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

Question 1/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

वेन आरेख में (U) के अंदर लेकिन (A) के बाहर का क्षेत्र किससे दर्शाया जाता है?

In a Venn diagram, which region is inside (U) but outside (A)?

Explanation opens after your attempt

Correct Answer

B. (A')

Step 1

Concept

(A') contains the elements of (U) that are not in (A). Always take (U) as the base while finding complement.

Step 2

Why this answer is correct

The correct answer is B. (A'). (A') contains the elements of (U) that are not in (A). Always take (U) as the base while finding complement.

Step 3

Exam Tip

(A') में (U) के वे अवयव होते हैं जो (A) में नहीं होते। पूरक निकालते समय हमेशा (U) को आधार मानें।

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Question 2/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=36), (n(B)=28), और (n\(A\cap B\)=12), तो (n\(A\cup B\)) क्या है?

If (n(A)=36), (n(B)=28), and (n\(A\cap B\)=12), what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (52)

Step 1

Concept

Using (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)), we get (36+28-12=52). Subtract the common part once.

Step 2

Why this answer is correct

The correct answer is A. (52). Using (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)), we get (36+28-12=52). Subtract the common part once.

Step 3

Exam Tip

सूत्र (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)) से (36+28-12=52) मिलता है। साझा भाग को एक बार घटाएं।

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Question 3/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

वेन आरेख में \(A\cup B\) को छायांकित करने पर कौन सा भाग छूटता है?

When \(A\cup B\) is shaded in a Venn diagram, which part is left unshaded?

Explanation opens after your attempt

Correct Answer

D. (\(A\cup B\)')

Step 1

Concept

\(A\cup B\) includes the whole of both circles. The part left is outside both, that is (\(A\cup B\)').

Step 2

Why this answer is correct

The correct answer is D. (\(A\cup B\)'). \(A\cup B\) includes the whole of both circles. The part left is outside both, that is (\(A\cup B\)').

Step 3

Exam Tip

\(A\cup B\) में दोनों वृत्तों का पूरा भाग आता है। जो भाग छूटता है वह दोनों से बाहर यानी (\(A\cup B\)') है।

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Question 4/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(U)=92) और (n\(A\cup B\)=67), तो वेन आरेख में न (A) न (B) वाले क्षेत्र में कितने अवयव होंगे?

If (n(U)=92) and (n\(A\cup B\)=67), how many elements will be in the region neither in (A) nor in (B) in the Venn diagram?

Explanation opens after your attempt

Correct Answer

A. (25)

Step 1

Concept

The region neither in (A) nor in (B) is (\(A\cup B\)'). Therefore the number is (92-67=25).

Step 2

Why this answer is correct

The correct answer is A. (25). The region neither in (A) nor in (B) is (\(A\cup B\)'). Therefore the number is (92-67=25).

Step 3

Exam Tip

न (A) न (B) वाला क्षेत्र (\(A\cup B\)') है। इसलिए संख्या (92-67=25) होगी।

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Question 5/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (A) और (B) के वेन आरेख में केवल बीच वाला भाग छायांकित है, तो वह कौन सा समुच्चय है?

If only the middle common part is shaded in the Venn diagram of (A) and (B), which set is it?

Explanation opens after your attempt

Correct Answer

C. \(A\cap B\)

Step 1

Concept

The middle common part is called \(A\cap B\). Intersection contains only elements common to both sets.

Step 2

Why this answer is correct

The correct answer is C. \(A\cap B\). The middle common part is called \(A\cap B\). Intersection contains only elements common to both sets.

Step 3

Exam Tip

बीच का साझा भाग \(A\cap B\) कहलाता है। प्रतिच्छेद में केवल दोनों में आने वाले अवयव होते हैं।

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Question 6/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(A=\{1,3,5,7,9\}\) और \(B=\{5,7,11\}\), तो केवल (A) वाला क्षेत्र क्या है?

If \(A=\{1,3,5,7,9\}\) and \(B=\{5,7,11\}\), what is the only (A) region?

Explanation opens after your attempt

Correct Answer

A. ({1,3,9})

Step 1

Concept

For only (A), find (A-B). After removing (5) and (7), ({1,3,9}) remains.

Step 2

Why this answer is correct

The correct answer is A. ({1,3,9}). For only (A), find (A-B). After removing (5) and (7), ({1,3,9}) remains.

Step 3

Exam Tip

केवल (A) के लिए (A-B) निकालते हैं। (5) और (7) हटाने पर ({1,3,9}) बचता है।

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Question 7/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि केवल (A) वाला क्षेत्र छायांकित है, तो उसे किस रूप में लिखा जा सकता है?

If only the (A) region is shaded, how can it be written?

Explanation opens after your attempt

Correct Answer

B. \(A\cap B'\)

Step 1

Concept

Only (A) means being in (A) and not in (B). Therefore, it is \(A\cap B'\).

Step 2

Why this answer is correct

The correct answer is B. \(A\cap B'\). Only (A) means being in (A) and not in (B). Therefore, it is \(A\cap B'\).

Step 3

Exam Tip

केवल (A) का अर्थ (A) में होना और (B) में न होना है। इसलिए यह \(A\cap B'\) है।

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Question 8/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=44) और (n\(A\cap B\)=18), तो केवल (A) में कितने अवयव होंगे?

If (n(A)=44) and (n\(A\cap B\)=18), how many elements will be only in (A)?

Explanation opens after your attempt

Correct Answer

B. (26)

Step 1

Concept

The number only in (A) is (44-18=26). Subtract the common part from total (A).

Step 2

Why this answer is correct

The correct answer is B. (26). The number only in (A) is (44-18=26). Subtract the common part from total (A).

Step 3

Exam Tip

केवल (A) की संख्या (44-18=26) है। कुल (A) से साझा भाग घटाएं।

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Question 9/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि केवल (B) वाला क्षेत्र छायांकित है, तो उसे किस रूप में लिखा जा सकता है?

If only the (B) region is shaded, how can it be written?

Explanation opens after your attempt

Correct Answer

C. \(A'\cap B\)

Step 1

Concept

Only (B) means being in (B) and not in (A). Therefore, it is \(A'\cap B\).

Step 2

Why this answer is correct

The correct answer is C. \(A'\cap B\). Only (B) means being in (B) and not in (A). Therefore, it is \(A'\cap B\).

Step 3

Exam Tip

केवल (B) का अर्थ (B) में होना और (A) में न होना है। इसलिए यह \(A'\cap B\) है।

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Question 10/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(U=\{a,b,c,d,e,f,h\}\), \(A=\{a,c,e\}\), और \(B=\{c,d,f\}\), तो (\(A\cup B\)') क्या है?

If \(U=\{a,b,c,d,e,f,h\}\), \(A=\{a,c,e\}\), and \(B=\{c,d,f\}\), what is (\(A\cup B\)')?

Explanation opens after your attempt

Correct Answer

A. ({b,h})

Step 1

Concept

\(A\cup B={a,c,d,e,f}\), so (\(A\cup B\)'={b,h}). First find the union and then take the complement.

Step 2

Why this answer is correct

The correct answer is A. ({b,h}). \(A\cup B={a,c,d,e,f}\), so (\(A\cup B\)'={b,h}). First find the union and then take the complement.

Step 3

Exam Tip

\(A\cup B={a,c,d,e,f}\), इसलिए (\(A\cup B\)'={b,h})। पहले संघ निकालें फिर पूरक लें।

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Question 11/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=31), (n(B)=22), और (n\(A\cap B\)=9), तो (n\(A\cup B\)) क्या है?

If (n(A)=31), (n(B)=22), and (n\(A\cap B\)=9), what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (44)

Step 1

Concept

(n\(A\cup B\)=31+22-9=44). The common part is subtracted once to avoid double counting.

Step 2

Why this answer is correct

The correct answer is A. (44). (n\(A\cup B\)=31+22-9=44). The common part is subtracted once to avoid double counting.

Step 3

Exam Tip

(n\(A\cup B\)=31+22-9=44)। साझा भाग को दो बार गिनने से बचाने के लिए एक बार घटाते हैं।

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Question 12/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n\(A\cup B\)=81), केवल (A) (29), और केवल (B) (34) है, तो (n\(A\cap B\)) क्या है?

If (n\(A\cup B\)=81), only (A) is (29), and only (B) is (34), what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (18)

Step 1

Concept

The union contains only (A), the common part, and only (B). Therefore the common part is (81-29-34=18).

Step 2

Why this answer is correct

The correct answer is A. (18). The union contains only (A), the common part, and only (B). Therefore the common part is (81-29-34=18).

Step 3

Exam Tip

संघ में केवल (A), साझा भाग और केवल (B) आते हैं। इसलिए साझा भाग (81-29-34=18) है।

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

यदि (n(A)=28), (n(B)=19), और (n\(A\cup B\)=39), तो (n\(A\cap B\)) क्या है?

If (n(A)=28), (n(B)=19), and (n\(A\cup B\)=39), what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

B. (8)

Step 1

Concept

(n\(A\cap B\)=28+19-39=8). When union is given, add both sets and subtract the union.

Step 2

Why this answer is correct

The correct answer is B. (8). (n\(A\cap B\)=28+19-39=8). When union is given, add both sets and subtract the union.

Step 3

Exam Tip

(n\(A\cap B\)=28+19-39=8)। संघ दिए होने पर दोनों समुच्चयों का योग लेकर संघ घटाएं।

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

यदि (n(U)=72) और (n(A)=29), तो (n(A')) क्या होगा?

If (n(U)=72) and (n(A)=29), what will (n(A')) be?

Explanation opens after your attempt

Correct Answer

B. (43)

Step 1

Concept

(n(A')=72-29=43). (A') is the region inside (U) and outside (A).

Step 2

Why this answer is correct

The correct answer is B. (43). (n(A')=72-29=43). (A') is the region inside (U) and outside (A).

Step 3

Exam Tip

(n(A')=72-29=43)। (A') (U) के अंदर (A) से बाहर का क्षेत्र है।

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Question 15/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(U)=85) और (n\(A\cup B\)=56), तो न (A) न (B) में कितने अवयव हैं?

If (n(U)=85) and (n\(A\cup B\)=56), how many elements are in neither (A) nor (B)?

Explanation opens after your attempt

Correct Answer

A. (29)

Step 1

Concept

The number in neither (A) nor (B) is (85-56=29). It is outside both circles but inside (U).

Step 2

Why this answer is correct

The correct answer is A. (29). The number in neither (A) nor (B) is (85-56=29). It is outside both circles but inside (U).

Step 3

Exam Tip

न (A) न (B) की संख्या (85-56=29) है। यह दोनों वृत्तों के बाहर लेकिन (U) के अंदर का क्षेत्र है।

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Question 16/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=35) और (n\(A\cap B\)=12), तो केवल (A) में कितने अवयव होंगे?

If (n(A)=35) and (n\(A\cap B\)=12), how many elements will be only in (A)?

Explanation opens after your attempt

Correct Answer

B. (23)

Step 1

Concept

The number only in (A) is (35-12=23). Subtract the common part from total (A).

Step 2

Why this answer is correct

The correct answer is B. (23). The number only in (A) is (35-12=23). Subtract the common part from total (A).

Step 3

Exam Tip

केवल (A) की संख्या (35-12=23) है। कुल (A) से साझा भाग घटाएं।

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Question 17/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(B)=41) और (n\(A\cap B\)=17), तो केवल (B) में कितने अवयव होंगे?

If (n(B)=41) and (n\(A\cap B\)=17), how many elements will be only in (B)?

Explanation opens after your attempt

Correct Answer

B. (24)

Step 1

Concept

The number only in (B) is (41-17=24). Remove the middle common part from circle (B).

Step 2

Why this answer is correct

The correct answer is B. (24). The number only in (B) is (41-17=24). Remove the middle common part from circle (B).

Step 3

Exam Tip

केवल (B) की संख्या (41-17=24) है। (B) वृत्त के बीच वाले भाग को हटाएं।

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Question 18/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि केवल (A) में (18), \(A\cap B\) में (7), और केवल (B) में (14) अवयव हैं, तो (n\(A\cup B\)) क्या है?

If only (A) has (18), \(A\cap B\) has (7), and only (B) has (14) elements, what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

C. (39)

Step 1

Concept

The union includes all three regions, so (18+7+14=39). In a Venn diagram, add each region once.

Step 2

Why this answer is correct

The correct answer is C. (39). The union includes all three regions, so (18+7+14=39). In a Venn diagram, add each region once.

Step 3

Exam Tip

संघ में तीनों क्षेत्र आते हैं, इसलिए (18+7+14=39)। वेन आरेख में हर क्षेत्र को एक बार जोड़ें।

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Question 19/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A-B)=16) और (n\(A\cap B\)=11), तो (n(A)) क्या है?

If (n(A-B)=16) and (n\(A\cap B\)=11), what is (n(A))?

Explanation opens after your attempt

Correct Answer

C. (27)

Step 1

Concept

Set (A) contains both only (A) and the common part. Therefore, (n(A)=16+11=27).

Step 2

Why this answer is correct

The correct answer is C. (27). Set (A) contains both only (A) and the common part. Therefore, (n(A)=16+11=27).

Step 3

Exam Tip

(A) में केवल (A) और साझा भाग दोनों आते हैं। इसलिए (n(A)=16+11=27)।

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Question 20/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(B-A)=21) और (n\(A\cap B\)=13), तो (n(B)) क्या है?

If (n(B-A)=21) and (n\(A\cap B\)=13), what is (n(B))?

Explanation opens after your attempt

Correct Answer

C. (34)

Step 1

Concept

Set (B) contains both only (B) and the common part. Therefore, (n(B)=21+13=34).

Step 2

Why this answer is correct

The correct answer is C. (34). Set (B) contains both only (B) and the common part. Therefore, (n(B)=21+13=34).

Step 3

Exam Tip

(B) में केवल (B) और साझा भाग दोनों होते हैं। इसलिए (n(B)=21+13=34)।

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Question 21/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(U)=94), केवल (A) में (26), \(A\cap B\) में (15), और केवल (B) में (31) हैं, तो बाहर का क्षेत्र कितना है?

If (n(U)=94), only (A) has (26), \(A\cap B\) has (15), and only (B) has (31), what is the outside region?

Explanation opens after your attempt

Correct Answer

A. (22)

Step 1

Concept

The known circular regions are (26+15+31=72). The outside region is (94-72=22).

Step 2

Why this answer is correct

The correct answer is A. (22). The known circular regions are (26+15+31=72). The outside region is (94-72=22).

Step 3

Exam Tip

ज्ञात वृत्तीय क्षेत्र (26+15+31=72) हैं। बाहर का क्षेत्र (94-72=22) है।

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Question 22/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(U)=76), बाहर का क्षेत्र (18), केवल (A) (20), और केवल (B) (23) है, तो (n\(A\cap B\)) क्या है?

If (n(U)=76), the outside region is (18), only (A) is (20), and only (B) is (23), what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (15)

Step 1

Concept

The common part is (76-18-20-23=15). For an unknown region, subtract known regions from the total.

Step 2

Why this answer is correct

The correct answer is A. (15). The common part is (76-18-20-23=15). For an unknown region, subtract known regions from the total.

Step 3

Exam Tip

साझा भाग (76-18-20-23=15) है। अज्ञात क्षेत्र के लिए कुल से ज्ञात क्षेत्र घटाएं।

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Question 23/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n\(A\cup B\)=63), केवल (A) (24), और केवल (B) (27) है, तो (n\(A\cap B\)) क्या है?

If (n\(A\cup B\)=63), only (A) is (24), and only (B) is (27), what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (12)

Step 1

Concept

The union contains only (A), the common part, and only (B). Therefore, the common part is (63-24-27=12).

Step 2

Why this answer is correct

The correct answer is A. (12). The union contains only (A), the common part, and only (B). Therefore, the common part is (63-24-27=12).

Step 3

Exam Tip

संघ में केवल (A), साझा भाग और केवल (B) आते हैं। इसलिए साझा भाग (63-24-27=12) है।

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Question 24/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(A=\{2,3,5,7,11\}\) और \(B=\{1,3,5,9\}\), तो \(A\cap B\) क्या है?

If \(A=\{2,3,5,7,11\}\) and \(B=\{1,3,5,9\}\), what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ({3,5})

Step 1

Concept

The common elements in both sets are (3) and (5). Therefore, \(A\cap B={3,5}\).

Step 2

Why this answer is correct

The correct answer is A. ({3,5}). The common elements in both sets are (3) and (5). Therefore, \(A\cap B={3,5}\).

Step 3

Exam Tip

दोनों समुच्चयों में (3) और (5) समान हैं। इसलिए \(A\cap B={3,5}\)।

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Question 25/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(A=\{4,6,8,10\}\) और \(B=\{6,10,12\}\), तो केवल (A) वाला भाग क्या है?

If \(A=\{4,6,8,10\}\) and \(B=\{6,10,12\}\), what is the only (A) part?

Explanation opens after your attempt

Correct Answer

A. ({4,8})

Step 1

Concept

For only (A), find (A-B). After removing (6) and (10), ({4,8}) remains.

Step 2

Why this answer is correct

The correct answer is A. ({4,8}). For only (A), find (A-B). After removing (6) and (10), ({4,8}) remains.

Step 3

Exam Tip

केवल (A) के लिए (A-B) निकालते हैं। (6) और (10) हटाने पर ({4,8}) बचता है।

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Question 26/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(A=\{p,q,r\}\) और \(B=\{q,r,s,t\}\), तो केवल (B) वाला भाग क्या है?

If \(A=\{p,q,r\}\) and \(B=\{q,r,s,t\}\), what is the only (B) part?

Explanation opens after your attempt

Correct Answer

C. ({s,t})

Step 1

Concept

For only (B), find (B-A). Since (q) and (r) are common, ({s,t}) remains.

Step 2

Why this answer is correct

The correct answer is C. ({s,t}). For only (B), find (B-A). Since (q) and (r) are common, ({s,t}) remains.

Step 3

Exam Tip

केवल (B) के लिए (B-A) निकालते हैं। (q) और (r) साझा हैं, इसलिए ({s,t}) बचता है।

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Question 27/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(U=\{a,b,c,d,e,g\}\), \(A=\{a,c,e\}\), और \(B=\{b,c,g\}\), तो (\(A\cup B\)') क्या है?

If \(U=\{a,b,c,d,e,g\}\), \(A=\{a,c,e\}\), and \(B=\{b,c,g\}\), what is (\(A\cup B\)')?

Explanation opens after your attempt

Correct Answer

A. ({d})

Step 1

Concept

\(A\cup B={a,b,c,e,g}\), so (\(A\cup B\)'={d}). First find the union and then the complement.

Step 2

Why this answer is correct

The correct answer is A. ({d}). \(A\cup B={a,b,c,e,g}\), so (\(A\cup B\)'={d}). First find the union and then the complement.

Step 3

Exam Tip

\(A\cup B={a,b,c,e,g}\), इसलिए (\(A\cup B\)'={d})। पहले संघ फिर पूरक निकालें।

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Question 28/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(A=\{1,2,3,4\}\) और \(B=\{3,4,5,6\}\), तो \(A\cup B\) क्या है?

If \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\), what is \(A\cup B\)?

Explanation opens after your attempt

Correct Answer

D. ({1,2,3,4,5,6})

Step 1

Concept

Union contains all distinct elements of both sets. Therefore, \(A\cup B={1,2,3,4,5,6}\).

Step 2

Why this answer is correct

The correct answer is D. ({1,2,3,4,5,6}). Union contains all distinct elements of both sets. Therefore, \(A\cup B={1,2,3,4,5,6}\).

Step 3

Exam Tip

संघ में दोनों समुच्चयों के सभी अलग-अलग अवयव आते हैं। इसलिए \(A\cup B={1,2,3,4,5,6}\)।

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Question 29/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

एक कक्षा में (65) विद्यार्थी हैं, (34) संस्कृत पढ़ते हैं, (27) कंप्यूटर पढ़ते हैं, और (11) दोनों पढ़ते हैं। कम से कम एक विषय पढ़ने वाले कितने हैं?

In a class of (65) students, (34) study Sanskrit, (27) study Computer, and (11) study both. How many study at least one subject?

Explanation opens after your attempt

Correct Answer

A. (50)

Step 1

Concept

Those who study at least one subject are (34+27-11=50). Students studying both should not be counted twice.

Step 2

Why this answer is correct

The correct answer is A. (50). Those who study at least one subject are (34+27-11=50). Students studying both should not be counted twice.

Step 3

Exam Tip

कम से कम एक विषय पढ़ने वाले (34+27-11=50) हैं। दोनों पढ़ने वालों को दो बार नहीं गिनना चाहिए।

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Question 30/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

एक सर्वे में (90) लोग हैं, (46) रेडियो सुनते हैं, (38) पॉडकास्ट सुनते हैं, और (16) दोनों सुनते हैं। कोई भी नहीं सुनने वाले कितने हैं?

In a survey of (90) people, (46) listen to radio, (38) listen to podcasts, and (16) listen to both. How many listen to neither?

Explanation opens after your attempt

Correct Answer

A. (22)

Step 1

Concept

Those who listen to at least one are (46+38-16=68). Those who listen to neither are (90-68=22).

Step 2

Why this answer is correct

The correct answer is A. (22). Those who listen to at least one are (46+38-16=68). Those who listen to neither are (90-68=22).

Step 3

Exam Tip

कम से कम एक सुनने वाले (46+38-16=68) हैं। कोई भी नहीं सुनने वाले (90-68=22) हैं।

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Question 31/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

एक समूह में (58) लोग हैं, (32) आम पसंद करते हैं, (21) केला पसंद करते हैं, और (9) दोनों पसंद करते हैं। केवल आम पसंद करने वाले कितने हैं?

In a group of (58) people, (32) like mango, (21) like banana, and (9) like both. How many like only mango?

Explanation opens after your attempt

Correct Answer

B. (23)

Step 1

Concept

Those who like only mango are (32-9=23). Subtract those who like both from total mango lovers.

Step 2

Why this answer is correct

The correct answer is B. (23). Those who like only mango are (32-9=23). Subtract those who like both from total mango lovers.

Step 3

Exam Tip

केवल आम पसंद करने वाले (32-9=23) हैं। कुल आम पसंद करने वालों से दोनों पसंद करने वालों को घटाएं।

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Question 32/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

एक क्लब में (74) सदस्य हैं, (29) गायन में हैं, (33) चित्रकला में हैं, और (12) दोनों में हैं। केवल चित्रकला में कितने सदस्य हैं?

In a club of (74) members, (29) are in singing, (33) are in painting, and (12) are in both. How many members are only in painting?

Explanation opens after your attempt

Correct Answer

B. (21)

Step 1

Concept

Only painting has (33-12=21) members. Subtract the common part from the second circle.

Step 2

Why this answer is correct

The correct answer is B. (21). Only painting has (33-12=21) members. Subtract the common part from the second circle.

Step 3

Exam Tip

केवल चित्रकला में (33-12=21) सदस्य हैं। दूसरे वृत्त से साझा भाग घटाएं।

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Question 33/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

एक परीक्षा में (100) विद्यार्थियों में (62) ने गणित पास किया, (49) ने विज्ञान पास किया, और (35) ने दोनों पास किए। केवल विज्ञान पास करने वाले कितने हैं?

In an exam of (100) students, (62) passed Mathematics, (49) passed Science, and (35) passed both. How many passed only Science?

Explanation opens after your attempt

Correct Answer

A. (14)

Step 1

Concept

Those who passed only Science are (49-35=14). Subtract those who passed both from the total of that subject.

Step 2

Why this answer is correct

The correct answer is A. (14). Those who passed only Science are (49-35=14). Subtract those who passed both from the total of that subject.

Step 3

Exam Tip

केवल विज्ञान पास करने वाले (49-35=14) हैं। विषय के कुल से दोनों पास करने वालों को घटाएं।

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Question 34/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

एक मेले में (120) लोग आए, (70) झूला गए, (52) खेल स्टॉल गए, और (30) दोनों जगह गए। कम से कम एक जगह जाने वाले कितने हैं?

At a fair, (120) people came, (70) visited rides, (52) visited game stalls, and (30) visited both. How many visited at least one place?

Explanation opens after your attempt

Correct Answer

A. (92)

Step 1

Concept

Those who visited at least one place are (70+52-30=92). In a Venn diagram, subtract the common part once.

Step 2

Why this answer is correct

The correct answer is A. (92). Those who visited at least one place are (70+52-30=92). In a Venn diagram, subtract the common part once.

Step 3

Exam Tip

कम से कम एक जगह जाने वाले (70+52-30=92) हैं। वेन आरेख में साझा भाग को एक बार घटाते हैं।

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Question 35/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(A\cap B=\varnothing\), (n(A)=24), और (n(B)=37), तो (n\(A\cup B\)) क्या है?

If \(A\cap B=\varnothing\), (n(A)=24), and (n(B)=37), what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

D. (61)

Step 1

Concept

For disjoint sets, the common part is (0). Therefore, (n\(A\cup B\)=24+37=61).

Step 2

Why this answer is correct

The correct answer is D. (61). For disjoint sets, the common part is (0). Therefore, (n\(A\cup B\)=24+37=61).

Step 3

Exam Tip

असंबद्ध समुच्चयों में साझा भाग (0) होता है। इसलिए (n\(A\cup B\)=24+37=61)।

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Question 36/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(A\subseteq B\), (n(A)=18), और (n(B)=46), तो (n\(A\cup B\)) क्या है?

If \(A\subseteq B\), (n(A)=18), and (n(B)=46), what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

C. (46)

Step 1

Concept

When \(A\subseteq B\), \(A\cup B=B\). Therefore, (n\(A\cup B\)=46).

Step 2

Why this answer is correct

The correct answer is C. (46). When \(A\subseteq B\), \(A\cup B=B\). Therefore, (n\(A\cup B\)=46).

Step 3

Exam Tip

\(A\subseteq B\) होने पर \(A\cup B=B\) होता है। इसलिए (n\(A\cup B\)=46)।

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Question 37/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(A\subseteq B\), (n(A)=15), और (n(B)=52), तो (n\(A\cap B\)) क्या है?

If \(A\subseteq B\), (n(A)=15), and (n(B)=52), what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (15)

Step 1

Concept

When \(A\subseteq B\), \(A\cap B=A\). Therefore, (n\(A\cap B\)=15).

Step 2

Why this answer is correct

The correct answer is A. (15). When \(A\subseteq B\), \(A\cap B=A\). Therefore, (n\(A\cap B\)=15).

Step 3

Exam Tip

\(A\subseteq B\) होने पर \(A\cap B=A\) होता है। इसलिए (n\(A\cap B\)=15)।

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Question 38/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (A=B), तो वेन आरेख में (A-B) किसके बराबर होगा?

If (A=B), then in a Venn diagram (A-B) will be equal to what?

Explanation opens after your attempt

Correct Answer

C. \(\varnothing\)

Step 1

Concept

When (A=B), no element remains in (A) that is not in (B). Therefore, \(A-B=\varnothing\).

Step 2

Why this answer is correct

The correct answer is C. \(\varnothing\). When (A=B), no element remains in (A) that is not in (B). Therefore, \(A-B=\varnothing\).

Step 3

Exam Tip

जब (A=B), तो (A) में ऐसा कोई अवयव नहीं बचता जो (B) में न हो। इसलिए \(A-B=\varnothing\)।

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Question 39/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि \(A\cap B=A\), तो वेन आरेख के आधार पर कौन सा संबंध सही है?

If \(A\cap B=A\), which relation is correct based on the Venn diagram?

Explanation opens after your attempt

Correct Answer

A. \(A\subseteq B\)

Step 1

Concept

\(A\cap B=A\) means the whole of (A) lies inside (B). Therefore, \(A\subseteq B\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(A\subseteq B\). \(A\cap B=A\) means the whole of (A) lies inside (B). Therefore, \(A\subseteq B\) is correct.

Step 3

Exam Tip

\(A\cap B=A\) का अर्थ है (A) पूरा (B) के अंदर है। इसलिए \(A\subseteq B\) सही है।

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Question 40/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

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

If \(A\cup B=A\), which relation is correct based on the Venn diagram?

Explanation opens after your attempt

Correct Answer

B. \(B\subseteq A\)

Step 1

Concept

\(A\cup B=A\) means all elements of (B) are already in (A). Therefore, \(B\subseteq A\) is correct.

Step 2

Why this answer is correct

The correct answer is B. \(B\subseteq A\). \(A\cup B=A\) means all elements of (B) are already in (A). Therefore, \(B\subseteq A\) is correct.

Step 3

Exam Tip

\(A\cup B=A\) का अर्थ है (B) के सभी अवयव (A) में पहले से हैं। इसलिए \(B\subseteq A\) सही है।

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Question 41/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

तीन समुच्चयों के वेन आरेख में \(A\cap B\cap C\) कहाँ होता है?

Where is \(A\cap B\cap C\) in a Venn diagram of three sets?

Explanation opens after your attempt

Correct Answer

C. तीनों वृत्तों के साझा भाग मेंIn the common part of all three circles

Step 1

Concept

\(A\cap B\cap C\) is the common part of all three sets. In three circles, it is the central common region.

Step 2

Why this answer is correct

The correct answer is C. तीनों वृत्तों के साझा भाग में / In the common part of all three circles. \(A\cap B\cap C\) is the common part of all three sets. In three circles, it is the central common region.

Step 3

Exam Tip

\(A\cap B\cap C\) तीनों समुच्चयों का साझा भाग है। तीन वृत्तों में यह बीच का सामान्य क्षेत्र होता है।

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Question 42/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=12), (n(B)=14), (n(C)=10), (n\(A\cap B\)=5), (n\(A\cap C\)=3), (n\(B\cap C\)=4), और (n\(A\cap B\cap C\)=2), तो (n\(A\cup B\cup C\)) क्या है?

If (n(A)=12), (n(B)=14), (n(C)=10), (n\(A\cap B\)=5), (n\(A\cap C\)=3), (n\(B\cap C\)=4), and (n\(A\cap B\cap C\)=2), what is (n\(A\cup B\cup C\))?

Explanation opens after your attempt

Correct Answer

B. (26)

Step 1

Concept

By the three-set formula, (12+14+10-5-3-4+2=26). Subtract pairwise intersections and add the common part of all three.

Step 2

Why this answer is correct

The correct answer is B. (26). By the three-set formula, (12+14+10-5-3-4+2=26). Subtract pairwise intersections and add the common part of all three.

Step 3

Exam Tip

तीन समुच्चयों के सूत्र से (12+14+10-5-3-4+2=26)। जोड़ी प्रतिच्छेद घटाकर तीनों का साझा भाग जोड़ें।

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Question 43/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=16), (n(B)=18), (n(C)=9), (n\(A\cap B\)=6), (n\(A\cap C\)=2), (n\(B\cap C\)=3), और (n\(A\cap B\cap C\)=1), तो (n\(A\cup B\cup C\)) क्या है?

If (n(A)=16), (n(B)=18), (n(C)=9), (n\(A\cap B\)=6), (n\(A\cap C\)=2), (n\(B\cap C\)=3), and (n\(A\cap B\cap C\)=1), what is (n\(A\cup B\cup C\))?

Explanation opens after your attempt

Correct Answer

B. (33)

Step 1

Concept

The formula gives (16+18+9-6-2-3+1=33). In three sets, do not forget to add the final common part.

Step 2

Why this answer is correct

The correct answer is B. (33). The formula gives (16+18+9-6-2-3+1=33). In three sets, do not forget to add the final common part.

Step 3

Exam Tip

सूत्र से (16+18+9-6-2-3+1=33) मिलता है। तीन समुच्चयों में अंतिम साझा भाग जोड़ना न भूलें।

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Question 44/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=24), (n(B)=20), और (n\(A\cap B\)=6), तो केवल (A) और केवल (B) की कुल संख्या क्या है?

If (n(A)=24), (n(B)=20), and (n\(A\cap B\)=6), what is the total number of only (A) and only (B)?

Explanation opens after your attempt

Correct Answer

B. (32)

Step 1

Concept

Only (A=24-6=18) and only (B=20-6=14). The total is (18+14=32).

Step 2

Why this answer is correct

The correct answer is B. (32). Only (A=24-6=18) and only (B=20-6=14). The total is (18+14=32).

Step 3

Exam Tip

केवल (A=24-6=18) और केवल (B=20-6=14)। कुल (18+14=32) है।

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Question 45/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=45), (n(B)=38), और केवल (A) में (19) अवयव हैं, तो (n\(A\cap B\)) क्या है?

If (n(A)=45), (n(B)=38), and only (A) has (19) elements, what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

B. (26)

Step 1

Concept

Out of total (45) elements of (A), only (A) has (19). Therefore, the common part is (45-19=26).

Step 2

Why this answer is correct

The correct answer is B. (26). Out of total (45) elements of (A), only (A) has (19). Therefore, the common part is (45-19=26).

Step 3

Exam Tip

(A) के कुल (45) में केवल (A) (19) है। इसलिए साझा भाग (45-19=26) है।

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Question 46/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=39), (n(B)=50), और केवल (B) में (28) अवयव हैं, तो (n\(A\cap B\)) क्या है?

If (n(A)=39), (n(B)=50), and only (B) has (28) elements, what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

B. (22)

Step 1

Concept

Out of total (50) elements of (B), only (B) has (28). Therefore, the common part is (50-28=22).

Step 2

Why this answer is correct

The correct answer is B. (22). Out of total (50) elements of (B), only (B) has (28). Therefore, the common part is (50-28=22).

Step 3

Exam Tip

(B) के कुल (50) में केवल (B) (28) है। इसलिए साझा भाग (50-28=22) है।

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Question 47/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

कौन सा कथन वेन आरेख के लिए हमेशा सही है?

Which statement is always correct for a Venn diagram?

Explanation opens after your attempt

Correct Answer

A. \(A\cap B\subseteq A\)

Step 1

Concept

All elements of \(A\cap B\) must be in (A). Therefore, \(A\cap B\subseteq A\) is always true.

Step 2

Why this answer is correct

The correct answer is A. \(A\cap B\subseteq A\). All elements of \(A\cap B\) must be in (A). Therefore, \(A\cap B\subseteq A\) is always true.

Step 3

Exam Tip

\(A\cap B\) के सभी अवयव (A) में अवश्य होते हैं। इसलिए \(A\cap B\subseteq A\) हमेशा सत्य है।

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Question 48/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(U)=110), (n(A)=58), (n(B)=47), और (n\(A\cap B\)=20), तो (n(\(A\cup B\)')) क्या है?

If (n(U)=110), (n(A)=58), (n(B)=47), and (n\(A\cap B\)=20), what is (n(\(A\cup B\)'))?

Explanation opens after your attempt

Correct Answer

A. (25)

Step 1

Concept

First (n\(A\cup B\)=58+47-20=85). Therefore, (n(\(A\cup B\)')=110-85=25).

Step 2

Why this answer is correct

The correct answer is A. (25). First (n\(A\cup B\)=58+47-20=85). Therefore, (n(\(A\cup B\)')=110-85=25).

Step 3

Exam Tip

पहले (n\(A\cup B\)=58+47-20=85)। इसलिए (n(\(A\cup B\)')=110-85=25)।

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Question 49/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(U)=96) और (n\(A\cap B\)=34), तो (n(\(A\cap B\)')) क्या है?

If (n(U)=96) and (n\(A\cap B\)=34), what is (n(\(A\cap B\)'))?

Explanation opens after your attempt

Correct Answer

B. (62)

Step 1

Concept

(\(A\cap B\)') contains all elements of (U) except the common part. Therefore, (96-34=62).

Step 2

Why this answer is correct

The correct answer is B. (62). (\(A\cap B\)') contains all elements of (U) except the common part. Therefore, (96-34=62).

Step 3

Exam Tip

(\(A\cap B\)') में साझा भाग को छोड़कर (U) के बाकी सभी अवयव आते हैं। इसलिए (96-34=62)।

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Question 50/50 Easy Mathematics Sets Venn Diagrams Class 11 Level 15

यदि (n(A)=42), (n\(A\cup B\)=69), और (n\(A\cap B\)=18), तो (n(B)) क्या है?

If (n(A)=42), (n\(A\cup B\)=69), and (n\(A\cap B\)=18), what is (n(B))?

Explanation opens after your attempt

Correct Answer

B. (45)

Step 1

Concept

From (69=42+n(B)-18), we get (n(B)=45). Isolate the unknown in the union formula.

Step 2

Why this answer is correct

The correct answer is B. (45). From (69=42+n(B)-18), we get (n(B)=45). Isolate the unknown in the union formula.

Step 3

Exam Tip

सूत्र (69=42+n(B)-18) से (n(B)=45) मिलता है। संघ के सूत्र में अज्ञात को अलग करें।

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Class 11 Mathematics - Sets - Venn Diagrams Easy Quiz

वेन आरेख में (U) के अंदर लेकिन (A) के बाहर का क्षेत्र किससे दर्शाया जाता है?

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यदि (n(A)=36), (n(B)=28), और (n\(A\cap B\)=12), तो (n\(A\cup B\)) क्या है?

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वेन आरेख में \(A\cup B\) को छायांकित करने पर कौन सा भाग छूटता है?

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यदि (n(U)=92) और (n\(A\cup B\)=67), तो वेन आरेख में न (A) न (B) वाले क्षेत्र में कितने अवयव होंगे?

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Exam Tip

यदि (A) और (B) के वेन आरेख में केवल बीच वाला भाग छायांकित है, तो वह कौन सा समुच्चय है?

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यदि \(A=\{1,3,5,7,9\}\) और \(B=\{5,7,11\}\), तो केवल (A) वाला क्षेत्र क्या है?

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यदि केवल (A) वाला क्षेत्र छायांकित है, तो उसे किस रूप में लिखा जा सकता है?

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यदि (n(A)=44) और (n\(A\cap B\)=18), तो केवल (A) में कितने अवयव होंगे?

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Exam Tip

यदि केवल (B) वाला क्षेत्र छायांकित है, तो उसे किस रूप में लिखा जा सकता है?

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यदि \(U=\{a,b,c,d,e,f,h\}\), \(A=\{a,c,e\}\), और \(B=\{c,d,f\}\), तो (\(A\cup B\)') क्या है?

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यदि (n(A)=31), (n(B)=22), और (n\(A\cap B\)=9), तो (n\(A\cup B\)) क्या है?

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यदि (n\(A\cup B\)=81), केवल (A) (29), और केवल (B) (34) है, तो (n\(A\cap B\)) क्या है?

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यदि (n(A)=28), (n(B)=19), और (n\(A\cup B\)=39), तो (n\(A\cap B\)) क्या है?

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यदि (n(U)=72) और (n(A)=29), तो (n(A')) क्या होगा?

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यदि (n(U)=85) और (n\(A\cup B\)=56), तो न (A) न (B) में कितने अवयव हैं?

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यदि (n(A)=35) और (n\(A\cap B\)=12), तो केवल (A) में कितने अवयव होंगे?

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यदि (n(B)=41) और (n\(A\cap B\)=17), तो केवल (B) में कितने अवयव होंगे?

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यदि केवल (A) में (18), \(A\cap B\) में (7), और केवल (B) में (14) अवयव हैं, तो (n\(A\cup B\)) क्या है?

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यदि (n(A-B)=16) और (n\(A\cap B\)=11), तो (n(A)) क्या है?

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यदि (n(B-A)=21) और (n\(A\cap B\)=13), तो (n(B)) क्या है?

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