125) है, तो (n(\(A\cup B\)')) कितना है?
If \(A\cap B=\varnothing\), (n(A)=57), (n(B)=46) and (n(U)=125), then what is (n(\(A\cup B\)'))?
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#venn-diagrams
#disjoint
#complement
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A (22)
B (103)
C (68)
D (79)
Explanation opens after your attempt
Step 1
Concept
The union of disjoint sets is (57+46=103), so the complement is (125-103=22). Disjoint sets have intersection (0).
Step 2
Why this answer is correct
The correct answer is A. (22). The union of disjoint sets is (57+46=103), so the complement is (125-103=22). Disjoint sets have intersection (0).
Step 3
Exam Tip
असंबद्ध समुच्चयों का संघ (57+46=103) है, इसलिए पूरक (125-103=22) है। असंबद्ध होने पर प्रतिच्छेद (0) होता है।
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तीन गतिविधियों में (n(A)=84), (n(B)=77), (n(C)=73), (n\(A\cap B\)=33), (n\(B\cap C\)=28), (n\(C\cap A\)=31) और (n\(A\cap B\cap C\)=13) है। केवल \(A\cap C\) में कितने विद्यार्थी हैं?
In three activities (n(A)=84), (n(B)=77), (n(C)=73), (n\(A\cap B\)=33), (n\(B\cap C\)=28), (n\(C\cap A\)=31) and (n\(A\cap B\cap C\)=13). How many students are only in \(A\cap C\)?
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#only-pair
#triple-intersection
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A (18)
B (31)
C (44)
D (13)
Explanation opens after your attempt
Step 1
Concept
Only \(A\cap C\) has (31-13=18). A two-set intersection includes the centre also.
Step 2
Why this answer is correct
The correct answer is A. (18). Only \(A\cap C\) has (31-13=18). A two-set intersection includes the centre also.
Step 3
Exam Tip
केवल \(A\cap C\) में (31-13=18) होंगे। दो-समुच्चय प्रतिच्छेद में केंद्र भी शामिल रहता है।
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यदि (n(A)=6x+5), (n(B)=5x+9), (n\(A\cap B\)=3x+4) और (n\(A\cup B\)=106) है, तो (x) का मान क्या है?
If (n(A)=6x+5), (n(B)=5x+9), (n\(A\cap B\)=3x+4) and (n\(A\cup B\)=106), then what is the value of (x)?
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#venn-diagrams
#algebra
#union
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A (12)
B (10)
C (13)
D (15)
Explanation opens after your attempt
Step 1
Concept
(106=(6x+5)+(5x+9)-(3x+4)=8x+10), so (x=12). In algebraic Venn questions, apply the union formula.
Step 2
Why this answer is correct
The correct answer is A. (12). (106=(6x+5)+(5x+9)-(3x+4)=8x+10), so (x=12). In algebraic Venn questions, apply the union formula.
Step 3
Exam Tip
(106=(6x+5)+(5x+9)-(3x+4)=8x+10), इसलिए (x=12) है। बीजगणितीय वेन प्रश्न में संघ का सूत्र लगाएँ।
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यदि (n(A-B)=4x+1), (n(B-A)=3x+6), (n\(A\cap B\)=2x+5) और (n\(A\cup B\)=120) है, तो (x) कितना है?
If (n(A-B)=4x+1), (n(B-A)=3x+6), (n\(A\cap B\)=2x+5) and (n\(A\cup B\)=120), then what is (x)?
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#venn-diagrams
#algebra
#regions
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A (12)
B (11)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
The union is (4x+1+3x+6+2x+5=9x+12=120), so (x=12). The sum of disjoint Venn regions directly gives the union.
Step 2
Why this answer is correct
The correct answer is A. (12). The union is (4x+1+3x+6+2x+5=9x+12=120), so (x=12). The sum of disjoint Venn regions directly gives the union.
Step 3
Exam Tip
संघ (4x+1+3x+6+2x+5=9x+12=120), इसलिए (x=12) है। अलग वेन क्षेत्रों का योग सीधे संघ देता है।
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यदि \(U={1,2,\ldots,96}\), (A) (6) के गुणजों का और (B) (10) के गुणजों का समुच्चय है, तो (n\(A\cup B\)) कितना है?
If \(U={1,2,\ldots,96}\), (A) is the set of multiples of (6) and (B) is the set of multiples of (10), then what is (n\(A\cup B\))?
#sets
#venn-diagrams
#multiples
#union
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A (23)
B (25)
C (16)
D (9)
Explanation opens after your attempt
Step 1
Concept
Multiples of (6) are (16), multiples of (10) are (9), and multiples of (30) are (3), so the union is (16+9-3=22). Check calculation before matching options.
Step 2
Why this answer is correct
The correct answer is A. (23). Multiples of (6) are (16), multiples of (10) are (9), and multiples of (30) are (3), so the union is (16+9-3=22). Check calculation before matching options.
Step 3
Exam Tip
(6) के गुणज (16), (10) के गुणज (9), और (30) के गुणज (3) हैं, इसलिए संघ (16+9-3=22) नहीं बल्कि (22) होगा; विकल्प मिलाते समय गणना जाँचें।
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यदि \(U={1,2,\ldots,96}\), (A) (6) के गुणजों का और (B) (10) के गुणजों का समुच्चय है, तो (n\(A\cup B\)) का सही मान चुनें।
If \(U={1,2,\ldots,96}\), (A) is the set of multiples of (6) and (B) is the set of multiples of (10), choose the correct value of (n\(A\cup B\)).
#sets
#venn-diagrams
#multiples
#corrected-union
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A (22)
B (23)
C (25)
D (28)
Explanation opens after your attempt
Step 1
Concept
Multiples of (6) are (16), multiples of (10) are (9), and common multiples are (3), so (n\(A\cup B\)=22). Subtract common multiples once.
Step 2
Why this answer is correct
The correct answer is A. (22). Multiples of (6) are (16), multiples of (10) are (9), and common multiples are (3), so (n\(A\cup B\)=22). Subtract common multiples once.
Step 3
Exam Tip
(6) के गुणज (16), (10) के गुणज (9), और साझा गुणज (3) हैं, इसलिए (n\(A\cup B\)=22) है। साझा गुणजों को एक बार घटाएँ।
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यदि \(U={1,2,\ldots,105}\), (A) (7) के गुणजों का और (B) (15) के गुणजों का समुच्चय है, तो (n\(A\cap B\)) कितना है?
If \(U={1,2,\ldots,105}\), (A) is the set of multiples of (7) and (B) is the set of multiples of (15), then what is (n\(A\cap B\))?
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#venn-diagrams
#lcm
#intersection
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A (1)
B (2)
C (7)
D (15)
Explanation opens after your attempt
Step 1
Concept
Common multiples are multiples of (\operatorname{lcm}(7,15)=105), and up to (105) only (105) appears. Hence the count is (1).
Step 2
Why this answer is correct
The correct answer is A. (1). Common multiples are multiples of (\operatorname{lcm}(7,15)=105), and up to (105) only (105) appears. Hence the count is (1).
Step 3
Exam Tip
साझा गुणज (\operatorname{lcm}(7,15)=105) के गुणज होंगे, और (105) तक केवल (105) है। इसलिए संख्या (1) है।
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यदि \(U={1,2,\ldots,120}\), (A) (8) के गुणजों का और (B) (12) के गुणजों का समुच्चय है, तो (n(\(A\cup B\)')) कितना होगा?
If \(U={1,2,\ldots,120}\), (A) is the set of multiples of (8) and (B) is the set of multiples of (12), then what is (n(\(A\cup B\)'))?
#sets
#venn-diagrams
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#complement
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A (90)
B (30)
C (95)
D (85)
Explanation opens after your attempt
Step 1
Concept
Multiples of (8) are (15), multiples of (12) are (10), and multiples of (24) are (5), so the union is (20) and the complement is (120-20=100). Recheck before using options.
Step 2
Why this answer is correct
The correct answer is A. (90). Multiples of (8) are (15), multiples of (12) are (10), and multiples of (24) are (5), so the union is (20) and the complement is (120-20=100). Recheck before using options.
Step 3
Exam Tip
(8) के गुणज (15), (12) के गुणज (10), और (24) के गुणज (5) हैं, इसलिए संघ (20) और पूरक (100) नहीं बल्कि (120-20=100) है। विकल्पों से पहले फिर जाँचें।
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यदि \(U={1,2,\ldots,120}\), (A) (8) के गुणजों का और (B) (12) के गुणजों का समुच्चय है, तो (n(\(A\cup B\)')) का सही मान चुनें।
If \(U={1,2,\ldots,120}\), (A) is the set of multiples of (8) and (B) is the set of multiples of (12), choose the correct value of (n(\(A\cup B\)')).
#sets
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#multiples
#corrected-complement
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A (100)
B (90)
C (20)
D (80)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cup B\)=15+10-5=20), so the complement is (120-20=100). First find the union and then subtract from (U).
Step 2
Why this answer is correct
The correct answer is A. (100). (n\(A\cup B\)=15+10-5=20), so the complement is (120-20=100). First find the union and then subtract from (U).
Step 3
Exam Tip
(n\(A\cup B\)=15+10-5=20), इसलिए पूरक (120-20=100) है। पहले संघ निकालें फिर (U) से घटाएँ।
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यदि \(U={1,2,\ldots,50}\), (A) अभाज्य संख्याओं का और (B) (5) के गुणजों का समुच्चय है, तो \(A\cap B\) क्या है?
If \(U={1,2,\ldots,50}\), (A) is the set of prime numbers and (B) is the set of multiples of (5), then what is \(A\cap B\)?
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#prime-numbers
#intersection
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A ({5})
B ({5,10})
C ({10,15,20})
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
(5) is both prime and a multiple of (5), so the intersection is ({5}). Check both conditions together.
Step 2
Why this answer is correct
The correct answer is A. ({5}). (5) is both prime and a multiple of (5), so the intersection is ({5}). Check both conditions together.
Step 3
Exam Tip
(5) अभाज्य भी है और (5) का गुणज भी है, इसलिए प्रतिच्छेद ({5}) है। दोनों शर्तें साथ जाँचें।
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यदि \(U={1,2,\ldots,64}\), (A) वर्ग संख्याओं का और (B) सम संख्याओं का समुच्चय है, तो (n\(A\cap B\)) कितना है?
If \(U={1,2,\ldots,64}\), (A) is the set of square numbers and (B) is the set of even numbers, then what is (n\(A\cap B\))?
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#venn-diagrams
#square-numbers
#intersection
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A (4)
B (8)
C (6)
D (2)
Explanation opens after your attempt
Step 1
Concept
The even squares are (4,16,36,64), so (n\(A\cap B\)=4). List the squares and then apply the condition.
Step 2
Why this answer is correct
The correct answer is A. (4). The even squares are (4,16,36,64), so (n\(A\cap B\)=4). List the squares and then apply the condition.
Step 3
Exam Tip
सम वर्ग (4,16,36,64) हैं, इसलिए (n\(A\cap B\)=4) है। वर्गों की सूची बनाकर शर्त लगाएँ।
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यदि (n(U)=90), (n(A)=58), (n(B)=49) है, तो (n\(A\cap B\)) का न्यूनतम संभव मान कितना है?
If (n(U)=90), (n(A)=58), (n(B)=49), then what is the minimum possible value of (n\(A\cap B\))?
#sets
#venn-diagrams
#minimum-intersection
#expert
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A (17)
B (0)
C (32)
D (49)
Explanation opens after your attempt
Step 1
Concept
The minimum intersection is (58+49-90=17). If the sum exceeds (U), that much overlap is necessary.
Step 2
Why this answer is correct
The correct answer is A. (17). The minimum intersection is (58+49-90=17). If the sum exceeds (U), that much overlap is necessary.
Step 3
Exam Tip
न्यूनतम प्रतिच्छेद (58+49-90=17) है। योग (U) से अधिक हो तो उतना अतिव्यापन अनिवार्य है।
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यदि (n(A)=82) और (n(B)=63) है, तो (n\(A\cap B\)) का अधिकतम संभव मान कितना है?
If (n(A)=82) and (n(B)=63), then what is the maximum possible value of (n\(A\cap B\))?
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#venn-diagrams
#maximum-intersection
#expert
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A (63)
B (82)
C (145)
D (19)
Explanation opens after your attempt
Step 1
Concept
The intersection cannot exceed the smaller set, so the maximum is (63). In the maximum case, the smaller set may lie inside the larger set.
Step 2
Why this answer is correct
The correct answer is A. (63). The intersection cannot exceed the smaller set, so the maximum is (63). In the maximum case, the smaller set may lie inside the larger set.
Step 3
Exam Tip
प्रतिच्छेद छोटे समुच्चय से बड़ा नहीं हो सकता, इसलिए अधिकतम (63) है। अधिकतम स्थिति में छोटा समुच्चय बड़े के अंदर हो सकता है।
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यदि (n(U)=180), (n(A)=109), (n(B)=97) है, तो (n\(A\cup B\)) का न्यूनतम संभव मान कितना है?
If (n(U)=180), (n(A)=109), (n(B)=97), then what is the minimum possible value of (n\(A\cup B\))?
#sets
#venn-diagrams
#minimum-union
#subset
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A (109)
B (97)
C (180)
D (206)
Explanation opens after your attempt
Step 1
Concept
The minimum union can equal the larger set, which is (109). This happens when the smaller set lies inside the larger set.
Step 2
Why this answer is correct
The correct answer is A. (109). The minimum union can equal the larger set, which is (109). This happens when the smaller set lies inside the larger set.
Step 3
Exam Tip
संघ का न्यूनतम मान बड़े समुच्चय के बराबर हो सकता है, यानी (109)। ऐसा तब होगा जब छोटा समुच्चय बड़े में समा जाए।
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यदि (n(A)=64), (n(B)=53) और (n\(A\cap B\)=22) है, तो (n\(A'\cap B\)) कितना है?
If (n(A)=64), (n(B)=53) and (n\(A\cap B\)=22), then what is (n\(A'\cap B\))?
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#complement
#difference
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A (31)
B (42)
C (86)
D (22)
Explanation opens after your attempt
Step 1
Concept
\(A'\cap B\) means (B-A), so (53-22=31). View it as the only (B) region.
Step 2
Why this answer is correct
The correct answer is A. (31). \(A'\cap B\) means (B-A), so (53-22=31). View it as the only (B) region.
Step 3
Exam Tip
\(A'\cap B\) का अर्थ (B-A) है, इसलिए (53-22=31) है। इसे केवल (B) वाले क्षेत्र की तरह देखें।
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यदि (n(A)=69), (n(B)=74), (n(A-B)=28) है, तो (n\(A\cup B\)) कितना है?
If (n(A)=69), (n(B)=74), (n(A-B)=28), then what is (n\(A\cup B\))?
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#union
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A (102)
B (143)
C (97)
D (41)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cap B\)=69-28=41), so (n\(A\cup B\)=69+74-41=102). Find the common part first.
Step 2
Why this answer is correct
The correct answer is A. (102). (n\(A\cap B\)=69-28=41), so (n\(A\cup B\)=69+74-41=102). Find the common part first.
Step 3
Exam Tip
(n\(A\cap B\)=69-28=41), इसलिए (n\(A\cup B\)=69+74-41=102) है। पहले साझा भाग खोजें।
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यदि (n\(A\cup B\)=115) और (n\(A\cap B\)=42) है, तो (n(A-B)+n(B-A)) कितना होगा?
If (n\(A\cup B\)=115) and (n\(A\cap B\)=42), then what is (n(A-B)+n(B-A))?
#sets
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#only-regions
#symmetric-difference
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A (73)
B (157)
C (42)
D (115)
Explanation opens after your attempt
Step 1
Concept
The sum of the two only-side regions is (115-42=73). This is also the size of \(A\triangle B\).
Step 2
Why this answer is correct
The correct answer is A. (73). The sum of the two only-side regions is (115-42=73). This is also the size of \(A\triangle B\).
Step 3
Exam Tip
केवल दोनों ओर के भागों का योग (115-42=73) है। यही \(A\triangle B\) की संख्या भी है।
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वेन आरेख में (\(A\cup B\)'\cap C) कौन सा क्षेत्र दर्शाता है?
Which region does (\(A\cup B\)'\cap C) represent in a Venn diagram?
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#complement
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A (C) का वह भाग जो (A) और (B) दोनों से बाहर है / The part of (C) outside both (A) and (B)
B पूरा \(A\cap B\cap C\) / Whole \(A\cap B\cap C\)
C पूरा \(A\cup B\) / Whole \(A\cup B\)
D (A) का केवल भाग / Only part of (A)
Explanation opens after your attempt
Correct Answer
A. (C) का वह भाग जो (A) और (B) दोनों से बाहर है / The part of (C) outside both (A) and (B)
Step 1
Concept
(\(A\cup B\)') is outside (A) and (B), and intersecting with (C) gives the part of (C) outside both.
Step 2
Why this answer is correct
The correct answer is A. (C) का वह भाग जो (A) और (B) दोनों से बाहर है / The part of (C) outside both (A) and (B). (\(A\cup B\)') is outside (A) and (B), and intersecting with (C) gives the part of (C) outside both.
Step 3
Exam Tip
(\(A\cup B\)') (A) और (B) के बाहर का भाग है, और (C) से प्रतिच्छेद लेने पर केवल (C) वाला बाहरी भाग मिलता है।
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वेन आरेख में (A-\(B\cup C\)) किसके बराबर है?
In a Venn diagram, (A-\(B\cup C\)) is equal to what?
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#venn-diagrams
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#identity
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A \(A\cap B'\cap C'\)
B \(A\cap B\cap C\)
C (A'\cap\(B\cup C\))
D \(B\cap C\)
Explanation opens after your attempt
Correct Answer
A. \(A\cap B'\cap C'\)
Step 1
Concept
(A-\(B\cup C\)) means being in (A) while outside (B) and (C). Therefore it is \(A\cap B'\cap C'\).
Step 2
Why this answer is correct
The correct answer is A. \(A\cap B'\cap C'\). (A-\(B\cup C\)) means being in (A) while outside (B) and (C). Therefore it is \(A\cap B'\cap C'\).
Step 3
Exam Tip
(A-\(B\cup C\)) का अर्थ (A) में रहकर (B) और (C) से बाहर होना है। इसलिए यह \(A\cap B'\cap C'\) है।
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यदि \(A\subseteq B\), तो \(B'\subseteq A'\) कथन वेन आरेख के अनुसार कैसा है?
If \(A\subseteq B\), how is the statement \(B'\subseteq A'\) according to the Venn diagram?
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#complement
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A सही / True
B गलत / False
C केवल जब (A=B) / Only when (A=B)
D केवल जब \(A=\varnothing\) / Only when \(A=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. सही / True
Step 1
Concept
If (A) is inside (B), every element outside (B) is also outside (A). Hence \(B'\subseteq A'\) is true.
Step 2
Why this answer is correct
The correct answer is A. सही / True. If (A) is inside (B), every element outside (B) is also outside (A). Hence \(B'\subseteq A'\) is true.
Step 3
Exam Tip
यदि (A) (B) के अंदर है, तो (B) के बाहर का हर तत्व (A) के बाहर भी होगा। इसलिए \(B'\subseteq A'\) सही है।
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यदि \(A\cap B=A\) और \(B\cap C=B\) है, तो \(A\cap C\) किसके बराबर होगा?
If \(A\cap B=A\) and \(B\cap C=B\), then what is \(A\cap C\) equal to?
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#venn-diagrams
#nested-sets
#reasoning
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A (A)
B (B)
C (C)
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
First \(A\subseteq B\) and \(B\subseteq C\), so \(A\subseteq C\). Therefore, \(A\cap C=A\).
Step 2
Why this answer is correct
The correct answer is A. (A). First \(A\subseteq B\) and \(B\subseteq C\), so \(A\subseteq C\). Therefore, \(A\cap C=A\).
Step 3
Exam Tip
पहले \(A\subseteq B\) और \(B\subseteq C\) मिलता है, इसलिए \(A\subseteq C\)। अतः \(A\cap C=A\) है।
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यदि \(A\cap B=\varnothing\), तो (\(A\cup B\)-A) किसके बराबर है?
If \(A\cap B=\varnothing\), then (\(A\cup B\)-A) is equal to what?
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#venn-diagrams
#disjoint
#difference
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A (B)
B (A)
C \(\varnothing\)
D \(A\cap B\)
Explanation opens after your attempt
Step 1
Concept
When the sets are disjoint, removing (A) from \(A\cup B\) leaves the whole of (B). Hence the answer is (B).
Step 2
Why this answer is correct
The correct answer is A. (B). When the sets are disjoint, removing (A) from \(A\cup B\) leaves the whole of (B). Hence the answer is (B).
Step 3
Exam Tip
असंबद्ध होने पर \(A\cup B\) से (A) हटाने पर पूरा (B) बचता है। इसलिए उत्तर (B) है।
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यदि (n\(A\cup B\)=n(B)), तो वेन आरेख के अनुसार कौन सा संबंध सही है?
If (n\(A\cup B\)=n(B)), which relation is correct according to the Venn diagram?
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#venn-diagrams
#subset
#union
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A \(A\subseteq B\)
B \(B\subseteq A\)
C \(A\cap B=\varnothing\)
D (A=B')
Explanation opens after your attempt
Correct Answer
A. \(A\subseteq B\)
Step 1
Concept
The union is the same as (B), so (A) adds no new region. This means \(A\subseteq B\).
Step 2
Why this answer is correct
The correct answer is A. \(A\subseteq B\). The union is the same as (B), so (A) adds no new region. This means \(A\subseteq B\).
Step 3
Exam Tip
संघ (B) जितना ही है, इसलिए (A) कोई नया क्षेत्र नहीं जोड़ता। इसका अर्थ \(A\subseteq B\) है।
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यदि (n\(A\cap B\)=0), (n(A)=39) और (n(B)=48) है, तो (n\(A\triangle B\)) कितना है?
If (n\(A\cap B\)=0), (n(A)=39) and (n(B)=48), then what is (n\(A\triangle B\))?
#sets
#venn-diagrams
#symmetric-difference
#disjoint
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A (87)
B (48)
C (39)
D (9)
Explanation opens after your attempt
Step 1
Concept
The intersection is zero, so the symmetric difference is the whole union (39+48=87). For disjoint sets, no common part needs removal.
Step 2
Why this answer is correct
The correct answer is A. (87). The intersection is zero, so the symmetric difference is the whole union (39+48=87). For disjoint sets, no common part needs removal.
Step 3
Exam Tip
प्रतिच्छेद शून्य है, इसलिए सममित अंतर पूरा संघ (39+48=87) है। असंबद्ध समुच्चयों में कोई साझा भाग हटाना नहीं पड़ता।
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किसी पुस्तकालय में (150) विद्यार्थियों में (83) उपन्यास पढ़ते हैं, (69) कविता पढ़ते हैं और (28) कोई भी नहीं पढ़ते। दोनों पढ़ने वाले कितने हैं?
In a library, among (150) students, (83) read novels, (69) read poetry and (28) read neither. How many read both?
#sets
#venn-diagrams
#survey
#intersection
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A (30)
B (122)
C (14)
D (41)
Explanation opens after your attempt
Step 1
Concept
At least one is (150-28=122), so both is (83+69-122=30). First get the union from the outside part.
Step 2
Why this answer is correct
The correct answer is A. (30). At least one is (150-28=122), so both is (83+69-122=30). First get the union from the outside part.
Step 3
Exam Tip
कम से कम एक (150-28=122) है, इसलिए दोनों (83+69-122=30) हैं। पहले संघ को बाहर वाले भाग से निकालें।
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एक परीक्षा में (180) विद्यार्थियों में (97) ने प्रश्न (A), (88) ने प्रश्न (B), (82) ने प्रश्न (C), (41) ने (A) और (B), (36) ने (B) और (C), (34) ने (C) और (A), तथा (18) ने तीनों हल किए। कम से कम एक प्रश्न हल करने वाले कितने हैं?
In an exam, among (180) students, (97) solved question (A), (88) solved question (B), (82) solved question (C), (41) solved (A) and (B), (36) solved (B) and (C), (34) solved (C) and (A), and (18) solved all three. How many solved at least one question?
#sets
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#three-sets
#exam-survey
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A (174)
B (156)
C (180)
D (168)
Explanation opens after your attempt
Step 1
Concept
At least one is (97+88+82-41-36-34+18=174). In three sets, the centre must be added at the end.
Step 2
Why this answer is correct
The correct answer is A. (174). At least one is (97+88+82-41-36-34+18=174). In three sets, the centre must be added at the end.
Step 3
Exam Tip
कम से कम एक (97+88+82-41-36-34+18=174) है। तीन समुच्चयों में केंद्र को अंत में जोड़ना जरूरी है।
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यदि केवल \(A\cap B\) में (19), केवल \(B\cap C\) में (17), केवल \(C\cap A\) में (21) और \(A\cap B\cap C\) में (11) तत्व हैं, तो कम से कम दो समुच्चयों में आने वाले तत्व कितने हैं?
If only \(A\cap B\) has (19), only \(B\cap C\) has (17), only \(C\cap A\) has (21), and \(A\cap B\cap C\) has (11) elements, then how many elements are in at least two sets?
#sets
#venn-diagrams
#at-least-two
#pairwise-regions
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A (68)
B (57)
C (79)
D (49)
Explanation opens after your attempt
Step 1
Concept
At least two includes the pairwise-only regions and the centre, so (19+17+21+11=68). Count the centre once.
Step 2
Why this answer is correct
The correct answer is A. (68). At least two includes the pairwise-only regions and the centre, so (19+17+21+11=68). Count the centre once.
Step 3
Exam Tip
कम से कम दो में केवल दो-दो वाले भाग और केंद्र शामिल हैं, इसलिए (19+17+21+11=68) है। केंद्र को एक बार गिनें।
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यदि केवल (A) में (38), केवल (B) में (35), केवल (C) में (29), ठीक दो समुच्चयों में कुल (47) और तीनों में (14) तत्व हैं, तो (n\(A\cup B\cup C\)) कितना है?
If only (A) has (38), only (B) has (35), only (C) has (29), exactly two sets have total (47), and all three have (14) elements, then what is (n\(A\cup B\cup C\))?
#sets
#venn-diagrams
#regions
#union
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A (163)
B (149)
C (116)
D (177)
Explanation opens after your attempt
Step 1
Concept
The union is the sum of all disjoint regions (38+35+29+47+14=163). Do not add separate Venn regions twice.
Step 2
Why this answer is correct
The correct answer is A. (163). The union is the sum of all disjoint regions (38+35+29+47+14=163). Do not add separate Venn regions twice.
Step 3
Exam Tip
संघ सभी अलग क्षेत्रों का योग (38+35+29+47+14=163) है। अलग वेन क्षेत्रों को दोबारा न जोड़ें।
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यदि (n(A)=82), (n(B)=77), (n(C)=69), (n\(A\cup B\cup C\)=151), (n\(A\cap B\)=32), (n\(B\cap C\)=28), (n\(C\cap A\)=25) है, तो (n\(A\cap B\cap C\)) कितना है?
If (n(A)=82), (n(B)=77), (n(C)=69), (n\(A\cup B\cup C\)=151), (n\(A\cap B\)=32), (n\(B\cap C\)=28), (n\(C\cap A\)=25), then what is (n\(A\cap B\cap C\))?
#sets
#venn-diagrams
#unknown-triple
#equation
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A (8)
B (12)
C (15)
D (20)
Explanation opens after your attempt
Step 1
Concept
Using (151=82+77+69-32-28-25+x), we get (x=8). Let the unknown centre be (x) and form an equation.
Step 2
Why this answer is correct
The correct answer is A. (8). Using (151=82+77+69-32-28-25+x), we get (x=8). Let the unknown centre be (x) and form an equation.
Step 3
Exam Tip
सूत्र में (151=82+77+69-32-28-25+x), इसलिए (x=8) है। अज्ञात केंद्र को (x) मानकर समीकरण बनाएं।
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यदि (n(A\cap\(B\cup C\))=52), केवल \(A\cap B\) में (23) और केवल \(A\cap C\) में (18) तत्व हैं, तो (n\(A\cap B\cap C\)) कितना है?
If (n(A\cap\(B\cup C\))=52), only \(A\cap B\) has (23) and only \(A\cap C\) has (18) elements, then what is (n\(A\cap B\cap C\))?
#sets
#venn-diagrams
#compound-region
#triple-intersection
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A (11)
B (41)
C (52)
D (7)
Explanation opens after your attempt
Step 1
Concept
(A\cap\(B\cup C\)) includes only \(A\cap B\), only \(A\cap C\), and the centre, so the centre is (52-23-18=11).
Step 2
Why this answer is correct
The correct answer is A. (11). (A\cap\(B\cup C\)) includes only \(A\cap B\), only \(A\cap C\), and the centre, so the centre is (52-23-18=11).
Step 3
Exam Tip
(A\cap\(B\cup C\)) में केवल \(A\cap B\), केवल \(A\cap C\) और केंद्र आते हैं, इसलिए केंद्र (52-23-18=11) है।
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यदि (A), (B) और (C) परस्पर असंबद्ध हैं, (n(A)=27), (n(B)=34), (n(C)=41) और (n(U)=125) है, तो (n(\(A\cup B\cup C\)')) कितना है?
If (A), (B) and (C) are mutually disjoint, (n(A)=27), (n(B)=34), (n(C)=41) and (n(U)=125), then what is (n(\(A\cup B\cup C\)'))?
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#mutually-disjoint
#complement
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A (23)
B (102)
C (64)
D (84)
Explanation opens after your attempt
Step 1
Concept
For mutually disjoint sets, the union is (27+34+41=102), so the complement is (125-102=23). No common part needs to be subtracted.
Step 2
Why this answer is correct
The correct answer is A. (23). For mutually disjoint sets, the union is (27+34+41=102), so the complement is (125-102=23). No common part needs to be subtracted.
Step 3
Exam Tip
परस्पर असंबद्ध होने पर संघ (27+34+41=102) है, इसलिए पूरक (125-102=23) है। साझा भाग घटाने की जरूरत नहीं होती।
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यदि \(A\subseteq B\subseteq C\subseteq U\) है, तो (\(A\cup B\cup C\)') किसके बराबर होगा?
If \(A\subseteq B\subseteq C\subseteq U\), then (\(A\cup B\cup C\)') is equal to what?
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#venn-diagrams
#nested-sets
#complement
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A (C')
B (A')
C (B')
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
In the chain, the union is the largest set (C), so its complement is (C'). Simplify the union first.
Step 2
Why this answer is correct
The correct answer is A. (C'). In the chain, the union is the largest set (C), so its complement is (C'). Simplify the union first.
Step 3
Exam Tip
श्रृंखला में संघ सबसे बड़ा समुच्चय (C) है, इसलिए उसका पूरक (C') होगा। पहले संघ को सरल करें।
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यदि (n(A-B)=0), (n(B-C)=0) और (n(A)>0) है, तो कौन सा संबंध अवश्य सही है?
If (n(A-B)=0), (n(B-C)=0) and (n(A)>0), which relation must be true?
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#venn-diagrams
#subset
#reasoning
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A \(A\subseteq C\)
B \(C\subseteq A\)
C \(A\cap C=\varnothing\)
D \(B\cap C=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(A\subseteq C\)
Step 1
Concept
(A-B=0) gives \(A\subseteq B\), and (B-C=0) gives \(B\subseteq C\). Therefore, \(A\subseteq C\) must be true.
Step 2
Why this answer is correct
The correct answer is A. \(A\subseteq C\). (A-B=0) gives \(A\subseteq B\), and (B-C=0) gives \(B\subseteq C\). Therefore, \(A\subseteq C\) must be true.
Step 3
Exam Tip
(A-B=0) से \(A\subseteq B\) और (B-C=0) से \(B\subseteq C\) मिलता है। इसलिए \(A\subseteq C\) अवश्य सही है।
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यदि (n\(A\cup B\cup C\)=184), (n(A)=86), (n(B)=91), (n(C)=88) और (n\(A\cap B\cap C\)=23) है, तो (n\(A\cap B\)+n\(B\cap C\)+n\(C\cap A\)) कितना है?
If (n\(A\cup B\cup C\)=184), (n(A)=86), (n(B)=91), (n(C)=88) and (n\(A\cap B\cap C\)=23), then what is (n\(A\cap B\)+n\(B\cap C\)+n\(C\cap A\))?
#sets
#venn-diagrams
#pairwise-sum
#inclusion-exclusion
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A (104)
B (81)
C (127)
D (265)
Explanation opens after your attempt
Step 1
Concept
Using the formula (184=86+91+88-S+23), so (S=104). Here (S) is the sum of the three pairwise intersections.
Step 2
Why this answer is correct
The correct answer is A. (104). Using the formula (184=86+91+88-S+23), so (S=104). Here (S) is the sum of the three pairwise intersections.
Step 3
Exam Tip
सूत्र से (184=86+91+88-S+23), इसलिए (S=104) है। यहाँ (S) तीनों युग्म प्रतिच्छेदों का योग है।
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यदि (n(A-B)=24), (n(B-C)=27) और (n(C-A)=22) ही दिए गए हैं, तो क्या केवल इनसे (n\(A\cup B\cup C\)) निश्चित किया जा सकता है?
If only (n(A-B)=24), (n(B-C)=27) and (n(C-A)=22) are given, can (n\(A\cup B\cup C\)) be determined uniquely?
#sets
#venn-diagrams
#insufficient-data
#reasoning
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A नहीं, साझा क्षेत्रों की जानकारी चाहिए / No, information about common regions is needed
B हाँ, मान (73) है / Yes, the value is (73)
C हाँ, मान (0) है / Yes, the value is (0)
D हाँ, मान (24) है / Yes, the value is (24)
Explanation opens after your attempt
Correct Answer
A. नहीं, साझा क्षेत्रों की जानकारी चाहिए / No, information about common regions is needed
Step 1
Concept
These differences do not determine all Venn regions. To find the union, information about both only-regions and common regions is needed.
Step 2
Why this answer is correct
The correct answer is A. नहीं, साझा क्षेत्रों की जानकारी चाहिए / No, information about common regions is needed. These differences do not determine all Venn regions. To find the union, information about both only-regions and common regions is needed.
Step 3
Exam Tip
इन अंतरों से सभी वेन क्षेत्र नहीं मिलते। संघ निकालने के लिए केवल और साझा दोनों क्षेत्रों की जानकारी चाहिए।
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अभिकथन: (\(A\cup B\)'=A'\cap B')। कारण: \(A\cup B\) से बाहर रहने के लिए तत्व को (A) और (B) दोनों से बाहर होना चाहिए। सही विकल्प चुनें।
Assertion: (\(A\cup B\)'=A'\cap B'). Reason: To be outside \(A\cup B\), an element must be outside both (A) and (B). Choose the correct option.
#sets
#venn-diagrams
#assertion-reason
#de-morgan
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A अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या है / Both assertion and reason are true, and the reason is the correct explanation
B अभिकथन सही है पर कारण गलत है / Assertion is true but reason is false
C अभिकथन गलत है पर कारण सही है / Assertion is false but reason is true
D दोनों गलत हैं / Both are false
Explanation opens after your attempt
Correct Answer
A. अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या है / Both assertion and reason are true, and the reason is the correct explanation
Step 1
Concept
This is De Morgan's law, and the reason correctly explains its Venn meaning. In complement questions, focus on the outside region.
Step 2
Why this answer is correct
The correct answer is A. अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या है / Both assertion and reason are true, and the reason is the correct explanation. This is De Morgan's law, and the reason correctly explains its Venn meaning. In complement questions, focus on the outside region.
Step 3
Exam Tip
यह डी मॉर्गन नियम है और कारण उसके वेन आरेखीय अर्थ को सही बताता है। पूरक वाले प्रश्नों में बाहर वाले क्षेत्र पर ध्यान दें।
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अभिकथन: यदि \(A\subseteq B\), तो \(A\cap B=A\)। कारण: (A) का हर तत्व (B) में भी होता है। सही विकल्प चुनें।
Assertion: If \(A\subseteq B\), then \(A\cap B=A\). Reason: Every element of (A) is also in (B). Choose the correct option.
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#assertion-reason
#subset
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A अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या है / Both assertion and reason are true, and the reason is the correct explanation
B अभिकथन सही है पर कारण गलत है / Assertion is true but reason is false
C अभिकथन गलत है पर कारण सही है / Assertion is false but reason is true
D दोनों गलत हैं / Both are false
Explanation opens after your attempt
Correct Answer
A. अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या है / Both assertion and reason are true, and the reason is the correct explanation
Step 1
Concept
Both are true because (A) lies completely inside (B). In a subset relation, the smaller set gives the intersection.
Step 2
Why this answer is correct
The correct answer is A. अभिकथन और कारण दोनों सही हैं और कारण सही व्याख्या है / Both assertion and reason are true, and the reason is the correct explanation. Both are true because (A) lies completely inside (B). In a subset relation, the smaller set gives the intersection.
Step 3
Exam Tip
दोनों सही हैं क्योंकि (A) पूरा (B) के भीतर है। उपसमुच्चय में छोटा समुच्चय प्रतिच्छेद देता है।
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किसी वेन आरेख में (n\(A\cup B\cup C\)=215), (n(\(A\cup B\cup C\)')=35), और ठीक दो समुच्चयों में (62) तत्व हैं। यदि (n(U)) पूछा जाए, तो उत्तर क्या होगा?
In a Venn diagram, (n\(A\cup B\cup C\)=215), (n(\(A\cup B\cup C\)')=35), and exactly two sets have (62) elements. If (n(U)) is asked, what is the answer?
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#venn-diagrams
#universal-set
#extra-data
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A (250)
B (215)
C (277)
D (180)
Explanation opens after your attempt
Step 1
Concept
The universal set is the sum of the union and outside region, so (215+35=250). The exactly-two data is extra in this question.
Step 2
Why this answer is correct
The correct answer is A. (250). The universal set is the sum of the union and outside region, so (215+35=250). The exactly-two data is extra in this question.
Step 3
Exam Tip
सार्वत्रिक समुच्चय संघ और बाहरी भाग का योग है, इसलिए (215+35=250) है। ठीक दो वाला आंकड़ा इस प्रश्न में अतिरिक्त है।
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