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Mathematics Quiz - Class 11 Mathematics Sets Operations o...

Question 1/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A={x\in\mathbb{Z}: -2\le x<5}\) और \(B={x\in\mathbb{Z}: x^2\le 9}\) हैं, तो (A-B) क्या है?

If \(A={x\in\mathbb{Z}: -2\le x<5}\) and \(B={x\in\mathbb{Z}: x^2\le 9}\), then what is (A-B)?

Explanation opens after your attempt

Correct Answer

A. (A-B={4})

Step 1

Concept

\(A=\{-2,-1,0,1,2,3,4\}\) and \(B=\{-3,-2,-1,0,1,2,3\}\), so only (4) remains. In exams, list both sets clearly before taking difference.

Step 2

Why this answer is correct

The correct answer is A. (A-B={4}). \(A=\{-2,-1,0,1,2,3,4\}\) and \(B=\{-3,-2,-1,0,1,2,3\}\), so only (4) remains. In exams, list both sets clearly before taking difference.

Step 3

Exam Tip

\(A=\{-2,-1,0,1,2,3,4\}\) और \(B=\{-3,-2,-1,0,1,2,3\}\) है, इसलिए केवल (4) बचता है। परीक्षा में अंतर निकालते समय पहले दोनों समुच्चय स्पष्ट लिखें।

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Question 2/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि (n(A)=40), (n(B)=36), (n(C)=28), (n\(A\cap B\)=14), (n\(B\cap C\)=10), (n\(C\cap A\)=12) और (n\(A\cap B\cap C\)=5) है, तो (n(\(A\cup B\cup C\)-C)) कितना है?

If (n(A)=40), (n(B)=36), (n(C)=28), (n\(A\cap B\)=14), (n\(B\cap C\)=10), (n\(C\cap A\)=12), and (n\(A\cap B\cap C\)=5), then what is (n(\(A\cup B\cup C\)-C))?

Explanation opens after your attempt

Correct Answer

A. (45)

Step 1

Concept

First (n\(A\cup B\cup C\)=73), then removing (28) elements of (C) leaves (45). In such questions, find the complete union first.

Step 2

Why this answer is correct

The correct answer is A. (45). First (n\(A\cup B\cup C\)=73), then removing (28) elements of (C) leaves (45). In such questions, find the complete union first.

Step 3

Exam Tip

पहले (n\(A\cup B\cup C\)=73) मिलता है, फिर (C) के (28) तत्व हटाने पर (45) बचते हैं। ऐसे प्रश्न में पहले पूरा संघ निकालें।

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Question 3/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

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

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

Explanation opens after your attempt

Correct Answer

A. (B-A={3,6})

Step 1

Concept

\(A\cup B\) is split into (A-B), \(A\cap B\), and (B-A). The remaining elements are (3) and (6).

Step 2

Why this answer is correct

The correct answer is A. (B-A={3,6}). \(A\cup B\) is split into (A-B), \(A\cap B\), and (B-A). The remaining elements are (3) and (6).

Step 3

Exam Tip

\(A\cup B\) को तीन भागों (A-B), \(A\cap B\) और (B-A) में बांटा जाता है। बचे हुए तत्व (3) और (6) हैं।

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Question 4/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A={x\in\mathbb{R}: -2<x\le 6}\), \(B={x\in\mathbb{R}: 1\le x<8}\) और \(C={x\in\mathbb{R}: 4<x\le 10}\), तो (\(A\cup C\)-B) क्या है?

If \(A={x\in\mathbb{R}: -2<x\le 6}\), \(B={x\in\mathbb{R}: 1\le x<8}\), and \(C={x\in\mathbb{R}: 4<x\le 10}\), what is (\(A\cup C\)-B)?

Explanation opens after your attempt

Correct Answer

A. \((-2,1)\cup[8,10]\)

Step 1

Concept

\(A\cup C=(-2,10]), and removing (B=[1,8)\) gives \((-2,1)\cup[8,10]\). Watch open and closed endpoints carefully.

Step 2

Why this answer is correct

The correct answer is A. \((-2,1)\cup[8,10]\). \(A\cup C=(-2,10]), and removing (B=[1,8)\) gives \((-2,1)\cup[8,10]\). Watch open and closed endpoints carefully.

Step 3

Exam Tip

\(A\cup C=(-2,10]) है और (B=[1,8)\) हटाने पर \((-2,1)\cup[8,10]\) मिलता है। सिरों के खुले-बंद होने पर ध्यान दें।

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Question 5/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि (n(A)=45), (n(B)=38) और (n\(A\cup B\)=63) है, तो (n\(A\cap B\)) ज्ञात कीजिए।

If (n(A)=45), (n(B)=38), and (n\(A\cup B\)=63), find (n\(A\cap B\)).

Explanation opens after your attempt

Correct Answer

A. (20)

Step 1

Concept

Using (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)), (63=45+38-x), so (x=20). In exams, remember to subtract the double count.

Step 2

Why this answer is correct

The correct answer is A. (20). Using (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)), (63=45+38-x), so (x=20). In exams, remember to subtract the double count.

Step 3

Exam Tip

सूत्र (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)) से (63=45+38-x), इसलिए (x=20)। परीक्षा में अधिक गिनती को घटाना न भूलें।

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Question 6/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि (A), (B) और (C) समुच्चय हैं, तो \(A\cap(B-C)\) किसके बराबर है?

If (A), (B), and (C) are sets, then \(A\cap(B-C)\) is equal to which expression?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

(B-C) contains elements in (B) and not in (C). Intersecting with (A) gives exactly (\(A\cap B\)-C).

Step 2

Why this answer is correct

The correct answer is A. (\(A\cap B\)-C). (B-C) contains elements in (B) and not in (C). Intersecting with (A) gives exactly (\(A\cap B\)-C).

Step 3

Exam Tip

(B-C) में वे तत्व हैं जो (B) में हैं और (C) में नहीं हैं। (A) से प्रतिच्छेद करने पर यही (\(A\cap B\)-C) बनता है।

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Question 7/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A\subseteq B\) है, तो (\(A\cup B\)-\(A\cap B\)) किसके बराबर है?

If \(A\subseteq B\), then (\(A\cup B\)-\(A\cap B\)) is equal to which set?

Explanation opens after your attempt

Correct Answer

A. (B-A)

Step 1

Concept

When \(A\subseteq B\), \(A\cup B=B\) and \(A\cap B=A\). Hence the result is (B-A).

Step 2

Why this answer is correct

The correct answer is A. (B-A). When \(A\subseteq B\), \(A\cup B=B\) and \(A\cap B=A\). Hence the result is (B-A).

Step 3

Exam Tip

जब \(A\subseteq B\), तब \(A\cup B=B\) और \(A\cap B=A\) होता है। इसलिए परिणाम (B-A) है।

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Question 8/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(U={1,2,\ldots,12}\), \(A=\{2,4,6,8,10,12\}\) और \(B=\{3,6,9,12\}\) हैं, तो (\(A\cup B\)') क्या है?

If \(U={1,2,\ldots,12}\), \(A=\{2,4,6,8,10,12\}\), and \(B=\{3,6,9,12\}\), what is (\(A\cup B\)')?

Explanation opens after your attempt

Correct Answer

A. ({1,5,7,11})

Step 1

Concept

\(A\cup B={2,3,4,6,8,9,10,12}\). The elements outside it in (U) are (1,5,7,11).

Step 2

Why this answer is correct

The correct answer is A. ({1,5,7,11}). \(A\cup B={2,3,4,6,8,9,10,12}\). The elements outside it in (U) are (1,5,7,11).

Step 3

Exam Tip

\(A\cup B={2,3,4,6,8,9,10,12}\) है। (U) में इसके बाहर के तत्व (1,5,7,11) हैं।

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Question 9/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A=\{1,2,3,4,5\}\), \(B=\{2,4,6,8\}\) और \(C=\{1,4,7,8\}\) हैं, तो (A\cap\(B\cup C\)) क्या है?

If \(A=\{1,2,3,4,5\}\), \(B=\{2,4,6,8\}\), and \(C=\{1,4,7,8\}\), what is (A\cap\(B\cup C\))?

Explanation opens after your attempt

Correct Answer

A. ({1,2,4})

Step 1

Concept

First \(B\cup C={1,2,4,6,7,8}\). Its intersection with (A) is ({1,2,4}).

Step 2

Why this answer is correct

The correct answer is A. ({1,2,4}). First \(B\cup C={1,2,4,6,7,8}\). Its intersection with (A) is ({1,2,4}).

Step 3

Exam Tip

पहले \(B\cup C={1,2,4,6,7,8}\) मिलता है। इसके साथ (A) का प्रतिच्छेद ({1,2,4}) है।

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Question 10/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A-B=\varnothing\) और \(B-A\ne\varnothing\) है, तो सही निष्कर्ष कौन-सा है?

If \(A-B=\varnothing\) and \(B-A\ne\varnothing\), which conclusion is correct?

Explanation opens after your attempt

Correct Answer

A. \(A\subset B\)

Step 1

Concept

\(A-B=\varnothing\) means every element of (A) lies in (B). \(B-A\ne\varnothing\) means (B) has at least one extra element.

Step 2

Why this answer is correct

The correct answer is A. \(A\subset B\). \(A-B=\varnothing\) means every element of (A) lies in (B). \(B-A\ne\varnothing\) means (B) has at least one extra element.

Step 3

Exam Tip

\(A-B=\varnothing\) बताता है कि (A) का हर तत्व (B) में है। \(B-A\ne\varnothing\) बताता है कि (B) में कुछ अतिरिक्त तत्व हैं।

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Question 11/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A\triangle B=(A-B)\cup(B-A)\) है और \(A=\{a,b,c,d\}\), \(B=\{b,d,e,f\}\) हैं, तो \(A\triangle B\) क्या है?

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

Explanation opens after your attempt

Correct Answer

A. ({a,c,e,f})

Step 1

Concept

Common elements (b,d) are removed. Only elements that belong to exactly one set are taken.

Step 2

Why this answer is correct

The correct answer is A. ({a,c,e,f}). Common elements (b,d) are removed. Only elements that belong to exactly one set are taken.

Step 3

Exam Tip

समान तत्व (b,d) हट जाते हैं। केवल वे तत्व लिए जाते हैं जो ठीक एक समुच्चय में हों।

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Question 12/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A\cap B=A\cap C\) और \(A\cup B=A\cup C\) हैं, तो कौन-सा निष्कर्ष सही है?

If \(A\cap B=A\cap C\) and \(A\cup B=A\cup C\), which conclusion is correct?

Explanation opens after your attempt

Correct Answer

A. (B=C)

Step 1

Concept

For every element, the conditions inside and outside (A) force (B) and (C) to match. Hence (B=C).

Step 2

Why this answer is correct

The correct answer is A. (B=C). For every element, the conditions inside and outside (A) force (B) and (C) to match. Hence (B=C).

Step 3

Exam Tip

हर तत्व के लिए (A) के अंदर और बाहर दोनों स्थितियां (B) और (C) को समान बनाती हैं। इसलिए (B=C) है।

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Question 13/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A={x\in\mathbb{R}: 0\le x<3}\) और \(B={x\in\mathbb{R}: 1<x\le 5}\), तो \(A\cup B\) क्या है?

If \(A={x\in\mathbb{R}: 0\le x<3}\) and \(B={x\in\mathbb{R}: 1<x\le 5}\), what is \(A\cup B\)?

Explanation opens after your attempt

Correct Answer

A. ([0,5])

Step 1

Concept

The intervals overlap, so their union covers all points from (0) to (5). Both endpoints (0) and (5) are included.

Step 2

Why this answer is correct

The correct answer is A. ([0,5]). The intervals overlap, so their union covers all points from (0) to (5). Both endpoints (0) and (5) are included.

Step 3

Exam Tip

दोनों अंतराल ओवरलैप करते हैं, इसलिए उनका संघ (0) से (5) तक पूरा है। दोनों सिरों (0) और (5) शामिल हैं।

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Question 14/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A={x\in\mathbb{R}: -3\le x\le 2}\) और \(B={x\in\mathbb{R}: -1<x<4}\), तो (A-B) क्या है?

If \(A={x\in\mathbb{R}: -3\le x\le 2}\) and \(B={x\in\mathbb{R}: -1<x<4}\), what is (A-B)?

Explanation opens after your attempt

Correct Answer

A. ([-3,-1])

Step 1

Concept

(B) does not include (-1), so (-1) remains. Removing (B) from (A) gives ([-3,-1]).

Step 2

Why this answer is correct

The correct answer is A. ([-3,-1]). (B) does not include (-1), so (-1) remains. Removing (B) from (A) gives ([-3,-1]).

Step 3

Exam Tip

(B) में (-1) शामिल नहीं है, इसलिए (-1) बचता है। (A) से (B) हटाने पर ([-3,-1]) मिलता है।

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Question 15/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि (n(A-B)=12), (n(B-A)=9) और (n\(A\cap B\)=7), तो (n\(A\cup B\)) क्या है?

If (n(A-B)=12), (n(B-A)=9), and (n\(A\cap B\)=7), what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (28)

Step 1

Concept

The union is the sum of three disjoint parts (A-B), (B-A), and \(A\cap B\). Thus (12+9+7=28).

Step 2

Why this answer is correct

The correct answer is A. (28). The union is the sum of three disjoint parts (A-B), (B-A), and \(A\cap B\). Thus (12+9+7=28).

Step 3

Exam Tip

संघ तीन अलग भागों (A-B), (B-A) और \(A\cap B\) का योग है। इसलिए (12+9+7=28)।

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Question 16/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

एक कक्षा में (60) छात्रों में से (34) गणित, (28) भौतिकी और (12) दोनों पढ़ते हैं। केवल गणित पढ़ने वाले छात्रों की संख्या कितनी है?

In a class of (60) students, (34) study Mathematics, (28) study Physics, and (12) study both. How many students study only Mathematics?

Explanation opens after your attempt

Correct Answer

A. (22)

Step 1

Concept

Only Mathematics (=n(M)-n\(M\cap P\)=34-12=22). In such questions, subtract the common part from the only part.

Step 2

Why this answer is correct

The correct answer is A. (22). Only Mathematics (=n(M)-n\(M\cap P\)=34-12=22). In such questions, subtract the common part from the only part.

Step 3

Exam Tip

केवल गणित (=n(M)-n\(M\cap P\)=34-12=22)। ऐसे प्रश्न में दोनों पढ़ने वालों को केवल वाले भाग से घटाएं।

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Question 17/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि (n(A)=52), (n(B)=47), (n\(A\cap B\)=21) और (n(U)=80), तो (n(\(A\cup B\)')) क्या है?

If (n(A)=52), (n(B)=47), (n\(A\cap B\)=21), and (n(U)=80), what is (n(\(A\cup B\)'))?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

(n\(A\cup B\)=52+47-21=78). Therefore the number outside is (80-78=2).

Step 2

Why this answer is correct

The correct answer is A. (2). (n\(A\cup B\)=52+47-21=78). Therefore the number outside is (80-78=2).

Step 3

Exam Tip

(n\(A\cup B\)=52+47-21=78)। अतः बाहर के तत्व (80-78=2) हैं।

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Question 18/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A\cap B=\varnothing\), (n(A)=15) और (n(B)=19), तो (n\(A\cup B\)) क्या है?

If \(A\cap B=\varnothing\), (n(A)=15), and (n(B)=19), what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (34)

Step 1

Concept

Disjoint sets have no common element. Hence (n\(A\cup B\)=15+19=34).

Step 2

Why this answer is correct

The correct answer is A. (34). Disjoint sets have no common element. Hence (n\(A\cup B\)=15+19=34).

Step 3

Exam Tip

असंबद्ध समुच्चयों में कोई सामान्य तत्व नहीं होता। इसलिए (n\(A\cup B\)=15+19=34)।

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Question 19/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A\cup B=A\) है, तो (B) के बारे में सही कथन क्या है?

If \(A\cup B=A\), which statement about (B) is correct?

Explanation opens after your attempt

Correct Answer

A. \(B\subseteq A\)

Step 1

Concept

Adding (B) to (A) by union does not change (A), so every element of (B) is in (A). Thus \(B\subseteq A\).

Step 2

Why this answer is correct

The correct answer is A. \(B\subseteq A\). Adding (B) to (A) by union does not change (A), so every element of (B) is in (A). Thus \(B\subseteq A\).

Step 3

Exam Tip

संघ में (B) जोड़ने पर (A) नहीं बदलता, इसलिए (B) का हर तत्व (A) में है। अतः \(B\subseteq A\)।

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Question 20/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A\cap B=B\) है, तो कौन-सा निष्कर्ष सही है?

If \(A\cap B=B\), which conclusion is correct?

Explanation opens after your attempt

Correct Answer

A. \(B\subseteq A\)

Step 1

Concept

The intersection equals (B) only when every element of (B) lies in (A). Hence \(B\subseteq A\).

Step 2

Why this answer is correct

The correct answer is A. \(B\subseteq A\). The intersection equals (B) only when every element of (B) lies in (A). Hence \(B\subseteq A\).

Step 3

Exam Tip

प्रतिच्छेद (B) के बराबर तभी होगा जब (B) का हर तत्व (A) में हो। इसलिए \(B\subseteq A\) है।

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Question 21/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A=\{1,3,5,7,9\}\), \(B=\{2,3,5,8,9\}\) और \(C=\{3,4,5,9\}\), तो \(A\cap B\cap C\) क्या है?

If \(A=\{1,3,5,7,9\}\), \(B=\{2,3,5,8,9\}\), and \(C=\{3,4,5,9\}\), what is \(A\cap B\cap C\)?

Explanation opens after your attempt

Correct Answer

A. ({3,5,9})

Step 1

Concept

The common elements in all three sets are (3,5,9). In a three-set intersection, each element must be in all three sets.

Step 2

Why this answer is correct

The correct answer is A. ({3,5,9}). The common elements in all three sets are (3,5,9). In a three-set intersection, each element must be in all three sets.

Step 3

Exam Tip

तीनों समुच्चयों में सामान्य तत्व (3,5,9) हैं। तीन समुच्चयों के प्रतिच्छेद में हर तत्व तीनों में होना चाहिए।

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Question 22/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

\(यदि (A={x\in\mathbb{N}: x\le 20,\ x\) is prime\(}) और (B={x\in\mathbb{N}: x<20,\ x\) is odd}), तो (A-B) क्या है?

\(If (A={x\in\mathbb{N}: x\le 20,\ x\) is prime\(}) and (B={x\in\mathbb{N}: x<20,\ x\) is odd}), what is (A-B)?

Explanation opens after your attempt

Correct Answer

A. ({2})

Step 1

Concept

All odd primes in (A) are in (B), so only (2) remains. (19) is also in (B) because it is odd and less than (20).

Step 2

Why this answer is correct

The correct answer is A. ({2}). All odd primes in (A) are in (B), so only (2) remains. (19) is also in (B) because it is odd and less than (20).

Step 3

Exam Tip

(A) के सभी विषम अभाज्य (B) में चले जाते हैं, केवल (2) बचता है। (19) भी (B) में है क्योंकि वह विषम और (20) से छोटा है।

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Question 23/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A={x:x=2k,\ k\in\mathbb{Z}}\) और \(B={x:x=4k,\ k\in\mathbb{Z}}\), तो सही संबंध कौन-सा है?

If \(A={x:x=2k,\ k\in\mathbb{Z}}\) and \(B={x:x=4k,\ k\in\mathbb{Z}}\), which relation is correct?

Explanation opens after your attempt

Correct Answer

A. \(B\subseteq A\)

Step 1

Concept

Every multiple of (4) is also a multiple of (2). Therefore \(B\subseteq A\).

Step 2

Why this answer is correct

The correct answer is A. \(B\subseteq A\). Every multiple of (4) is also a multiple of (2). Therefore \(B\subseteq A\).

Step 3

Exam Tip

हर (4) का गुणज (2) का भी गुणज होता है। इसलिए \(B\subseteq A\) है।

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Question 24/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A={x:x\) अंग्रेजी शब्द (MATHEMATICS) का अक्षर है(}) और \(B={x:x\) अंग्रेजी शब्द (STATISTICS) का अक्षर है(}), तो \(A\cap B\) क्या है?

If \(A={x:x\) is a letter of the English word (MATHEMATICS)(}) and \(B={x:x\) is a letter of the English word (STATISTICS)(}), what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ({A,I,M,S,T})

Step 1

Concept

The distinct letters common to both words are (A,I,M,S,T). Repeated letters are not counted in a set.

Step 2

Why this answer is correct

The correct answer is A. ({A,I,M,S,T}). The distinct letters common to both words are (A,I,M,S,T). Repeated letters are not counted in a set.

Step 3

Exam Tip

दोनों शब्दों में आने वाले अलग-अलग अक्षर (A,I,M,S,T) हैं। समुच्चय में दोहराए गए अक्षर नहीं गिने जाते।

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Question 25/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A\cap(B-C)=\varnothing\) है, तो इसका अर्थ क्या है?

If \(A\cap(B-C)=\varnothing\), what does it mean?

Explanation opens after your attempt

Correct Answer

A. (A) का कोई भी तत्व ऐसा नहीं है जो (B) में हो और (C) में न होNo element of (A) is in (B) but not in (C)

Step 1

Concept

(B-C) contains elements in (B) but not in (C). Empty intersection with (A) means none of these lies in (A).

Step 2

Why this answer is correct

The correct answer is A. (A) का कोई भी तत्व ऐसा नहीं है जो (B) में हो और (C) में न हो / No element of (A) is in (B) but not in (C). (B-C) contains elements in (B) but not in (C). Empty intersection with (A) means none of these lies in (A).

Step 3

Exam Tip

(B-C) वे तत्व हैं जो (B) में हैं पर (C) में नहीं। (A) के साथ प्रतिच्छेद खाली होने का यही अर्थ है।

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Question 26/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A=\{1,2,3,4\}\), तो \(A\cup\varnothing\), \(A\cap\varnothing\), और \(A-\varnothing\) क्रमशः क्या हैं?

If \(A=\{1,2,3,4\}\), what are \(A\cup\varnothing\), \(A\cap\varnothing\), and \(A-\varnothing\) respectively?

Explanation opens after your attempt

Correct Answer

A. \(A,\varnothing,A\)

Step 1

Concept

The empty set adds nothing in union, gives nothing in intersection, and removes nothing in difference. Hence the answer is \(A,\varnothing,A\).

Step 2

Why this answer is correct

The correct answer is A. \(A,\varnothing,A\). The empty set adds nothing in union, gives nothing in intersection, and removes nothing in difference. Hence the answer is \(A,\varnothing,A\).

Step 3

Exam Tip

खाली समुच्चय संघ में कुछ नहीं जोड़ता, प्रतिच्छेद में कुछ सामान्य नहीं देता और अंतर में कुछ नहीं हटाता। इसलिए उत्तर \(A,\varnothing,A\) है।

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Question 27/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A\cup B=U\) और \(A\cap B=\varnothing\), तो (B) किसके बराबर है?

If \(A\cup B=U\) and \(A\cap B=\varnothing\), then (B) is equal to which set?

Explanation opens after your attempt

Correct Answer

A. (A')

Step 1

Concept

(B) contains exactly the elements not in (A), and together they form (U). Thus (B=A').

Step 2

Why this answer is correct

The correct answer is A. (A'). (B) contains exactly the elements not in (A), and together they form (U). Thus (B=A').

Step 3

Exam Tip

(B) में ठीक वे तत्व हैं जो (A) में नहीं हैं और दोनों मिलकर (U) बनाते हैं। अतः (B=A')।

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Question 28/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6,8\}\) और \(C=\{1,2,8,9\}\), तो \((A-B)\cup(A-C)\) क्या है?

If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6,8\}\), and \(C=\{1,2,8,9\}\), what is \((A-B)\cup(A-C)\)?

Explanation opens after your attempt

Correct Answer

A. ({1,3,4,5,6})

Step 1

Concept

(A-B={1,3,5}) and (A-C={3,4,5,6}). Their union is ({1,3,4,5,6}).

Step 2

Why this answer is correct

The correct answer is A. ({1,3,4,5,6}). (A-B={1,3,5}) and (A-C={3,4,5,6}). Their union is ({1,3,4,5,6}).

Step 3

Exam Tip

(A-B={1,3,5}) और (A-C={3,4,5,6}) है। इनका संघ ({1,3,4,5,6}) है।

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Question 29/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A=\{2,3,5,7,11,13\}\) और \(B={x\in A:x>5}\), तो \(A\cap B\) क्या है?

If \(A=\{2,3,5,7,11,13\}\) and \(B={x\in A:x>5}\), what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ({7,11,13})

Step 1

Concept

(B) is a subset of (A) containing elements greater than (5). Therefore \(A\cap B=B={7,11,13}\).

Step 2

Why this answer is correct

The correct answer is A. ({7,11,13}). (B) is a subset of (A) containing elements greater than (5). Therefore \(A\cap B=B={7,11,13}\).

Step 3

Exam Tip

(B), (A) का उपसमुच्चय है जिसमें (5) से बड़े तत्व हैं। इसलिए \(A\cap B=B={7,11,13}\)।

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Question 30/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A={x\in\mathbb{Z}: |x|\le 3}\) और \(B={x\in\mathbb{Z}: x^2-2x\le 0}\), तो \(A\cap B\) क्या है?

If \(A={x\in\mathbb{Z}: |x|\le 3}\) and \(B={x\in\mathbb{Z}: x^2-2x\le 0}\), what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ({0,1,2})

Step 1

Concept

\(x^2-2x\le0\) gives \(0\le x\le2\). In integers, \(B=\{0,1,2\}\), which is also in (A).

Step 2

Why this answer is correct

The correct answer is A. ({0,1,2}). \(x^2-2x\le0\) gives \(0\le x\le2\). In integers, \(B=\{0,1,2\}\), which is also in (A).

Step 3

Exam Tip

\(x^2-2x\le0\) से \(0\le x\le2\) मिलता है। पूर्णांकों में \(B=\{0,1,2\}\), जो (A) में भी है।

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Question 31/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A={x\in\mathbb{N}: x\mid 36}\) और \(B={x\in\mathbb{N}: x\mid 48}\), तो \(A\cap B\) क्या है?

If \(A={x\in\mathbb{N}: x\mid 36}\) and \(B={x\in\mathbb{N}: x\mid 48}\), what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ({1,2,3,4,6,12})

Step 1

Concept

Common divisors of (36) and (48) are divisors of (\gcd(36,48)=12). Hence the set is ({1,2,3,4,6,12}).

Step 2

Why this answer is correct

The correct answer is A. ({1,2,3,4,6,12}). Common divisors of (36) and (48) are divisors of (\gcd(36,48)=12). Hence the set is ({1,2,3,4,6,12}).

Step 3

Exam Tip

सामान्य भाजक (36) और (48) के (\gcd(36,48)=12) के भाजक होते हैं। इसलिए ({1,2,3,4,6,12}) मिलेगा।

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Question 32/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A={x\in\mathbb{N}: x\mid 18}\) और \(B={x\in\mathbb{N}: x\mid 24}\), तो \(A\cup B\) क्या है?

If \(A={x\in\mathbb{N}: x\mid 18}\) and \(B={x\in\mathbb{N}: x\mid 24}\), what is \(A\cup B\)?

Explanation opens after your attempt

Correct Answer

A. ({1,2,3,4,6,8,9,12,18,24})

Step 1

Concept

Divisors of (18) are ({1,2,3,6,9,18}), and divisors of (24) are ({1,2,3,4,6,8,12,24}). Combining without repetition gives the union.

Step 2

Why this answer is correct

The correct answer is A. ({1,2,3,4,6,8,9,12,18,24}). Divisors of (18) are ({1,2,3,6,9,18}), and divisors of (24) are ({1,2,3,4,6,8,12,24}). Combining without repetition gives the union.

Step 3

Exam Tip

(18) के भाजक ({1,2,3,6,9,18}) और (24) के भाजक ({1,2,3,4,6,8,12,24}) हैं। दोनों को बिना दोहराव मिलाने पर सही संघ मिलता है।

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Question 33/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A={x\in\mathbb{R}: x^2<9}\) और \(B={x\in\mathbb{R}: x\ge 1}\), तो (A-B) क्या है?

If \(A={x\in\mathbb{R}: x^2<9}\) and \(B={x\in\mathbb{R}: x\ge 1}\), what is (A-B)?

Explanation opens after your attempt

Correct Answer

A. ((-3,1))

Step 1

Concept

(A=(-3,3)), and (B) contains (1) and all greater real numbers. Therefore (A-B=(-3,1)).

Step 2

Why this answer is correct

The correct answer is A. ((-3,1)). (A=(-3,3)), and (B) contains (1) and all greater real numbers. Therefore (A-B=(-3,1)).

Step 3

Exam Tip

(A=(-3,3)) है और (B) में (1) तथा उससे बड़े सभी वास्तविक संख्याएं हैं। इसलिए (A-B=(-3,1)) है।

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Question 34/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A={x\in\mathbb{R}: x<0}\), \(B={x\in\mathbb{R}: x^2\le4}\), तो \(A\cup B\) क्या है?

If \(A={x\in\mathbb{R}: x<0}\), \(B={x\in\mathbb{R}: x^2\le4}\), what is \(A\cup B\)?

Explanation opens after your attempt

Correct Answer

A. (\(-\infty,2]\)

Step 1

Concept

(B=[-2,2]), and (A) gives all negative numbers. Together they form (\(-\infty,2]\).

Step 2

Why this answer is correct

The correct answer is A. (\(-\infty,2]\). (B=[-2,2]), and (A) gives all negative numbers. Together they form (\(-\infty,2]\).

Step 3

Exam Tip

(B=[-2,2]) और (A) सभी ऋणात्मक संख्याएं देता है। मिलाकर (\(-\infty,2]\) मिलता है।

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Question 35/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A={x\in\mathbb{Z}: -5\le x\le5}\) और \(B={x\in\mathbb{Z}: x\) विषम है(}), तो \(A\cap B\) क्या है?

If \(A={x\in\mathbb{Z}: -5\le x\le5}\) and \(B={x\in\mathbb{Z}: x\) is odd(}), what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ({-5,-3,-1,1,3,5})

Step 1

Concept

(A) contains integers from (-5) to (5). The odd elements among them are ({-5,-3,-1,1,3,5}).

Step 2

Why this answer is correct

The correct answer is A. ({-5,-3,-1,1,3,5}). (A) contains integers from (-5) to (5). The odd elements among them are ({-5,-3,-1,1,3,5}).

Step 3

Exam Tip

(A) में (-5) से (5) तक के पूर्णांक हैं। इनमें विषम तत्व ({-5,-3,-1,1,3,5}) हैं।

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Question 36/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि (A-B=A) है, तो कौन-सा कथन सही है?

If (A-B=A), which statement is correct?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Removing (B) does not change (A), so (A) and (B) have no common element. Thus \(A\cap B=\varnothing\).

Step 2

Why this answer is correct

The correct answer is A. \(A\cap B=\varnothing\). Removing (B) does not change (A), so (A) and (B) have no common element. Thus \(A\cap B=\varnothing\).

Step 3

Exam Tip

(B) हटाने पर (A) में कोई बदलाव नहीं हुआ, इसलिए (A) और (B) में कोई सामान्य तत्व नहीं है। अतः \(A\cap B=\varnothing\)।

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Question 37/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि (A-B=B-A) है, तो सही निष्कर्ष कौन-सा है?

If (A-B=B-A), which conclusion is correct?

Explanation opens after your attempt

Correct Answer

A. (A=B)

Step 1

Concept

If an element lies only in (A), it is in (A-B) but not in (B-A). For equality, no such element can exist, so (A=B).

Step 2

Why this answer is correct

The correct answer is A. (A=B). If an element lies only in (A), it is in (A-B) but not in (B-A). For equality, no such element can exist, so (A=B).

Step 3

Exam Tip

यदि कोई तत्व केवल (A) में हो तो वह (A-B) में होगा पर (B-A) में नहीं। समानता के लिए ऐसे तत्व नहीं हो सकते, इसलिए (A=B)।

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Question 38/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A\cup B=A\cap B\) है, तो क्या निष्कर्ष निकलेगा?

If \(A\cup B=A\cap B\), what conclusion follows?

Explanation opens after your attempt

Correct Answer

A. (A=B)

Step 1

Concept

Always \(A\cap B\subseteq A\cup B\). They can be equal only when (A) and (B) are the same set.

Step 2

Why this answer is correct

The correct answer is A. (A=B). Always \(A\cap B\subseteq A\cup B\). They can be equal only when (A) and (B) are the same set.

Step 3

Exam Tip

सदैव \(A\cap B\subseteq A\cup B\) होता है। दोनों बराबर तभी हो सकते हैं जब (A) और (B) समान हों।

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Question 39/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A=\{1,2,3\}\) और \(B=\{3,4\}\), तो (\mathcal{P}\(A\cap B\)) में कितने तत्व हैं?

If \(A=\{1,2,3\}\) and \(B=\{3,4\}\), how many elements are in (\mathcal{P}\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

\(A\cap B={3}\), which has (1) element. Hence its power set has \(2^1=2\) elements.

Step 2

Why this answer is correct

The correct answer is A. (2). \(A\cap B={3}\), which has (1) element. Hence its power set has \(2^1=2\) elements.

Step 3

Exam Tip

\(A\cap B={3}\) है, जिसमें (1) तत्व है। इसलिए इसके घात समुच्चय में \(2^1=2\) तत्व होंगे।

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Question 40/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A=\{1,2,3,4\}\) और \(B=\{3,4,5,6\}\), तो (\mathcal{P}(A-B)) में कितने उपसमुच्चय हैं?

If \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\), how many subsets are in (\mathcal{P}(A-B))?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

(A-B={1,2}), which has (2) elements. Its power set has \(2^2=4\) subsets.

Step 2

Why this answer is correct

The correct answer is A. (4). (A-B={1,2}), which has (2) elements. Its power set has \(2^2=4\) subsets.

Step 3

Exam Tip

(A-B={1,2}) है, जिसमें (2) तत्व हैं। घात समुच्चय में \(2^2=4\) उपसमुच्चय होंगे।

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Question 41/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि (n\(A\cup B\)=75), (n(A-B)=28) और (n(B-A)=31), तो (n\(A\cap B\)) क्या है?

If (n\(A\cup B\)=75), (n(A-B)=28), and (n(B-A)=31), what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (16)

Step 1

Concept

The union is made of disjoint parts (A-B), (B-A), and \(A\cap B\). So (75=28+31+x), hence (x=16).

Step 2

Why this answer is correct

The correct answer is A. (16). The union is made of disjoint parts (A-B), (B-A), and \(A\cap B\). So (75=28+31+x), hence (x=16).

Step 3

Exam Tip

संघ (A-B), (B-A) और \(A\cap B\) के असंबद्ध भागों से बनता है। इसलिए (75=28+31+x), अतः (x=16)।

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Question 42/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A=\{1,2,3,4,5,6,7,8\}\), \(B=\{2,4,6,8,10\}\), तो (\(A\cup B\)-\(A\cap B\)) क्या है?

If \(A=\{1,2,3,4,5,6,7,8\}\), \(B=\{2,4,6,8,10\}\), what is (\(A\cup B\)-\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. ({1,3,5,7,10})

Step 1

Concept

This is the symmetric difference, where common elements are removed. Removing common elements (2,4,6,8) gives ({1,3,5,7,10}).

Step 2

Why this answer is correct

The correct answer is A. ({1,3,5,7,10}). This is the symmetric difference, where common elements are removed. Removing common elements (2,4,6,8) gives ({1,3,5,7,10}).

Step 3

Exam Tip

यह सममित अंतर है, जिसमें सामान्य तत्व हट जाते हैं। सामान्य तत्व (2,4,6,8) हटाने पर ({1,3,5,7,10}) मिलता है।

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Question 43/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A\cap B=\varnothing\), तो (A-(A-B)) किसके बराबर है?

If \(A\cap B=\varnothing\), then (A-(A-B)) is equal to which set?

Explanation opens after your attempt

Correct Answer

A. \(\varnothing\)

Step 1

Concept

When \(A\cap B=\varnothing\), (A-B=A). Hence (A-(A-B)=A-A=\varnothing).

Step 2

Why this answer is correct

The correct answer is A. \(\varnothing\). When \(A\cap B=\varnothing\), (A-B=A). Hence (A-(A-B)=A-A=\varnothing).

Step 3

Exam Tip

जब \(A\cap B=\varnothing\), तब (A-B=A) होता है। इसलिए (A-(A-B)=A-A=\varnothing)।

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Question 44/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

कौन-सा विकल्प (A\cap\(B\cup C\)) के बराबर है?

Which option is equal to (A\cap\(B\cup C\))?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Intersection distributes over union. Hence (A\cap\(B\cup C\)=\(A\cap B\)\cup\(A\cap C\)).

Step 2

Why this answer is correct

The correct answer is A. (\(A\cap B\)\cup\(A\cap C\)). Intersection distributes over union. Hence (A\cap\(B\cup C\)=\(A\cap B\)\cup\(A\cap C\)).

Step 3

Exam Tip

प्रतिच्छेद संघ पर वितरित होता है। इसलिए (A\cap\(B\cup C\)=\(A\cap B\)\cup\(A\cap C\))।

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Question 45/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

कौन-सा विकल्प (A\cup\(B\cap C\)) के बराबर है?

Which option is equal to (A\cup\(B\cap C\))?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Union distributes over intersection. Hence (A\cup\(B\cap C\)=\(A\cup B\)\cap\(A\cup C\)).

Step 2

Why this answer is correct

The correct answer is A. (\(A\cup B\)\cap\(A\cup C\)). Union distributes over intersection. Hence (A\cup\(B\cap C\)=\(A\cup B\)\cap\(A\cup C\)).

Step 3

Exam Tip

संघ प्रतिच्छेद पर वितरित होता है। इसलिए (A\cup\(B\cap C\)=\(A\cup B\)\cap\(A\cup C\))।

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Question 46/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A={x\in\mathbb{N}: x\le 15}\), \(B={x\in\mathbb{N}: 3\mid x}\) और \(C={x\in\mathbb{N}: 5\mid x}\), तो (A\cap\(B\cup C\)) क्या है?

If \(A={x\in\mathbb{N}: x\le 15}\), \(B={x\in\mathbb{N}: 3\mid x}\), and \(C={x\in\mathbb{N}: 5\mid x}\), what is (A\cap\(B\cup C\))?

Explanation opens after your attempt

Correct Answer

A. ({3,5,6,9,10,12,15})

Step 1

Concept

Numbers up to (15) divisible by (3) or (5) are taken. They are ({3,5,6,9,10,12,15}).

Step 2

Why this answer is correct

The correct answer is A. ({3,5,6,9,10,12,15}). Numbers up to (15) divisible by (3) or (5) are taken. They are ({3,5,6,9,10,12,15}).

Step 3

Exam Tip

(15) तक (3) या (5) से विभाज्य संख्याएं ली जाती हैं। वे ({3,5,6,9,10,12,15}) हैं।

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Question 47/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A={x\in\mathbb{N}: x\le 30,\ 2\mid x}\) और \(B={x\in\mathbb{N}: x\le 30,\ 3\mid x}\), तो \(A\cap B\) क्या है?

If \(A={x\in\mathbb{N}: x\le 30,\ 2\mid x}\) and \(B={x\in\mathbb{N}: x\le 30,\ 3\mid x}\), what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ({6,12,18,24,30})

Step 1

Concept

Numbers divisible by both (2) and (3) are divisible by (6). Up to (30), these are ({6,12,18,24,30}).

Step 2

Why this answer is correct

The correct answer is A. ({6,12,18,24,30}). Numbers divisible by both (2) and (3) are divisible by (6). Up to (30), these are ({6,12,18,24,30}).

Step 3

Exam Tip

जो संख्याएं (2) और (3) दोनों से विभाज्य हैं, वे (6) से विभाज्य हैं। (30) तक ऐसी संख्याएं ({6,12,18,24,30}) हैं।

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Question 48/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A=\{1,2,3,4,5\}\), \(B=\{2,3,6\}\) और \(C=\{3,4,7\}\), तो (A-\(B\cap C\)) क्या है?

If \(A=\{1,2,3,4,5\}\), \(B=\{2,3,6\}\), and \(C=\{3,4,7\}\), what is (A-\(B\cap C\))?

Explanation opens after your attempt

Correct Answer

A. ({1,2,4,5})

Step 1

Concept

\(B\cap C={3}\). Removing (3) from (A) gives ({1,2,4,5}).

Step 2

Why this answer is correct

The correct answer is A. ({1,2,4,5}). \(B\cap C={3}\). Removing (3) from (A) gives ({1,2,4,5}).

Step 3

Exam Tip

\(B\cap C={3}\) है। (A) से (3) हटाने पर ({1,2,4,5}) मिलता है।

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Question 49/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि \(A={x\in\mathbb{Z}: -4\le x\le4}\) और \(B={x\in\mathbb{Z}: x^2\ge9}\), तो \(A\cap B\) क्या है?

If \(A={x\in\mathbb{Z}: -4\le x\le4}\) and \(B={x\in\mathbb{Z}: x^2\ge9}\), what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ({-4,-3,3,4})

Step 1

Concept

(A) contains integers from (-4) to (4). Among them, \(x^2\ge9\) is true only for (-4,-3,3,4).

Step 2

Why this answer is correct

The correct answer is A. ({-4,-3,3,4}). (A) contains integers from (-4) to (4). Among them, \(x^2\ge9\) is true only for (-4,-3,3,4).

Step 3

Exam Tip

(A) में (-4) से (4) तक पूर्णांक हैं। इनमें \(x^2\ge9\) केवल (-4,-3,3,4) के लिए सत्य है।

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Question 50/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 16

यदि (A), (B) और (C) ऐसे समुच्चय हैं कि (A-B=A-C) और \(A\cap B=A\cap C\), तो (A) के संदर्भ में कौन-सा कथन सही है?

If (A), (B), and (C) are sets such that (A-B=A-C) and \(A\cap B=A\cap C\), which statement is correct with respect to (A)?

Explanation opens after your attempt

Correct Answer

A. (A) के अंदर (B) और (C) समान व्यवहार करते हैं(B) and (C) behave the same inside (A)

Step 1

Concept

The two given parts make membership of (B) and (C) the same inside (A). Outside (A), (B) and (C) may differ.

Step 2

Why this answer is correct

The correct answer is A. (A) के अंदर (B) और (C) समान व्यवहार करते हैं / (B) and (C) behave the same inside (A). The two given parts make membership of (B) and (C) the same inside (A). Outside (A), (B) and (C) may differ.

Step 3

Exam Tip

दिए गए दोनों भाग (A) के भीतर (B) और (C) की सदस्यता को समान बनाते हैं। (A) के बाहर (B) और (C) अलग हो सकते हैं।

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Question 51/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{Z}:-4\le x\le 6}\), \(B={x\in\mathbb{Z}:x^2\le16}\) और \(C={x\in\mathbb{Z}:2\mid x}\) हैं, तो (\(A\cap B\)-C) क्या है?

If \(A={x\in\mathbb{Z}:-4\le x\le 6}\), \(B={x\in\mathbb{Z}:x^2\le16}\), and \(C={x\in\mathbb{Z}:2\mid x}\), what is (\(A\cap B\)-C)?

Explanation opens after your attempt

Correct Answer

A. ({-3,-1,1,3})

Step 1

Concept

\(A\cap B={-4,-3,-2,-1,0,1,2,3,4}\), and the even elements of (C) are removed. Hence the remaining odd elements are ({-3,-1,1,3}).

Step 2

Why this answer is correct

The correct answer is A. ({-3,-1,1,3}). \(A\cap B={-4,-3,-2,-1,0,1,2,3,4}\), and the even elements of (C) are removed. Hence the remaining odd elements are ({-3,-1,1,3}).

Step 3

Exam Tip

\(A\cap B={-4,-3,-2,-1,0,1,2,3,4}\) है और (C) के सम तत्व हटते हैं। इसलिए विषम तत्व ({-3,-1,1,3}) बचते हैं।

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Question 52/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{Z}: -7\le x\le 7}\), \(B={x\in\mathbb{Z}: x^2\le 16}\) और \(C={x\in\mathbb{Z}: 3\mid x}\) हैं, तो \((A-B)\cap C\) क्या है?

If \(A={x\in\mathbb{Z}: -7\le x\le 7}\), \(B={x\in\mathbb{Z}: x^2\le 16}\), and \(C={x\in\mathbb{Z}: 3\mid x}\), what is \((A-B)\cap C\)?

Explanation opens after your attempt

Correct Answer

A. ({-6,6})

Step 1

Concept

\(B=\{-4,-3,-2,-1,0,1,2,3,4\}\), so (A-B={-7,-6,-5,5,6,7}). The elements divisible by (3) are ({-6,6}).

Step 2

Why this answer is correct

The correct answer is A. ({-6,6}). \(B=\{-4,-3,-2,-1,0,1,2,3,4\}\), so (A-B={-7,-6,-5,5,6,7}). The elements divisible by (3) are ({-6,6}).

Step 3

Exam Tip

\(B=\{-4,-3,-2,-1,0,1,2,3,4\}\) है, इसलिए (A-B={-7,-6,-5,5,6,7}) होगा। इनमें (3) से विभाज्य तत्व ({-6,6}) हैं।

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Question 53/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A\cup B={2,4,6,8,10,12,14}\), (A-B={2,10}) और (B-A={6,14}) है, तो \(A\cap B\) क्या है?

If \(A\cup B={2,4,6,8,10,12,14}\), (A-B={2,10}), and (B-A={6,14}), what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ({4,8,12})

Step 1

Concept

The union is made of three disjoint parts (A-B), \(A\cap B\), and (B-A). Removing the given only-parts leaves ({4,8,12}).

Step 2

Why this answer is correct

The correct answer is A. ({4,8,12}). The union is made of three disjoint parts (A-B), \(A\cap B\), and (B-A). Removing the given only-parts leaves ({4,8,12}).

Step 3

Exam Tip

संघ तीन अलग भागों (A-B), \(A\cap B\) और (B-A) से बनता है। दिए गए केवल वाले भाग हटाने पर ({4,8,12}) बचता है।

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Question 54/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{R}: -3\le x<5}\), \(B={x\in\mathbb{R}: 1<x\le 8}\) और \(C={x\in\mathbb{R}: x\le 2}\) हैं, तो (\(A\cup B\)\cap C) क्या है?

If \(A={x\in\mathbb{R}: -3\le x<5}\), \(B={x\in\mathbb{R}: 1<x\le 8}\), and \(C={x\in\mathbb{R}: x\le 2}\), what is (\(A\cup B\)\cap C)?

Explanation opens after your attempt

Correct Answer

A. ([-3,2])

Step 1

Concept

\(A\cup B=[-3,8]\). Intersecting it with \(x\le 2\) gives ([-3,2]).

Step 2

Why this answer is correct

The correct answer is A. ([-3,2]). \(A\cup B=[-3,8]\). Intersecting it with \(x\le 2\) gives ([-3,2]).

Step 3

Exam Tip

\(A\cup B=[-3,8]\) है। अब \(x\le 2\) से प्रतिच्छेद लेने पर ([-3,2]) मिलता है।

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Question 55/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि (n(A)=58), (n(B)=44), (n(A-B)=23) है, तो (n\(A\cup B\)) क्या होगा?

If (n(A)=58), (n(B)=44), and (n(A-B)=23), what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (,67,)

Step 1

Concept

(n\(A\cap B\)=58-23=35). Therefore (n\(A\cup B\)=58+44-35=67).

Step 2

Why this answer is correct

The correct answer is A. (,67,). (n\(A\cap B\)=58-23=35). Therefore (n\(A\cup B\)=58+44-35=67).

Step 3

Exam Tip

(n\(A\cap B\)=58-23=35) है। इसलिए (n\(A\cup B\)=58+44-35=67)।

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Question 56/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि (n(A)=64), (n(B)=57), (n\(A\cap B\)=29) और (n(U)=110) है, तो (n(\(A\cup B\)')) कितना है?

If (n(A)=64), (n(B)=57), (n\(A\cap B\)=29), and (n(U)=110), what is (n(\(A\cup B\)'))?

Explanation opens after your attempt

Correct Answer

A. (,18,)

Step 1

Concept

(n\(A\cup B\)=64+57-29=92). Therefore (n(\(A\cup B\)')=110-92=18).

Step 2

Why this answer is correct

The correct answer is A. (,18,). (n\(A\cup B\)=64+57-29=92). Therefore (n(\(A\cup B\)')=110-92=18).

Step 3

Exam Tip

(n\(A\cup B\)=64+57-29=92) है। इसलिए (n(\(A\cup B\)')=110-92=18)।

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Question 57/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{R}:x^2-5x+6\le0}\) और \(B={x\in\mathbb{R}:x<4}\), तो (A-B) क्या है?

If \(A={x\in\mathbb{R}:x^2-5x+6\le0}\) and \(B={x\in\mathbb{R}:x<4}\), what is (A-B)?

Explanation opens after your attempt

Correct Answer

A. \(\varnothing\)

Step 1

Concept

\(x^2-5x+6\le0\) gives (A=[2,3]). Every element of (A) lies in (B), so \(A-B=\varnothing\).

Step 2

Why this answer is correct

The correct answer is A. \(\varnothing\). \(x^2-5x+6\le0\) gives (A=[2,3]). Every element of (A) lies in (B), so \(A-B=\varnothing\).

Step 3

Exam Tip

\(x^2-5x+6\le0\) से (A=[2,3]) मिलता है। (A) का हर तत्व (B) में है, इसलिए \(A-B=\varnothing\)।

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Question 58/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A\subseteq B\) और \(C\cap B=\varnothing\) है, तो (\(A\cup C\)\cap B) किसके बराबर है?

If \(A\subseteq B\) and \(C\cap B=\varnothing\), then (\(A\cup C\)\cap B) is equal to which set?

Explanation opens after your attempt

Correct Answer

A. (A)

Step 1

Concept

Since \(A\subseteq B\), all of (A) lies in (B), and (C) has no common element with (B). Hence only (A) remains in the intersection.

Step 2

Why this answer is correct

The correct answer is A. (A). Since \(A\subseteq B\), all of (A) lies in (B), and (C) has no common element with (B). Hence only (A) remains in the intersection.

Step 3

Exam Tip

\(A\subseteq B\) होने से (A) का पूरा भाग (B) में रहता है और (C) का (B) से कोई सामान्य तत्व नहीं है। इसलिए प्रतिच्छेद में केवल (A) बचेगा।

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Question 59/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{R}:|x-2|\le3}\) और \(B={x\in\mathbb{R}:x^2\le4}\), तो \(A\cap B\) क्या है?

If \(A={x\in\mathbb{R}:|x-2|\le3}\) and \(B={x\in\mathbb{R}:x^2\le4}\), what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ([-1,2])

Step 1

Concept

(A=[-1,5]) and (B=[-2,2]). Their common part is ([-1,2]).

Step 2

Why this answer is correct

The correct answer is A. ([-1,2]). (A=[-1,5]) and (B=[-2,2]). Their common part is ([-1,2]).

Step 3

Exam Tip

(A=[-1,5]) और (B=[-2,2]) है। दोनों का समान भाग ([-1,2]) है।

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Question 60/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A\subseteq U\), \(B\subseteq U\) और \(A-B=A\cap B'\) है, तो ((A-B)\cup\(A\cap B\)) किसके बराबर है?

If \(A\subseteq U\), \(B\subseteq U\), and \(A-B=A\cap B'\), then ((A-B)\cup\(A\cap B\)) is equal to which set?

Explanation opens after your attempt

Correct Answer

A. (A)

Step 1

Concept

(A-B) and \(A\cap B\) are two disjoint parts of (A). Their union gives the whole set (A).

Step 2

Why this answer is correct

The correct answer is A. (A). (A-B) and \(A\cap B\) are two disjoint parts of (A). Their union gives the whole set (A).

Step 3

Exam Tip

(A-B) और \(A\cap B\), (A) के दो अलग भाग हैं। इनके संघ से पूरा (A) मिल जाता है।

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Question 61/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A=\{1,2,3,4,5,6,7\}\), \(B=\{2,4,6,8\}\) और \(C=\{1,4,7,8\}\), तो (\(A\cup B\)\cap C) क्या है?

If \(A=\{1,2,3,4,5,6,7\}\), \(B=\{2,4,6,8\}\), and \(C=\{1,4,7,8\}\), what is (\(A\cup B\)\cap C)?

Explanation opens after your attempt

Correct Answer

A. ({1,4,7,8})

Step 1

Concept

\(A\cup B={1,2,3,4,5,6,7,8}\). Its intersection with (C) gives the whole \(C=\{1,4,7,8\}\).

Step 2

Why this answer is correct

The correct answer is A. ({1,4,7,8}). \(A\cup B={1,2,3,4,5,6,7,8}\). Its intersection with (C) gives the whole \(C=\{1,4,7,8\}\).

Step 3

Exam Tip

\(A\cup B={1,2,3,4,5,6,7,8}\) है। इसका (C) से प्रतिच्छेद पूरा \(C=\{1,4,7,8\}\) देता है।

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Question 62/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि (A-B={p,q}), \(A\cap B={r,s,t}\) और (B-A={u}), तो (n(A)) कितना है?

If (A-B={p,q}), \(A\cap B={r,s,t}\), and (B-A={u}), what is (n(A))?

Explanation opens after your attempt

Correct Answer

A. (,5,)

Step 1

Concept

Set (A) contains the elements of (A-B) and \(A\cap B\). Hence (n(A)=2+3=5).

Step 2

Why this answer is correct

The correct answer is A. (,5,). Set (A) contains the elements of (A-B) and \(A\cap B\). Hence (n(A)=2+3=5).

Step 3

Exam Tip

समुच्चय (A) में (A-B) और \(A\cap B\) के तत्व आते हैं। इसलिए (n(A)=2+3=5)।

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Question 63/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A\cap B=\varnothing\) और \(A\cup B=A\cup C\) है, तो \(B\subseteq C\) होने के लिए कौन-सी अतिरिक्त शर्त पर्याप्त है?

If \(A\cap B=\varnothing\) and \(A\cup B=A\cup C\), which additional condition is sufficient for \(B\subseteq C\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

If \(A\cap C=\varnothing\), then the part outside (A) must match in the equal unions. Hence \(B\subseteq C\).

Step 2

Why this answer is correct

The correct answer is A. \(A\cap C=\varnothing\). If \(A\cap C=\varnothing\), then the part outside (A) must match in the equal unions. Hence \(B\subseteq C\).

Step 3

Exam Tip

यदि \(A\cap C=\varnothing\), तो संघ की समानता में (A) से बाहर वाला भाग समान होना चाहिए। इसलिए \(B\subseteq C\) मिलता है।

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Question 64/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{N}:x\le40,\ 4\mid x}\) और \(B={x\in\mathbb{N}:x\le40,\ 6\mid x}\), तो \(A\cap B\) क्या है?

If \(A={x\in\mathbb{N}:x\le40,\ 4\mid x}\) and \(B={x\in\mathbb{N}:x\le40,\ 6\mid x}\), what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ({12,24,36})

Step 1

Concept

A number divisible by both (4) and (6) is divisible by (\operatorname{lcm}(4,6)=12). Up to (40), the multiples are ({12,24,36}).

Step 2

Why this answer is correct

The correct answer is A. ({12,24,36}). A number divisible by both (4) and (6) is divisible by (\operatorname{lcm}(4,6)=12). Up to (40), the multiples are ({12,24,36}).

Step 3

Exam Tip

जो संख्या (4) और (6) दोनों से विभाज्य है, वह (\operatorname{lcm}(4,6)=12) से विभाज्य होगी। (40) तक ऐसे गुणज ({12,24,36}) हैं।

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Question 65/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{N}:x\mid 72}\) और \(B={x\in\mathbb{N}:x\mid 90}\), तो \(A\cap B\) क्या है?

If \(A={x\in\mathbb{N}:x\mid 72}\) and \(B={x\in\mathbb{N}:x\mid 90}\), what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ({1,2,3,6,9,18})

Step 1

Concept

Common divisors are divisors of (\gcd(72,90)=18). Thus \(A\cap B={1,2,3,6,9,18}\).

Step 2

Why this answer is correct

The correct answer is A. ({1,2,3,6,9,18}). Common divisors are divisors of (\gcd(72,90)=18). Thus \(A\cap B={1,2,3,6,9,18}\).

Step 3

Exam Tip

सामान्य भाजक (\gcd(72,90)=18) के भाजक होंगे। अतः \(A\cap B={1,2,3,6,9,18}\)।

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Question 66/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A=\{1,2,3,4,5\}\), \(B=\{3,4,5,6\}\) और \(C=\{5,6,7\}\), तो \((A-B)\cup(B-C)\) क्या है?

If \(A=\{1,2,3,4,5\}\), \(B=\{3,4,5,6\}\), and \(C=\{5,6,7\}\), what is \((A-B)\cup(B-C)\)?

Explanation opens after your attempt

Correct Answer

A. ({1,2,3,4})

Step 1

Concept

(A-B={1,2}) and (B-C={3,4}). Their union is ({1,2,3,4}).

Step 2

Why this answer is correct

The correct answer is A. ({1,2,3,4}). (A-B={1,2}) and (B-C={3,4}). Their union is ({1,2,3,4}).

Step 3

Exam Tip

(A-B={1,2}) और (B-C={3,4}) है। इनका संघ ({1,2,3,4}) है।

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Question 67/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

कौन-सा विकल्प (\(A\cup B\)-A) के बराबर है?

Which option is equal to (\(A\cup B\)-A)?

Explanation opens after your attempt

Correct Answer

A. (B-A)

Step 1

Concept

Removing (A) from the union leaves only the elements that are in (B) but not in (A). Hence the result is (B-A).

Step 2

Why this answer is correct

The correct answer is A. (B-A). Removing (A) from the union leaves only the elements that are in (B) but not in (A). Hence the result is (B-A).

Step 3

Exam Tip

संघ से (A) हटाने पर केवल वे तत्व बचते हैं जो (B) में हैं पर (A) में नहीं। इसलिए परिणाम (B-A) है।

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Question 68/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A\cap B=A\) और \(B\cap C=B\) हैं, तो कौन-सा निष्कर्ष सही है?

If \(A\cap B=A\) and \(B\cap C=B\), which conclusion is correct?

Explanation opens after your attempt

Correct Answer

A. \(A\subseteq C\)

Step 1

Concept

\(A\cap B=A\) gives \(A\subseteq B\), and \(B\cap C=B\) gives \(B\subseteq C\). Therefore \(A\subseteq C\).

Step 2

Why this answer is correct

The correct answer is A. \(A\subseteq C\). \(A\cap B=A\) gives \(A\subseteq B\), and \(B\cap C=B\) gives \(B\subseteq C\). Therefore \(A\subseteq C\).

Step 3

Exam Tip

\(A\cap B=A\) से \(A\subseteq B\) और \(B\cap C=B\) से \(B\subseteq C\) मिलता है। इसलिए \(A\subseteq C\)।

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Question 69/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{Z}:x^2-1=0}\) और \(B={x\in\mathbb{Z}:x^2=1}\), तो (A-B) क्या है?

If \(A={x\in\mathbb{Z}:x^2-1=0}\) and \(B={x\in\mathbb{Z}:x^2=1}\), what is (A-B)?

Explanation opens after your attempt

Correct Answer

A. \(\varnothing\)

Step 1

Concept

Both conditions give the same set ({-1,1}). The difference of equal sets is the empty set.

Step 2

Why this answer is correct

The correct answer is A. \(\varnothing\). Both conditions give the same set ({-1,1}). The difference of equal sets is the empty set.

Step 3

Exam Tip

दोनों शर्तों से वही समुच्चय ({-1,1}) मिलता है। समान समुच्चयों का अंतर खाली समुच्चय होता है।

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Question 70/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि (n\(A\cup B\)=96), (n\(A\cap B\)=18) और (n(A-B)=41) है, तो (n(B)) कितना है?

If (n\(A\cup B\)=96), (n\(A\cap B\)=18), and (n(A-B)=41), what is (n(B))?

Explanation opens after your attempt

Correct Answer

A. (,55,)

Step 1

Concept

The sum of (A-B), \(A\cap B\), and (B-A) is (96), so (B-A=96-41-18=37). Thus (n(B)=37+18=55).

Step 2

Why this answer is correct

The correct answer is A. (,55,). The sum of (A-B), \(A\cap B\), and (B-A) is (96), so (B-A=96-41-18=37). Thus (n(B)=37+18=55).

Step 3

Exam Tip

(A-B), \(A\cap B\) और (B-A) का योग (96) है, इसलिए (B-A=96-41-18=37)। अतः (n(B)=37+18=55)।

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Question 71/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x:x\) अंग्रेजी शब्द (ALGEBRA) का अक्षर है(}) और \(B={x:x\) अंग्रेजी शब्द (GEOMETRY) का अक्षर है(}), तो \(A\cup B\) क्या है?

If \(A={x:x\) is a letter of the English word (ALGEBRA)(}) and \(B={x:x\) is a letter of the English word (GEOMETRY)(}), what is \(A\cup B\)?

Explanation opens after your attempt

Correct Answer

A. ({A,B,E,G,L,M,O,R,T,Y})

Step 1

Concept

Repeated letters are written only once in a set. The union of all distinct letters from both words is ({A,B,E,G,L,M,O,R,T,Y}).

Step 2

Why this answer is correct

The correct answer is A. ({A,B,E,G,L,M,O,R,T,Y}). Repeated letters are written only once in a set. The union of all distinct letters from both words is ({A,B,E,G,L,M,O,R,T,Y}).

Step 3

Exam Tip

समुच्चय में दोहराए गए अक्षर एक बार ही लिखे जाते हैं। दोनों शब्दों के सभी अलग अक्षरों का संघ ({A,B,E,G,L,M,O,R,T,Y}) है।

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Question 72/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

\(यदि (A={x\in\mathbb{N}:x\le25,\ x\) अभाज्य है\(}) और (B={x\in\mathbb{N}:x\le25,\ x\) विषम है}), तो (B-A) क्या है?

\(If (A={x\in\mathbb{N}:x\le25,\ x\) is prime\(}) and (B={x\in\mathbb{N}:x\le25,\ x\) is odd}), what is (B-A)?

Explanation opens after your attempt

Correct Answer

A. ({1,9,15,21,25})

Step 1

Concept

From the odd numbers in (B), remove the primes in (A). The remaining odd composites and (1) are ({1,9,15,21,25}).

Step 2

Why this answer is correct

The correct answer is A. ({1,9,15,21,25}). From the odd numbers in (B), remove the primes in (A). The remaining odd composites and (1) are ({1,9,15,21,25}).

Step 3

Exam Tip

(B) की विषम संख्याओं में से अभाज्य संख्याएं हटानी हैं। इसलिए बची हुई विषम संयुक्त संख्याएं और (1), अर्थात ({1,9,15,21,25}), मिलती हैं।

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Question 73/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(U={1,2,\ldots,20}\), \(A={x\in U:2\mid x}\) और \(B={x\in U:5\mid x}\), तो (\(A\cup B\)') क्या है?

If \(U={1,2,\ldots,20}\), \(A={x\in U:2\mid x}\), and \(B={x\in U:5\mid x}\), what is (\(A\cup B\)')?

Explanation opens after your attempt

Correct Answer

A. ({1,3,7,9,11,13,17,19})

Step 1

Concept

Remove numbers divisible by (2) or (5) from (U). The remaining numbers are ({1,3,7,9,11,13,17,19}).

Step 2

Why this answer is correct

The correct answer is A. ({1,3,7,9,11,13,17,19}). Remove numbers divisible by (2) or (5) from (U). The remaining numbers are ({1,3,7,9,11,13,17,19}).

Step 3

Exam Tip

(2) या (5) से विभाज्य संख्याओं को (U) से हटाते हैं। बची संख्याएं ({1,3,7,9,11,13,17,19}) हैं।

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Question 74/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{R}:x\le1}\) और \(B={x\in\mathbb{R}:x>-2}\), तो \(A\cap B\) क्या है?

If \(A={x\in\mathbb{R}:x\le1}\) and \(B={x\in\mathbb{R}:x>-2}\), what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ((-2,1])

Step 1

Concept

Combining both conditions gives \(-2<x\le1\). Hence the intersection is ((-2,1]).

Step 2

Why this answer is correct

The correct answer is A. ((-2,1]). Combining both conditions gives \(-2<x\le1\). Hence the intersection is ((-2,1]).

Step 3

Exam Tip

दोनों शर्तें साथ रखने पर \(-2<x\le1\) मिलता है। इसलिए प्रतिच्छेद ((-2,1]) है।

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Question 75/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A\cup B=B\) और \(A\cap C=C\) हैं, तो कौन-सा कथन अवश्य सत्य है?

If \(A\cup B=B\) and \(A\cap C=C\), which statement must be true?

Explanation opens after your attempt

Correct Answer

A. \(C\subseteq B\)

Step 1

Concept

\(A\cup B=B\) gives \(A\subseteq B\), and \(A\cap C=C\) gives \(C\subseteq A\). Therefore \(C\subseteq B\).

Step 2

Why this answer is correct

The correct answer is A. \(C\subseteq B\). \(A\cup B=B\) gives \(A\subseteq B\), and \(A\cap C=C\) gives \(C\subseteq A\). Therefore \(C\subseteq B\).

Step 3

Exam Tip

\(A\cup B=B\) से \(A\subseteq B\) और \(A\cap C=C\) से \(C\subseteq A\) मिलता है। इसलिए \(C\subseteq B\)।

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Question 76/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

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

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

Explanation opens after your attempt

Correct Answer

A. ({1,3,5})

Step 1

Concept

(A-B={1,3,5}). Its intersection with (C) gives the same set ({1,3,5}).

Step 2

Why this answer is correct

The correct answer is A. ({1,3,5}). (A-B={1,3,5}). Its intersection with (C) gives the same set ({1,3,5}).

Step 3

Exam Tip

(A-B={1,3,5}) है। इसका (C) से प्रतिच्छेद वही ({1,3,5}) देता है।

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Question 77/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{Z}: -6\le x\le6}\) और \(B={x\in\mathbb{Z}:x^2<10}\), तो (A-B) क्या है?

If \(A={x\in\mathbb{Z}: -6\le x\le6}\) and \(B={x\in\mathbb{Z}:x^2<10}\), what is (A-B)?

Explanation opens after your attempt

Correct Answer

A. ({-6,-5,-4,4,5,6})

Step 1

Concept

\(B=\{-3,-2,-1,0,1,2,3\}\). Removing it from (A) leaves ({-6,-5,-4,4,5,6}).

Step 2

Why this answer is correct

The correct answer is A. ({-6,-5,-4,4,5,6}). \(B=\{-3,-2,-1,0,1,2,3\}\). Removing it from (A) leaves ({-6,-5,-4,4,5,6}).

Step 3

Exam Tip

\(B=\{-3,-2,-1,0,1,2,3\}\) है। इसे (A) से हटाने पर ({-6,-5,-4,4,5,6}) बचता है।

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Question 78/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A\triangle B=(A-B)\cup(B-A)\) और (n\(A\triangle B\)=26), (n\(A\cap B\)=9) है, तो (n\(A\cup B\)) कितना है?

If \(A\triangle B=(A-B)\cup(B-A)\) and (n\(A\triangle B\)=26), (n\(A\cap B\)=9), what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (,35,)

Step 1

Concept

\(A\cup B\) is made of the disjoint parts symmetric difference and intersection. Hence (n\(A\cup B\)=26+9=35).

Step 2

Why this answer is correct

The correct answer is A. (,35,). \(A\cup B\) is made of the disjoint parts symmetric difference and intersection. Hence (n\(A\cup B\)=26+9=35).

Step 3

Exam Tip

\(A\cup B\) सममित अंतर और प्रतिच्छेद के अलग भागों से बनता है। इसलिए (n\(A\cup B\)=26+9=35)।

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Question 79/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A-B=\varnothing\) और \(B-C=\varnothing\) है, तो कौन-सा निष्कर्ष सही है?

If \(A-B=\varnothing\) and \(B-C=\varnothing\), which conclusion is correct?

Explanation opens after your attempt

Correct Answer

A. \(A\subseteq C\)

Step 1

Concept

\(A-B=\varnothing\) gives \(A\subseteq B\), and \(B-C=\varnothing\) gives \(B\subseteq C\). Therefore \(A\subseteq C\).

Step 2

Why this answer is correct

The correct answer is A. \(A\subseteq C\). \(A-B=\varnothing\) gives \(A\subseteq B\), and \(B-C=\varnothing\) gives \(B\subseteq C\). Therefore \(A\subseteq C\).

Step 3

Exam Tip

\(A-B=\varnothing\) से \(A\subseteq B\) और \(B-C=\varnothing\) से \(B\subseteq C\) मिलता है। इसलिए \(A\subseteq C\)।

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Question 80/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{R}:1\le x\le9}\), \(B={x\in\mathbb{R}:3<x<7}\), तो (A-B) क्या है?

If \(A={x\in\mathbb{R}:1\le x\le9}\), \(B={x\in\mathbb{R}:3<x<7}\), what is (A-B)?

Explanation opens after your attempt

Correct Answer

A. \([1,3]\cup[7,9]\)

Step 1

Concept

(B) does not include (3) and (7), so they remain in (A-B). The result is \([1,3]\cup[7,9]\).

Step 2

Why this answer is correct

The correct answer is A. \([1,3]\cup[7,9]\). (B) does not include (3) and (7), so they remain in (A-B). The result is \([1,3]\cup[7,9]\).

Step 3

Exam Tip

(B) में (3) और (7) शामिल नहीं हैं, इसलिए वे (A-B) में रहेंगे। परिणाम \([1,3]\cup[7,9]\) है।

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Question 81/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि (A) और (B) ऐसे समुच्चय हैं कि \(A\cap B=\varnothing\), तो (\(A\cup B\)-B) क्या है?

If (A) and (B) are sets such that \(A\cap B=\varnothing\), what is (\(A\cup B\)-B)?

Explanation opens after your attempt

Correct Answer

A. (A)

Step 1

Concept

For disjoint sets, removing (B) from the union leaves only (A). Hence (\(A\cup B\)-B=A).

Step 2

Why this answer is correct

The correct answer is A. (A). For disjoint sets, removing (B) from the union leaves only (A). Hence (\(A\cup B\)-B=A).

Step 3

Exam Tip

असंबद्ध समुच्चयों में (B) हटाने पर संघ से केवल (A) बचता है। इसलिए (\(A\cup B\)-B=A)।

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Question 82/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि (n(U)=120), (n(A)=70), (n(B)=65) और (n\(A\cap B\)=40), तो (n\(A'\cap B'\)) क्या है?

If (n(U)=120), (n(A)=70), (n(B)=65), and (n\(A\cap B\)=40), what is (n\(A'\cap B'\))?

Explanation opens after your attempt

Correct Answer

A. (,25,)

Step 1

Concept

(n\(A\cup B\)=70+65-40=95). Therefore (n\(A'\cap B'\)=n(\(A\cup B\)')=120-95=25).

Step 2

Why this answer is correct

The correct answer is A. (,25,). (n\(A\cup B\)=70+65-40=95). Therefore (n\(A'\cap B'\)=n(\(A\cup B\)')=120-95=25).

Step 3

Exam Tip

(n\(A\cup B\)=70+65-40=95) है। इसलिए (n\(A'\cap B'\)=n(\(A\cup B\)')=120-95=25)।

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Question 83/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A=\{1,2,4,8,16\}\), \(B=\{1,3,9,27\}\) और \(C=\{1,5,25\}\), तो (\(A\cap B\)\cup\(B\cap C\)\cup\(C\cap A\)) क्या है?

If \(A=\{1,2,4,8,16\}\), \(B=\{1,3,9,27\}\), and \(C=\{1,5,25\}\), what is (\(A\cap B\)\cup\(B\cap C\)\cup\(C\cap A\))?

Explanation opens after your attempt

Correct Answer

A. ({1})

Step 1

Concept

The only common element in each pair of sets is (1). Hence the union of all pairwise intersections is ({1}).

Step 2

Why this answer is correct

The correct answer is A. ({1}). The only common element in each pair of sets is (1). Hence the union of all pairwise intersections is ({1}).

Step 3

Exam Tip

हर दो समुच्चयों का सामान्य तत्व केवल (1) है। इसलिए सभी युग्म प्रतिच्छेदों का संघ ({1}) है।

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Question 84/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{Z}: -3\le x\le8}\), \(B={x\in\mathbb{Z}:0\le x\le5}\) और \(C={x\in\mathbb{Z}:x\) सम है(}), तो \((A-B)\cap C\) क्या है?

If \(A={x\in\mathbb{Z}: -3\le x\le8}\), \(B={x\in\mathbb{Z}:0\le x\le5}\), and \(C={x\in\mathbb{Z}:x\) is even(}), what is \((A-B)\cap C\)?

Explanation opens after your attempt

Correct Answer

A. ({-2,6,8})

Step 1

Concept

(A-B={-3,-2,-1,6,7,8}). The even elements among these are ({-2,6,8}).

Step 2

Why this answer is correct

The correct answer is A. ({-2,6,8}). (A-B={-3,-2,-1,6,7,8}). The even elements among these are ({-2,6,8}).

Step 3

Exam Tip

(A-B={-3,-2,-1,6,7,8}) है। इनमें सम तत्व ({-2,6,8}) हैं।

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Question 85/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{N}:x\le10}\), \(B={x\in\mathbb{N}:x\) विषम है(}) और \(C={x\in\mathbb{N}:x\) अभाज्य है(}), तो \(A\cap(B-C)\) क्या है?

If \(A={x\in\mathbb{N}:x\le10}\), \(B={x\in\mathbb{N}:x\) is odd(}), and \(C={x\in\mathbb{N}:x\) is prime(}), what is \(A\cap(B-C)\)?

Explanation opens after your attempt

Correct Answer

A. ({1,9})

Step 1

Concept

The odd numbers up to (10) are ({1,3,5,7,9}). Removing primes leaves ({1,9}).

Step 2

Why this answer is correct

The correct answer is A. ({1,9}). The odd numbers up to (10) are ({1,3,5,7,9}). Removing primes leaves ({1,9}).

Step 3

Exam Tip

(10) तक की विषम संख्याएं ({1,3,5,7,9}) हैं। इनमें अभाज्य हटाने पर ({1,9}) बचता है।

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Question 86/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A\cup B=A\cup C\) और \(A\cap B=A\cap C\), तो निम्न में कौन-सा सही है?

If \(A\cup B=A\cup C\) and \(A\cap B=A\cap C\), which of the following is correct?

Explanation opens after your attempt

Correct Answer

A. (B=C)

Step 1

Concept

These two equalities make the membership of (B) and (C) the same both inside and outside (A). Hence (B=C).

Step 2

Why this answer is correct

The correct answer is A. (B=C). These two equalities make the membership of (B) and (C) the same both inside and outside (A). Hence (B=C).

Step 3

Exam Tip

इन दोनों समानताओं से (A) के अंदर और बाहर (B) और (C) की सदस्यता समान हो जाती है। अतः (B=C)।

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Question 87/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{R}:x^2-4x+3>0}\) और \(B={x\in\mathbb{R}:x>1}\), तो \(A\cap B\) क्या है?

If \(A={x\in\mathbb{R}:x^2-4x+3>0}\) and \(B={x\in\mathbb{R}:x>1}\), what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. (\(3,\infty\))

Step 1

Concept

\(x^2-4x+3>0\) gives (x<1) or (x>3). With (x>1), the common part is (\(3,\infty\)).

Step 2

Why this answer is correct

The correct answer is A. (\(3,\infty\)). \(x^2-4x+3>0\) gives (x<1) or (x>3). With (x>1), the common part is (\(3,\infty\)).

Step 3

Exam Tip

\(x^2-4x+3>0\) से (x<1) या (x>3) मिलता है। (x>1) के साथ सामान्य भाग (\(3,\infty\)) है।

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Question 88/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{R}:x^2\le9}\) और \(B={x\in\mathbb{R}:x^2<1}\), तो (A-B) क्या है?

If \(A={x\in\mathbb{R}:x^2\le9}\) and \(B={x\in\mathbb{R}:x^2<1}\), what is (A-B)?

Explanation opens after your attempt

Correct Answer

A. \([-3,-1]\cup[1,3]\)

Step 1

Concept

(A=[-3,3]) and (B=(-1,1)). Removing (B) gives \([-3,-1]\cup[1,3]\).

Step 2

Why this answer is correct

The correct answer is A. \([-3,-1]\cup[1,3]\). (A=[-3,3]) and (B=(-1,1)). Removing (B) gives \([-3,-1]\cup[1,3]\).

Step 3

Exam Tip

(A=[-3,3]) और (B=(-1,1)) है। (B) हटाने पर \([-3,-1]\cup[1,3]\) मिलता है।

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Question 89/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A=\{1,2,3\}\) और \(B=\{2,3,4,5\}\), तो (\mathcal{P}\(A\cup B\)) में कितने तत्व हैं?

If \(A=\{1,2,3\}\) and \(B=\{2,3,4,5\}\), how many elements are in (\mathcal{P}\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (,32,)

Step 1

Concept

\(A\cup B={1,2,3,4,5}\) has (5) elements. Its power set has \(2^5=32\) elements.

Step 2

Why this answer is correct

The correct answer is A. (,32,). \(A\cup B={1,2,3,4,5}\) has (5) elements. Its power set has \(2^5=32\) elements.

Step 3

Exam Tip

\(A\cup B={1,2,3,4,5}\) में (5) तत्व हैं। घात समुच्चय में \(2^5=32\) तत्व होते हैं।

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Question 90/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6\}\), तो (n(\mathcal{P}(A-B))) कितना है?

If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,4,6\}\), what is (n(\mathcal{P}(A-B)))?

Explanation opens after your attempt

Correct Answer

A. (,8,)

Step 1

Concept

(A-B={1,3,5}) has (3) elements. Therefore (n(\mathcal{P}(A-B))=2³=8).

Step 2

Why this answer is correct

The correct answer is A. (,8,). (A-B={1,3,5}) has (3) elements. Therefore (n(\mathcal{P}(A-B))=2³=8).

Step 3

Exam Tip

(A-B={1,3,5}) में (3) तत्व हैं। इसलिए (n(\mathcal{P}(A-B))=2³=8)।

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Question 91/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि (n(A-B)=17), (n(B-C)=22), और (B-C) में (A) के साथ (6) सामान्य तत्व हैं, तो (n\((A-B)\cup(B-C)\)) क्या है?

If (n(A-B)=17), (n(B-C)=22), and (B-C) has (6) elements common with (A), what is (n\((A-B)\cup(B-C)\))?

Explanation opens after your attempt

Correct Answer

A. (,33,)

Step 1

Concept

\((A-B)\cap(B-C)\) contains those (6) elements common to (B-C) and (A). Hence the union count is (17+22-6=33).

Step 2

Why this answer is correct

The correct answer is A. (,33,). \((A-B)\cap(B-C)\) contains those (6) elements common to (B-C) and (A). Hence the union count is (17+22-6=33).

Step 3

Exam Tip

\((A-B)\cap(B-C)\) में वही (6) तत्व हैं जो (B-C) में (A) के साथ सामान्य हैं। इसलिए संघ का मान (17+22-6=33) है।

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Question 92/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि (A), (B), (C) ऐसे हैं कि \(A\subseteq B\subseteq C\), तो ((C-A)-(B-A)) किसके बराबर है?

If (A), (B), (C) satisfy \(A\subseteq B\subseteq C\), then ((C-A)-(B-A)) is equal to which set?

Explanation opens after your attempt

Correct Answer

A. (C-B)

Step 1

Concept

Removing (B-A) from (C-A) leaves the elements inside (C) but outside (B). Hence the result is (C-B).

Step 2

Why this answer is correct

The correct answer is A. (C-B). Removing (B-A) from (C-A) leaves the elements inside (C) but outside (B). Hence the result is (C-B).

Step 3

Exam Tip

(C-A) में से (B-A) हटाने पर (B) के बाहर और (C) के अंदर वाले तत्व बचते हैं। इसलिए परिणाम (C-B) है।

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Question 93/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A\cap B=B\cap C=C\cap A=\varnothing\), (n(A)=12), (n(B)=15), (n(C)=18), तो (n\(A\cup B\cup C\)) क्या है?

If \(A\cap B=B\cap C=C\cap A=\varnothing\), (n(A)=12), (n(B)=15), (n(C)=18), what is (n\(A\cup B\cup C\))?

Explanation opens after your attempt

Correct Answer

A. (,45,)

Step 1

Concept

The three sets are pairwise disjoint, so the union count is the direct sum. (12+15+18=45).

Step 2

Why this answer is correct

The correct answer is A. (,45,). The three sets are pairwise disjoint, so the union count is the direct sum. (12+15+18=45).

Step 3

Exam Tip

तीनों समुच्चय परस्पर असंबद्ध हैं, इसलिए संघ की संख्या सीधा योग है। (12+15+18=45)।

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Question 94/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

\(यदि (A={x\in\mathbb{N}:x\le30,\ x\) पूर्ण वर्ग है\(}) और (B={x\in\mathbb{N}:x\le30,\ 3\mid x}), तो (A-B) क्या है\)?

\(If (A={x\in\mathbb{N}:x\le30,\ x\) is a perfect square\(}) and (B={x\in\mathbb{N}:x\le30,\ 3\mid x}), what is (A-B)\)?

Explanation opens after your attempt

Correct Answer

A. ({1,4,16,25})

Step 1

Concept

Perfect squares up to (30) are ({1,4,9,16,25}). Removing (9), which is divisible by (3), gives ({1,4,16,25}).

Step 2

Why this answer is correct

The correct answer is A. ({1,4,16,25}). Perfect squares up to (30) are ({1,4,9,16,25}). Removing (9), which is divisible by (3), gives ({1,4,16,25}).

Step 3

Exam Tip

(30) तक पूर्ण वर्ग ({1,4,9,16,25}) हैं। इनमें (3) से विभाज्य (9) हटाने पर ({1,4,16,25}) मिलता है।

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Question 95/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{Z}:x^2\le25}\), \(B={x\in\mathbb{Z}:x\ge0}\) और \(C={x\in\mathbb{Z}:x<4}\), तो \(A\cap B\cap C\) क्या है?

If \(A={x\in\mathbb{Z}:x^2\le25}\), \(B={x\in\mathbb{Z}:x\ge0}\), and \(C={x\in\mathbb{Z}:x<4}\), what is \(A\cap B\cap C\)?

Explanation opens after your attempt

Correct Answer

A. ({0,1,2,3})

Step 1

Concept

(A) contains integers from (-5) to (5). Applying \(x\ge0\) and (x<4) gives ({0,1,2,3}).

Step 2

Why this answer is correct

The correct answer is A. ({0,1,2,3}). (A) contains integers from (-5) to (5). Applying \(x\ge0\) and (x<4) gives ({0,1,2,3}).

Step 3

Exam Tip

(A) में (-5) से (5) तक पूर्णांक हैं। \(x\ge0\) और (x<4) लगाने पर ({0,1,2,3}) मिलता है।

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Question 96/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{R}:x\ne0}\) और \(B={x\in\mathbb{R}:x^2>0}\), तो \(A\triangle B\) क्या है?

If \(A={x\in\mathbb{R}:x\ne0}\) and \(B={x\in\mathbb{R}:x^2>0}\), what is \(A\triangle B\)?

Explanation opens after your attempt

Correct Answer

A. \(\varnothing\)

Step 1

Concept

For real numbers, \(x^2>0\) exactly when \(x\ne0\). Thus (A=B), and the symmetric difference is \(\varnothing\).

Step 2

Why this answer is correct

The correct answer is A. \(\varnothing\). For real numbers, \(x^2>0\) exactly when \(x\ne0\). Thus (A=B), and the symmetric difference is \(\varnothing\).

Step 3

Exam Tip

वास्तविक संख्याओं में \(x^2>0\) ठीक तब होता है जब \(x\ne0\)। इसलिए (A=B) और सममित अंतर \(\varnothing\) है।

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Question 97/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि (A) और (B) सीमित समुच्चय हैं तथा (n\(A\cup B\)=n(A)+n(B)), तो कौन-सा निष्कर्ष सही है?

If (A) and (B) are finite sets and (n\(A\cup B\)=n(A)+n(B)), which conclusion is correct?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

In the general formula, (n\(A\cap B\)) is subtracted. The equality holds only when (n\(A\cap B\)=0), that is \(A\cap B=\varnothing\).

Step 2

Why this answer is correct

The correct answer is A. \(A\cap B=\varnothing\). In the general formula, (n\(A\cap B\)) is subtracted. The equality holds only when (n\(A\cap B\)=0), that is \(A\cap B=\varnothing\).

Step 3

Exam Tip

सामान्य सूत्र में (n\(A\cap B\)) घटता है। योग बराबर तभी होगा जब (n\(A\cap B\)=0), यानी \(A\cap B=\varnothing\)।

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Question 98/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि (A-B=A) और (B-C=B) हैं, तो कौन-सा कथन अवश्य सत्य है?

If (A-B=A) and (B-C=B), which statement must be true?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

(A-B=A) means \(A\cap B=\varnothing\). Similarly, (B-C=B) means \(B\cap C=\varnothing\).

Step 2

Why this answer is correct

The correct answer is A. \(A\cap B=\varnothing\) और \(B\cap C=\varnothing\). (A-B=A) means \(A\cap B=\varnothing\). Similarly, (B-C=B) means \(B\cap C=\varnothing\).

Step 3

Exam Tip

(A-B=A) का अर्थ \(A\cap B=\varnothing\) है। इसी तरह (B-C=B) का अर्थ \(B\cap C=\varnothing\) है।

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Question 99/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि \(A={x\in\mathbb{R}:x\ge2}\), \(B={x\in\mathbb{R}:x<6}\) और \(C={x\in\mathbb{R}:x=4}\), तो (\(A\cap B\)-C) क्या है?

If \(A={x\in\mathbb{R}:x\ge2}\), \(B={x\in\mathbb{R}:x<6}\), and \(C={x\in\mathbb{R}:x=4}\), what is (\(A\cap B\)-C)?

Explanation opens after your attempt

Correct Answer

A. ([2,4)\cup(4,6))

Step 1

Concept

\(A\cap B=[2,6\)). Removing (4) from it gives ([2,4)\cup(4,6)).

Step 2

Why this answer is correct

The correct answer is A. ([2,4)\cup(4,6)). \(A\cap B=[2,6\)). Removing (4) from it gives ([2,4)\cup(4,6)).

Step 3

Exam Tip

\(A\cap B=[2,6\)) है। इसमें से (4) हटाने पर ([2,4)\cup(4,6)) मिलता है।

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Question 100/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 17

यदि (n\(A\cup B\cup C\)=88), (n(A-B)=19), (n(B-A)=24), (n\(A\cap B\)=13) और (C-\(A\cup B\)) में (32) तत्व हैं, तो (n(\(A\cup B\)-C)) क्या है यदि (C) में \(A\cup B\) का कोई तत्व नहीं है?

If (n\(A\cup B\cup C\)=88), (n(A-B)=19), (n(B-A)=24), (n\(A\cap B\)=13), and (C-\(A\cup B\)) has (32) elements, what is (n(\(A\cup B\)-C)) if (C) has no element of \(A\cup B\)?

Explanation opens after your attempt

Correct Answer

A. (,56,)

Step 1

Concept

Since (C) and \(A\cup B\) are disjoint, (\(A\cup B\)-C=A\cup B). Its value is (19+24+13=56).

Step 2

Why this answer is correct

The correct answer is A. (,56,). Since (C) and \(A\cup B\) are disjoint, (\(A\cup B\)-C=A\cup B). Its value is (19+24+13=56).

Step 3

Exam Tip

क्योंकि (C) और \(A\cup B\) असंबद्ध हैं, इसलिए (\(A\cup B\)-C=A\cup B)। इसका मान (19+24+13=56) है।

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Question 101/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि (n(A)=42), (n(B)=35) और (n\(A\cup B\)=60) है, तो (n\(A\cap B\)) कितना होगा?

If (n(A)=42), (n(B)=35), and (n\(A\cup B\)=60), then what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (17)

Step 1

Concept

Use (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). In exams, do not forget to subtract the common part.

Step 2

Why this answer is correct

The correct answer is A. (17). Use (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)). In exams, do not forget to subtract the common part.

Step 3

Exam Tip

सूत्र (n\(A\cup B\)=n(A)+n(B)-n\(A\cap B\)) लगाइए। परीक्षा में संघ के प्रश्न में समान भाग घटाना न भूलें।

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Question 102/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि (n\(A\setminus B\)=28) और (n\(A\cap B\)=16) है, तो (n(A)) कितना है?

If (n\(A\setminus B\)=28) and (n\(A\cap B\)=16), then what is (n(A))?

Explanation opens after your attempt

Correct Answer

A. (44)

Step 1

Concept

The set (A) splits into disjoint parts \(A\setminus B\) and \(A\cap B\). Hence (n(A)=28+16=44).

Step 2

Why this answer is correct

The correct answer is A. (44). The set (A) splits into disjoint parts \(A\setminus B\) and \(A\cap B\). Hence (n(A)=28+16=44).

Step 3

Exam Tip

समुच्चय (A) दो असंबद्ध भागों \(A\setminus B\) और \(A\cap B\) में बंटता है। इसलिए (n(A)=28+16=44)।

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Question 103/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A={x:x\in\mathbb{Z},-3\le x\le 5}\) और \(B={x:x\in\mathbb{Z},x^2\le 9}\) है, तो \(A\setminus B\) क्या है?

If \(A={x:x\in\mathbb{Z},-3\le x\le 5}\) and \(B={x:x\in\mathbb{Z},x^2\le 9}\), then what is \(A\setminus B\)?

Explanation opens after your attempt

Correct Answer

A. ({4,5})

Step 1

Concept

Here \(B=\{-3,-2,-1,0,1,2,3\}\). Removing elements of (B) from (A) leaves ({4,5}).

Step 2

Why this answer is correct

The correct answer is A. ({4,5}). Here \(B=\{-3,-2,-1,0,1,2,3\}\). Removing elements of (B) from (A) leaves ({4,5}).

Step 3

Exam Tip

यहां \(B=\{-3,-2,-1,0,1,2,3\}\) है। (A) से (B) के तत्व हटाने पर ({4,5}) बचता है।

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Question 104/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि (A=[-2,4]) और (B=(1,6)) है, तो \(A\cap B\) क्या है?

If (A=[-2,4]) and (B=(1,6)), then what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ((1,4])

Step 1

Concept

The common part is greater than (1) and up to (4). Therefore the correct interval is ((1,4]).

Step 2

Why this answer is correct

The correct answer is A. ((1,4]). The common part is greater than (1) and up to (4). Therefore the correct interval is ((1,4]).

Step 3

Exam Tip

साझा भाग (1) से बड़ा और (4) तक है। इसलिए सही अंतराल ((1,4]) है।

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Question 105/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि (A=\(-\infty,3]\) और \(B=[1,\infty\)) है, तो \(A\cup B\) क्या होगा?

If (A=\(-\infty,3]\) and \(B=[1,\infty\)), then what is \(A\cup B\)?

Explanation opens after your attempt

Correct Answer

A. \(\mathbb{R}\)

Step 1

Concept

The first interval gives all numbers up to (3), and the second gives all numbers from (1) onward. Together they form all of \(\mathbb{R}\).

Step 2

Why this answer is correct

The correct answer is A. \(\mathbb{R}\). The first interval gives all numbers up to (3), and the second gives all numbers from (1) onward. Together they form all of \(\mathbb{R}\).

Step 3

Exam Tip

पहला अंतराल (3) तक और दूसरा (1) से आगे सभी संख्याएं देता है। दोनों मिलकर पूरी \(\mathbb{R}\) बनाते हैं।

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Question 106/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A=\{2,4,6,8,10,12\}\), \(B=\{3,6,9,12,15\}\) और \(C=\{6,12,18\}\) है, तो (\(A\cap B\)\setminus C) क्या है?

If \(A=\{2,4,6,8,10,12\}\), \(B=\{3,6,9,12,15\}\), and \(C=\{6,12,18\}\), then what is (\(A\cap B\)\setminus C)?

Explanation opens after your attempt

Correct Answer

A. \(\varnothing\)

Step 1

Concept

\(A\cap B={6,12}\), and both elements are in (C). Hence the difference is \(\varnothing\).

Step 2

Why this answer is correct

The correct answer is A. \(\varnothing\). \(A\cap B={6,12}\), and both elements are in (C). Hence the difference is \(\varnothing\).

Step 3

Exam Tip

\(A\cap B={6,12}\) है और ये दोनों (C) में हैं। इसलिए अंतर \(\varnothing\) है।

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Question 107/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

\(यदि (U={1,2,\ldots,20}), (A={x:x\in U,\ x\) सम है\(}) और (B={x:x\in U,\ x\) 3 से विभाज्य है\(}) है, तो (n((A\cup B)')) कितना है\)?

\(If (U={1,2,\ldots,20}), (A={x:x\in U,\ x\) is even\(}), and (B={x:x\in U,\ x\) is divisible by \(3}), then what is (n((A\cup B)'))\)?

Explanation opens after your attempt

Correct Answer

A. (7)

Step 1

Concept

(n(A)=10), (n(B)=6), (n\(A\cap B\)=3), so (n\(A\cup B\)=13). The complement has (20-13=7) elements.

Step 2

Why this answer is correct

The correct answer is A. (7). (n(A)=10), (n(B)=6), (n\(A\cap B\)=3), so (n\(A\cup B\)=13). The complement has (20-13=7) elements.

Step 3

Exam Tip

(n(A)=10), (n(B)=6), (n\(A\cap B\)=3), अतः (n\(A\cup B\)=13)। पूरक में (20-13=7) तत्व हैं।

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Question 108/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A\subseteq B\) है, तो (A\cup\(B\setminus A\)) के बराबर क्या है?

If \(A\subseteq B\), then what is (A\cup\(B\setminus A\)) equal to?

Explanation opens after your attempt

Correct Answer

A. (B)

Step 1

Concept

Every element of (B) is either in (A) or in \(B\setminus A\). Therefore their union is (B).

Step 2

Why this answer is correct

The correct answer is A. (B). Every element of (B) is either in (A) or in \(B\setminus A\). Therefore their union is (B).

Step 3

Exam Tip

(B) के तत्व या तो (A) में हैं या \(B\setminus A\) में। इसलिए उनका संघ (B) है।

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Question 109/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A\cap B=A\) और \(A\cup B=B\) है, तो सही निष्कर्ष क्या है?

If \(A\cap B=A\) and \(A\cup B=B\), then what is the correct conclusion?

Explanation opens after your attempt

Correct Answer

A. \(A\subseteq B\)

Step 1

Concept

Both conditions show that every element of (A) is in (B). Hence \(A\subseteq B\).

Step 2

Why this answer is correct

The correct answer is A. \(A\subseteq B\). Both conditions show that every element of (A) is in (B). Hence \(A\subseteq B\).

Step 3

Exam Tip

दोनों शर्तें बताती हैं कि (A) का हर तत्व (B) में है। इसलिए \(A\subseteq B\) है।

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Question 110/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि (n(A)=30), (n(B)=24), (n\(A\setminus B\)=18) है, तो (n\(A\cup B\)) कितना है?

If (n(A)=30), (n(B)=24), and (n\(A\setminus B\)=18), then what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (42)

Step 1

Concept

(n\(A\cap B\)=30-18=12). Thus (n\(A\cup B\)=30+24-12=42).

Step 2

Why this answer is correct

The correct answer is A. (42). (n\(A\cap B\)=30-18=12). Thus (n\(A\cup B\)=30+24-12=42).

Step 3

Exam Tip

(n\(A\cap B\)=30-18=12) है। अतः (n\(A\cup B\)=30+24-12=42)।

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Question 111/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A\cup B=A\cap B\) है, तो कौन-सा निष्कर्ष सदैव सत्य है?

If \(A\cup B=A\cap B\), which conclusion is always true?

Explanation opens after your attempt

Correct Answer

A. (A=B)

Step 1

Concept

The union and intersection can be equal only when the two sets are equal. Hence (A=B).

Step 2

Why this answer is correct

The correct answer is A. (A=B). The union and intersection can be equal only when the two sets are equal. Hence (A=B).

Step 3

Exam Tip

संघ और प्रतिच्छेद तभी समान हो सकते हैं जब दोनों समुच्चय समान हों। अतः (A=B) है।

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Question 112/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

\(यदि (A={x:x\in\mathbb{N},x\le 12}), (B={x:x\in\mathbb{N},x\) अभाज्य है\(}) और (B) को (A) तक सीमित माना गया है, तो (A\setminus B) क्या है\)?

\(If (A={x:x\in\mathbb{N},x\le 12}), (B={x:x\in\mathbb{N},x\) is prime\(}), and (B) is restricted to (A), then what is (A\setminus B)\)?

Explanation opens after your attempt

Correct Answer

A. ({1,4,6,8,9,10,12})

Step 1

Concept

The prime elements in (A) are ({2,3,5,7,11}). Removing them gives ({1,4,6,8,9,10,12}).

Step 2

Why this answer is correct

The correct answer is A. ({1,4,6,8,9,10,12}). The prime elements in (A) are ({2,3,5,7,11}). Removing them gives ({1,4,6,8,9,10,12}).

Step 3

Exam Tip

(A) में अभाज्य तत्व ({2,3,5,7,11}) हैं। उन्हें हटाने पर ({1,4,6,8,9,10,12}) मिलता है।

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Question 113/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A\setminus B=\varnothing\) और \(B\setminus A=\varnothing\) है, तो (A) और (B) के बीच क्या संबंध है?

If \(A\setminus B=\varnothing\) and \(B\setminus A=\varnothing\), what is the relation between (A) and (B)?

Explanation opens after your attempt

Correct Answer

A. (A=B)

Step 1

Concept

The first condition gives \(A\subseteq B\), and the second gives \(B\subseteq A\). Therefore (A=B).

Step 2

Why this answer is correct

The correct answer is A. (A=B). The first condition gives \(A\subseteq B\), and the second gives \(B\subseteq A\). Therefore (A=B).

Step 3

Exam Tip

पहली शर्त से \(A\subseteq B\) और दूसरी से \(B\subseteq A\) है। इसलिए (A=B) है।

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Question 114/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

कौन-सा व्यंजक (A\setminus\(B\cap C\)) के बराबर है?

Which expression is equal to (A\setminus\(B\cap C\))?

Explanation opens after your attempt

Correct Answer

A. (\(A\setminus B\)\cup\(A\setminus C\))

Step 1

Concept

By the complement rule, (A\setminus\(B\cap C\)=A\cap\(B\cap C\)'). This equals (\(A\setminus B\)\cup\(A\setminus C\)).

Step 2

Why this answer is correct

The correct answer is A. (\(A\setminus B\)\cup\(A\setminus C\)). By the complement rule, (A\setminus\(B\cap C\)=A\cap\(B\cap C\)'). This equals (\(A\setminus B\)\cup\(A\setminus C\)).

Step 3

Exam Tip

पूरक नियम से (A\setminus\(B\cap C\)=A\cap\(B\cap C\)') होता है। यह (\(A\setminus B\)\cup\(A\setminus C\)) के बराबर है।

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Question 115/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

कौन-सा व्यंजक (A\setminus\(B\cup C\)) के बराबर है?

Which expression is equal to (A\setminus\(B\cup C\))?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Removing elements of \(B\cup C\) means being outside both (B) and (C). Hence the answer is (\(A\setminus B\)\cap\(A\setminus C\)).

Step 2

Why this answer is correct

The correct answer is A. (\(A\setminus B\)\cap\(A\setminus C\)). Removing elements of \(B\cup C\) means being outside both (B) and (C). Hence the answer is (\(A\setminus B\)\cap\(A\setminus C\)).

Step 3

Exam Tip

\(B\cup C\) के तत्व हटाने का मतलब (B) और (C) दोनों से बाहर रहना है। इसलिए उत्तर (\(A\setminus B\)\cap\(A\setminus C\)) है।

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Question 116/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि (n\(A\cup B\)=75), (n\(A\cap B\)=18) और (n(A)=46) है, तो (n(B)) कितना है?

If (n\(A\cup B\)=75), (n\(A\cap B\)=18), and (n(A)=46), then what is (n(B))?

Explanation opens after your attempt

Correct Answer

A. (47)

Step 1

Concept

Using the formula, (75=46+n(B)-18). Hence (n(B)=47).

Step 2

Why this answer is correct

The correct answer is A. (47). Using the formula, (75=46+n(B)-18). Hence (n(B)=47).

Step 3

Exam Tip

सूत्र से (75=46+n(B)-18) मिलेगा। इसलिए (n(B)=47) है।

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Question 117/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

कक्षा में (64) विद्यार्थी हैं। (38) गणित, (32) भौतिकी और (20) दोनों पढ़ते हैं। ठीक एक विषय पढ़ने वाले विद्यार्थियों की संख्या कितनी है?

In a class of (64) students, (38) study Mathematics, (32) study Physics, and (20) study both. How many students study exactly one subject?

Explanation opens after your attempt

Correct Answer

A. (30)

Step 1

Concept

Exactly one subject (=(38-20)+(32-20)=30). In a Venn diagram, separate the common part from both sides.

Step 2

Why this answer is correct

The correct answer is A. (30). Exactly one subject (=(38-20)+(32-20)=30). In a Venn diagram, separate the common part from both sides.

Step 3

Exam Tip

ठीक एक विषय (=(38-20)+(32-20)=30) है। वेंन आरेख में साझा भाग को दोनों तरफ से अलग करें।

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Question 118/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

एक सर्वे में (90) लोगों में से (52) चाय, (47) कॉफी और (19) दोनों पसंद करते हैं। न चाय न कॉफी पसंद करने वाले कितने हैं?

In a survey of (90) people, (52) like tea, (47) like coffee, and (19) like both. How many like neither tea nor coffee?

Explanation opens after your attempt

Correct Answer

A. (10)

Step 1

Concept

(n\(T\cup C\)=52+47-19=80). Therefore the number outside is (90-80=10).

Step 2

Why this answer is correct

The correct answer is A. (10). (n\(T\cup C\)=52+47-19=80). Therefore the number outside is (90-80=10).

Step 3

Exam Tip

(n\(T\cup C\)=52+47-19=80) है। इसलिए बाहर वाले (90-80=10) हैं।

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Question 119/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(U={1,2,\ldots,30}\), \(A={x:x\in U,\ 2\mid x}\) और \(B={x:x\in U,\ 5\mid x}\) है, तो (n\(A\setminus B\)) कितना है?

If \(U={1,2,\ldots,30}\), \(A={x:x\in U,\ 2\mid x}\), and \(B={x:x\in U,\ 5\mid x}\), then what is (n\(A\setminus B\))?

Explanation opens after your attempt

Correct Answer

A. (12)

Step 1

Concept

There are (15) even numbers in (A), and (3) multiples of (10). Thus (n\(A\setminus B\)=15-3=12).

Step 2

Why this answer is correct

The correct answer is A. (12). There are (15) even numbers in (A), and (3) multiples of (10). Thus (n\(A\setminus B\)=15-3=12).

Step 3

Exam Tip

(A) में (15) सम संख्याएं हैं और (10) के गुणज (3) हैं। इसलिए (n\(A\setminus B\)=15-3=12)।

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Question 120/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A={x:x\in\mathbb{R},x^2-5x+6=0}\) और \(B={x:x\in\mathbb{R},x^2-4x+3=0}\) है, तो \(A\cap B\) क्या है?

If \(A={x:x\in\mathbb{R},x^2-5x+6=0}\) and \(B={x:x\in\mathbb{R},x^2-4x+3=0}\), then what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ({3})

Step 1

Concept

The first equation gives \(A=\{2,3\}\), and the second gives \(B=\{1,3\}\). The common element is ({3}).

Step 2

Why this answer is correct

The correct answer is A. ({3}). The first equation gives \(A=\{2,3\}\), and the second gives \(B=\{1,3\}\). The common element is ({3}).

Step 3

Exam Tip

पहले समीकरण से \(A=\{2,3\}\) और दूसरे से \(B=\{1,3\}\) है। समान तत्व ({3}) है।

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Question 121/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A={x:x\in\mathbb{R},x^2\le 16}\) और \(B={x:x\in\mathbb{R},x>1}\) है, तो \(A\cap B\) क्या है?

If \(A={x:x\in\mathbb{R},x^2\le 16}\) and \(B={x:x\in\mathbb{R},x>1}\), then what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ((1,4])

Step 1

Concept

From \(x^2\le 16\), (A=[-4,4]). With (x>1), the common part is ((1,4]).

Step 2

Why this answer is correct

The correct answer is A. ((1,4]). From \(x^2\le 16\), (A=[-4,4]). With (x>1), the common part is ((1,4]).

Step 3

Exam Tip

\(x^2\le 16\) से (A=[-4,4]) है। (x>1) के साथ साझा भाग ((1,4]) है।

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Question 122/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A={x:x\in\mathbb{R},-1<x\le 5}\) और \(B={x:x\in\mathbb{R},2\le x<7}\) है, तो \(A\setminus B\) क्या है?

If \(A={x:x\in\mathbb{R},-1<x\le 5}\) and \(B={x:x\in\mathbb{R},2\le x<7}\), then what is \(A\setminus B\)?

Explanation opens after your attempt

Correct Answer

A. ((-1,2))

Step 1

Concept

Since (2) is included in (B), (2) and the common part after it are removed from (A). The remaining part is ((-1,2)).

Step 2

Why this answer is correct

The correct answer is A. ((-1,2)). Since (2) is included in (B), (2) and the common part after it are removed from (A). The remaining part is ((-1,2)).

Step 3

Exam Tip

(B) में (2) शामिल है, इसलिए (A) से (2) और उसके बाद का साझा भाग हटेगा। बचा भाग ((-1,2)) है।

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Question 123/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A=\{1,2,3,4,5\}\), \(B=\{2,4,6\}\) और \(C=\{1,4,7\}\) है, तो (A\cap\(B\cup C\)) क्या है?

If \(A=\{1,2,3,4,5\}\), \(B=\{2,4,6\}\), and \(C=\{1,4,7\}\), then what is (A\cap\(B\cup C\))?

Explanation opens after your attempt

Correct Answer

A. ({1,2,4})

Step 1

Concept

\(B\cup C={1,2,4,6,7}\). Its common part with (A) is ({1,2,4}).

Step 2

Why this answer is correct

The correct answer is A. ({1,2,4}). \(B\cup C={1,2,4,6,7}\). Its common part with (A) is ({1,2,4}).

Step 3

Exam Tip

\(B\cup C={1,2,4,6,7}\) है। इसका (A) से साझा भाग ({1,2,4}) है।

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Question 124/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A=\{1,3,5,7,9\}\), \(B=\{3,6,9\}\) और \(C=\{1,2,3,4\}\) है, तो (\(A\cup B\)\setminus C) क्या है?

If \(A=\{1,3,5,7,9\}\), \(B=\{3,6,9\}\), and \(C=\{1,2,3,4\}\), then what is (\(A\cup B\)\setminus C)?

Explanation opens after your attempt

Correct Answer

A. ({5,6,7,9})

Step 1

Concept

\(A\cup B={1,3,5,6,7,9}\). Removing elements of (C) gives ({5,6,7,9}).

Step 2

Why this answer is correct

The correct answer is A. ({5,6,7,9}). \(A\cup B={1,3,5,6,7,9}\). Removing elements of (C) gives ({5,6,7,9}).

Step 3

Exam Tip

\(A\cup B={1,3,5,6,7,9}\) है। (C) के तत्व हटाने पर ({5,6,7,9}) मिलता है।

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Question 125/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A\setminus B=A\) है, तो कौन-सा कथन सदैव सत्य है?

If \(A\setminus B=A\), which statement is always true?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Removing (B) from (A) still leaves (A), so (A) and (B) have no common element. Hence \(A\cap B=\varnothing\).

Step 2

Why this answer is correct

The correct answer is A. \(A\cap B=\varnothing\). Removing (B) from (A) still leaves (A), so (A) and (B) have no common element. Hence \(A\cap B=\varnothing\).

Step 3

Exam Tip

(A) से (B) हटाने पर भी (A) बच रहा है, इसलिए (A) और (B) में कोई साझा तत्व नहीं है। अतः \(A\cap B=\varnothing\) है।

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Question 126/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A\cap B=\varnothing\), (n(A)=21) और (n(B)=17) है, तो (n\(A\cup B\)) कितना होगा?

If \(A\cap B=\varnothing\), (n(A)=21), and (n(B)=17), then what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (38)

Step 1

Concept

Disjoint sets have no common element. Therefore (n\(A\cup B\)=21+17=38).

Step 2

Why this answer is correct

The correct answer is A. (38). Disjoint sets have no common element. Therefore (n\(A\cup B\)=21+17=38).

Step 3

Exam Tip

असंबद्ध समुच्चयों में कोई साझा तत्व नहीं होता। इसलिए (n\(A\cup B\)=21+17=38)।

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Question 127/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

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

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

Explanation opens after your attempt

Correct Answer

A. ({1,2,3,5,7})

Step 1

Concept

The union is formed from the three disjoint parts \(A\setminus B\), \(B\setminus A\), and \(A\cap B\). Hence the answer is ({1,2,3,5,7}).

Step 2

Why this answer is correct

The correct answer is A. ({1,2,3,5,7}). The union is formed from the three disjoint parts \(A\setminus B\), \(B\setminus A\), and \(A\cap B\). Hence the answer is ({1,2,3,5,7}).

Step 3

Exam Tip

संघ तीन असंबद्ध भागों \(A\setminus B\), \(B\setminus A\) और \(A\cap B\) से बनता है। इसलिए उत्तर ({1,2,3,5,7}) है।

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Question 128/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि (n\(A\setminus B\)=12), (n\(B\setminus A\)=9) और (n\(A\cap B\)=6) है, तो (n\(A\cup B\)) कितना है?

If (n\(A\setminus B\)=12), (n\(B\setminus A\)=9), and (n\(A\cap B\)=6), then what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (27)

Step 1

Concept

The union is the sum of these three disjoint parts. Therefore (n\(A\cup B\)=12+9+6=27).

Step 2

Why this answer is correct

The correct answer is A. (27). The union is the sum of these three disjoint parts. Therefore (n\(A\cup B\)=12+9+6=27).

Step 3

Exam Tip

संघ इन तीन असंबद्ध भागों का योग है। इसलिए (n\(A\cup B\)=12+9+6=27)।

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Question 129/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A\cup B=A\) है, तो \(B\setminus A\) क्या होगा?

If \(A\cup B=A\), then what is \(B\setminus A\)?

Explanation opens after your attempt

Correct Answer

A. \(\varnothing\)

Step 1

Concept

From \(A\cup B=A\), we get \(B\subseteq A\). Thus (B) has no element outside (A).

Step 2

Why this answer is correct

The correct answer is A. \(\varnothing\). From \(A\cup B=A\), we get \(B\subseteq A\). Thus (B) has no element outside (A).

Step 3

Exam Tip

\(A\cup B=A\) से \(B\subseteq A\) मिलता है। इसलिए (B) में (A) के बाहर कोई तत्व नहीं है।

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Question 130/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A\cap B=B\) है, तो \(A\setminus B\) के बारे में कौन-सा कथन निश्चित रूप से सही नहीं है?

If \(A\cap B=B\), which statement about \(A\setminus B\) is not definitely true?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(A\cap B=B\) gives \(B\subseteq A\), but \(A\setminus B\) may or may not be empty. The other statements are always true.

Step 2

Why this answer is correct

The correct answer is A. \(A\setminus B=\varnothing\). \(A\cap B=B\) gives \(B\subseteq A\), but \(A\setminus B\) may or may not be empty. The other statements are always true.

Step 3

Exam Tip

\(A\cap B=B\) से \(B\subseteq A\) मिलता है, पर \(A\setminus B\) खाली भी हो सकता है और नहीं भी। बाकी कथन सदैव सत्य हैं।

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Question 131/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(U={1,2,\ldots,50}\), \(A={x:x\in U,\ 4\mid x}\) और \(B={x:x\in U,\ 6\mid x}\) है, तो (n\(A\cap B\)) कितना है?

If \(U={1,2,\ldots,50}\), \(A={x:x\in U,\ 4\mid x}\), and \(B={x:x\in U,\ 6\mid x}\), then what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

Common elements are multiples of (\operatorname{lcm}(4,6)=12). Up to (50), they are (12,24,36,48), so there are (4) elements.

Step 2

Why this answer is correct

The correct answer is A. (4). Common elements are multiples of (\operatorname{lcm}(4,6)=12). Up to (50), they are (12,24,36,48), so there are (4) elements.

Step 3

Exam Tip

साझा तत्व (\operatorname{lcm}(4,6)=12) के गुणज होंगे। (50) तक (12,24,36,48) यानी (4) तत्व हैं।

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Question 132/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A={x:x\in\mathbb{Z},|x|\le 4}\) और \(B={x:x\in\mathbb{Z},x^2-2x-3=0}\) है, तो \(A\setminus B\) में कितने तत्व हैं?

If \(A={x:x\in\mathbb{Z},|x|\le 4}\) and \(B={x:x\in\mathbb{Z},x^2-2x-3=0}\), then how many elements are in \(A\setminus B\)?

Explanation opens after your attempt

Correct Answer

A. (7)

Step 1

Concept

(A) has (9) elements, and \(B=\{-1,3\}\). Therefore \(A\setminus B\) has (9-2=7) elements.

Step 2

Why this answer is correct

The correct answer is A. (7). (A) has (9) elements, and \(B=\{-1,3\}\). Therefore \(A\setminus B\) has (9-2=7) elements.

Step 3

Exam Tip

(A) में (9) तत्व हैं और \(B=\{-1,3\}\) है। इसलिए \(A\setminus B\) में (9-2=7) तत्व हैं।

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Question 133/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A\triangle B\) को (\(A\setminus B\)\cup\(B\setminus A\)) से परिभाषित किया जाए और (n\(A\cup B\)=40), (n\(A\cap B\)=13) हो, तो (n\(A\triangle B\)) कितना है?

If \(A\triangle B\) is defined as (\(A\setminus B\)\cup\(B\setminus A\)) and (n\(A\cup B\)=40), (n\(A\cap B\)=13), then what is (n\(A\triangle B\))?

Explanation opens after your attempt

Correct Answer

A. (27)

Step 1

Concept

\(A\triangle B\) removes the common part from the union. Therefore (n\(A\triangle B\)=40-13=27).

Step 2

Why this answer is correct

The correct answer is A. (27). \(A\triangle B\) removes the common part from the union. Therefore (n\(A\triangle B\)=40-13=27).

Step 3

Exam Tip

\(A\triangle B\) संघ में से साझा भाग हटाता है। इसलिए (n\(A\triangle B\)=40-13=27)।

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Question 134/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A=\{a,b,c,d\}\) और \(B=\{c,d,e\}\) है, तो (\mathcal{P}\(A\cap B\)) में कितने तत्व होंगे?

If \(A=\{a,b,c,d\}\) and \(B=\{c,d,e\}\), then how many elements are in (\mathcal{P}\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

\(A\cap B={c,d}\) has (2) elements. Hence (\mathcal{P}\(A\cap B\)) has \(2^2=4\) elements.

Step 2

Why this answer is correct

The correct answer is A. (4). \(A\cap B={c,d}\) has (2) elements. Hence (\mathcal{P}\(A\cap B\)) has \(2^2=4\) elements.

Step 3

Exam Tip

\(A\cap B={c,d}\) में (2) तत्व हैं। इसलिए (\mathcal{P}\(A\cap B\)) में \(2^2=4\) तत्व होंगे।

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Question 135/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A\subseteq U\) और \(B\subseteq U\), तो (\(A\setminus B\)') किसके बराबर है?

If \(A\subseteq U\) and \(B\subseteq U\), then (\(A\setminus B\)') is equal to what?

Explanation opens after your attempt

Correct Answer

A. \(A'\cup B\)

Step 1

Concept

\(A\setminus B=A\cap B'\). Its complement is (\(A\cap B'\)'=A'\cup B).

Step 2

Why this answer is correct

The correct answer is A. \(A'\cup B\). \(A\setminus B=A\cap B'\). Its complement is (\(A\cap B'\)'=A'\cup B).

Step 3

Exam Tip

\(A\setminus B=A\cap B'\) है। इसका पूरक (\(A\cap B'\)'=A'\cup B) होगा।

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Question 136/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि (A) और (B) सीमित समुच्चय हैं, तो (n\(A\setminus B\)) के लिए सही सूत्र कौन-सा है?

If (A) and (B) are finite sets, which is the correct formula for (n\(A\setminus B\))?

Explanation opens after your attempt

Correct Answer

A. (n(A)-n\(A\cap B\))

Step 1

Concept

\(A\setminus B\) contains elements of (A) that are not in the common part. Hence (n\(A\setminus B\)=n(A)-n\(A\cap B\)).

Step 2

Why this answer is correct

The correct answer is A. (n(A)-n\(A\cap B\)). \(A\setminus B\) contains elements of (A) that are not in the common part. Hence (n\(A\setminus B\)=n(A)-n\(A\cap B\)).

Step 3

Exam Tip

\(A\setminus B\) में (A) के वे तत्व हैं जो साझा भाग में नहीं हैं। इसलिए (n\(A\setminus B\)=n(A)-n\(A\cap B\))।

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Question 137/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A=\{1,2,3,4,5,6\}\), \(B=\{2,3,5,7\}\), \(C=\{3,4,5,8\}\) है, तो (\(A\setminus B\)\cap C) क्या है?

If \(A=\{1,2,3,4,5,6\}\), \(B=\{2,3,5,7\}\), and \(C=\{3,4,5,8\}\), then what is (\(A\setminus B\)\cap C)?

Explanation opens after your attempt

Correct Answer

A. ({4})

Step 1

Concept

\(A\setminus B={1,4,6}\). Its only common element with (C) is (4).

Step 2

Why this answer is correct

The correct answer is A. ({4}). \(A\setminus B={1,4,6}\). Its only common element with (C) is (4).

Step 3

Exam Tip

\(A\setminus B={1,4,6}\) है। इसका (C) से साझा तत्व केवल (4) है।

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Question 138/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि (A\cap\(B\cup C\)=\(A\cap B\)\cup\(A\cap C\)) है, तो यह कौन-सा नियम है?

If (A\cap\(B\cup C\)=\(A\cap B\)\cup\(A\cap C\)), which law is this?

Explanation opens after your attempt

Correct Answer

A. वितरण नियमDistributive law

Step 1

Concept

This is the distributive law of intersection over union. In identity questions, observe the position of symbols carefully.

Step 2

Why this answer is correct

The correct answer is A. वितरण नियम / Distributive law. This is the distributive law of intersection over union. In identity questions, observe the position of symbols carefully.

Step 3

Exam Tip

यह प्रतिच्छेद का संघ पर वितरण है। पहचान वाले प्रश्नों में प्रतीकों की स्थिति ध्यान से देखें।

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Question 139/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि (A\cup\(B\cap C\)=\(A\cup B\)\cap\(A\cup C\)) है, तो यह कौन-सा नियम है?

If (A\cup\(B\cap C\)=\(A\cup B\)\cap\(A\cup C\)), which law is this?

Explanation opens after your attempt

Correct Answer

A. वितरण नियमDistributive law

Step 1

Concept

This is the distributive law of union over intersection. Remember both forms of the distributive law separately.

Step 2

Why this answer is correct

The correct answer is A. वितरण नियम / Distributive law. This is the distributive law of union over intersection. Remember both forms of the distributive law separately.

Step 3

Exam Tip

यह संघ का प्रतिच्छेद पर वितरण है। दोनों वितरण नियम अलग-अलग रूपों में याद रखें।

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Question 140/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि (A\cup\(A\cap B\)=A) है, तो यह कौन-सा नियम दर्शाता है?

If (A\cup\(A\cap B\)=A), which law does this represent?

Explanation opens after your attempt

Correct Answer

A. अवशोषण नियमAbsorption law

Step 1

Concept

This is a form of the absorption law. Adding \(A\cap B\) to (A) still gives (A).

Step 2

Why this answer is correct

The correct answer is A. अवशोषण नियम / Absorption law. This is a form of the absorption law. Adding \(A\cap B\) to (A) still gives (A).

Step 3

Exam Tip

यह अवशोषण नियम का रूप है। (A) के साथ \(A\cap B\) जोड़ने से (A) ही रहता है।

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Question 141/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि (A\cap\(A\cup B\)=A) है, तो यह कौन-सा नियम दर्शाता है?

If (A\cap\(A\cup B\)=A), which law does this represent?

Explanation opens after your attempt

Correct Answer

A. अवशोषण नियमAbsorption law

Step 1

Concept

This is also the absorption law. (A) is already contained inside \(A\cup B\).

Step 2

Why this answer is correct

The correct answer is A. अवशोषण नियम / Absorption law. This is also the absorption law. (A) is already contained inside \(A\cup B\).

Step 3

Exam Tip

यह भी अवशोषण नियम है। \(A\cup B\) के भीतर (A) पहले से शामिल है।

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Question 142/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

कौन-सा विकल्प \(A\cap B'\) के बराबर है?

Which option is equal to \(A\cap B'\)?

Explanation opens after your attempt

Correct Answer

A. \(A\setminus B\)

Step 1

Concept

\(A\cap B'\) means being in (A) and not being in (B). This is exactly \(A\setminus B\).

Step 2

Why this answer is correct

The correct answer is A. \(A\setminus B\). \(A\cap B'\) means being in (A) and not being in (B). This is exactly \(A\setminus B\).

Step 3

Exam Tip

\(A\cap B'\) का अर्थ है (A) में रहना और (B) में न रहना। यही \(A\setminus B\) है।

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Question 143/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A={x:x\in\mathbb{Z},-5\le x<3}\) और \(B={x:x\in\mathbb{Z},-2<x\le 6}\) है, तो \(A\cup B\) क्या है?

If \(A={x:x\in\mathbb{Z},-5\le x<3}\) and \(B={x:x\in\mathbb{Z},-2<x\le 6}\), then what is \(A\cup B\)?

Explanation opens after your attempt

Correct Answer

A. ({-5,-4,-3,-2,-1,0,1,2,3,4,5,6})

Step 1

Concept

The two integer intervals are connected with no gap. Therefore the union is all integers from (-5) to (6).

Step 2

Why this answer is correct

The correct answer is A. ({-5,-4,-3,-2,-1,0,1,2,3,4,5,6}). The two integer intervals are connected with no gap. Therefore the union is all integers from (-5) to (6).

Step 3

Exam Tip

दोनों पूर्णांक अंतराल जुड़े हुए हैं और बीच में कोई खाली स्थान नहीं है। इसलिए संघ (-5) से (6) तक के सभी पूर्णांक हैं।

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Question 144/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A\subseteq B\subseteq C\) है, तो (A\cap\(C\setminus B\)) क्या होगा?

If \(A\subseteq B\subseteq C\), then what is (A\cap\(C\setminus B\))?

Explanation opens after your attempt

Correct Answer

A. \(\varnothing\)

Step 1

Concept

\(C\setminus B\) contains elements outside (B). Since \(A\subseteq B\), no element of (A) can be there.

Step 2

Why this answer is correct

The correct answer is A. \(\varnothing\). \(C\setminus B\) contains elements outside (B). Since \(A\subseteq B\), no element of (A) can be there.

Step 3

Exam Tip

\(C\setminus B\) में (B) से बाहर के तत्व होते हैं। \(A\subseteq B\) होने से (A) का कोई तत्व वहां नहीं होगा।

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Question 145/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A\cap B\ne\varnothing\) और \(A\setminus B=\varnothing\) है, तो कौन-सा निष्कर्ष सही है?

If \(A\cap B\ne\varnothing\) and \(A\setminus B=\varnothing\), which conclusion is correct?

Explanation opens after your attempt

Correct Answer

A. \(A\subseteq B\) और \(A\ne\varnothing\)

Step 1

Concept

\(A\setminus B=\varnothing\) gives \(A\subseteq B\). \(A\cap B\ne\varnothing\) shows that (A) is not empty.

Step 2

Why this answer is correct

The correct answer is A. \(A\subseteq B\) और \(A\ne\varnothing\). \(A\setminus B=\varnothing\) gives \(A\subseteq B\). \(A\cap B\ne\varnothing\) shows that (A) is not empty.

Step 3

Exam Tip

\(A\setminus B=\varnothing\) से \(A\subseteq B\) है। \(A\cap B\ne\varnothing\) बताता है कि (A) खाली नहीं है।

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Question 146/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि (n(A)=18), (n(B)=25) और (n\(A\cup B\)=25) है, तो (n\(A\setminus B\)) कितना है?

If (n(A)=18), (n(B)=25), and (n\(A\cup B\)=25), then what is (n\(A\setminus B\))?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

Since (n\(A\cup B\)=n(B)), we have \(A\subseteq B\). Hence \(A\setminus B=\varnothing\) and the number is (0).

Step 2

Why this answer is correct

The correct answer is A. (0). Since (n\(A\cup B\)=n(B)), we have \(A\subseteq B\). Hence \(A\setminus B=\varnothing\) and the number is (0).

Step 3

Exam Tip

(n\(A\cup B\)=n(B)) से \(A\subseteq B\) है। इसलिए \(A\setminus B=\varnothing\) और संख्या (0) है।

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Question 147/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(A={x:x\in\mathbb{R},0\le x<5}\) और \(B={x:x\in\mathbb{R},3<x\le 8}\) है, तो (\(A\cup B\)\setminus\(A\cap B\)) क्या है?

If \(A={x:x\in\mathbb{R},0\le x<5}\) and \(B={x:x\in\mathbb{R},3<x\le 8}\), then what is (\(A\cup B\)\setminus\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. \([0,3]\cup[5,8]\)

Step 1

Concept

\(A\cap B=(3,5)\) and \(A\cup B=[0,8]\). Removing the common part leaves \([0,3]\cup[5,8]\).

Step 2

Why this answer is correct

The correct answer is A. \([0,3]\cup[5,8]\). \(A\cap B=(3,5)\) and \(A\cup B=[0,8]\). Removing the common part leaves \([0,3]\cup[5,8]\).

Step 3

Exam Tip

\(A\cap B=(3,5)\) और \(A\cup B=[0,8]\) है। साझा भाग हटाने पर \([0,3]\cup[5,8]\) बचता है।

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Question 148/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि (n\(A\cup B\cup C\)=86), (n(A)=38), (n(B)=34), (n(C)=31), (n\(A\cap B\)=12), (n\(B\cap C\)=10), (n\(C\cap A\)=9) है, तो (n\(A\cap B\cap C\)) कितना है?

If (n\(A\cup B\cup C\)=86), (n(A)=38), (n(B)=34), (n(C)=31), (n\(A\cap B\)=12), (n\(B\cap C\)=10), (n\(C\cap A\)=9), then what is (n\(A\cap B\cap C\))?

Explanation opens after your attempt

Correct Answer

A. (14)

Step 1

Concept

Use the formula for three sets: (86=38+34+31-12-10-9+x). This gives (x=14).

Step 2

Why this answer is correct

The correct answer is A. (14). Use the formula for three sets: (86=38+34+31-12-10-9+x). This gives (x=14).

Step 3

Exam Tip

तीन समुच्चयों का सूत्र लगाएं: (86=38+34+31-12-10-9+x)। इससे (x=14) मिलता है।

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Question 149/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि \(U={1,2,\ldots,40}\), \(A={x:x\in U,\ 2\mid x}\), \(B={x:x\in U,\ 3\mid x}\) और \(C={x:x\in U,\ 5\mid x}\) है, तो (n\(A\cup B\cup C\)) कितना है?

If \(U={1,2,\ldots,40}\), \(A={x:x\in U,\ 2\mid x}\), \(B={x:x\in U,\ 3\mid x}\), and \(C={x:x\in U,\ 5\mid x}\), then what is (n\(A\cup B\cup C\))?

Explanation opens after your attempt

Correct Answer

A. (30)

Step 1

Concept

Using the three-set formula gives (20+13+8-6-4-2+1=30). In exams, subtract pairwise intersections and add the triple intersection.

Step 2

Why this answer is correct

The correct answer is A. (30). Using the three-set formula gives (20+13+8-6-4-2+1=30). In exams, subtract pairwise intersections and add the triple intersection.

Step 3

Exam Tip

तीन समुच्चयों के सूत्र से (20+13+8-6-4-2+1=30) मिलता है। परीक्षा में युग्म प्रतिच्छेद घटाकर त्रिक प्रतिच्छेद जोड़ें।

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Question 150/150 Hard Mathematics Sets Operations on Sets (Union, Intersection, Difference) Class 11 Level 18

यदि (n\(A\cup B\)=70), (n\(A\setminus B\)=22) और (n\(B\setminus A\)=31) है, तो (n\(A\cap B\)) कितना होगा?

If (n\(A\cup B\)=70), (n\(A\setminus B\)=22), and (n\(B\setminus A\)=31), then what is (n\(A\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (17)

Step 1

Concept

The union is made of three disjoint parts \(A\setminus B\), \(B\setminus A\), and \(A\cap B\). Therefore (n\(A\cap B\)=70-22-31=17).

Step 2

Why this answer is correct

The correct answer is A. (17). The union is made of three disjoint parts \(A\setminus B\), \(B\setminus A\), and \(A\cap B\). Therefore (n\(A\cap B\)=70-22-31=17).

Step 3

Exam Tip

संघ तीन असंबद्ध भागों \(A\setminus B\), \(B\setminus A\) और \(A\cap B\) से बनता है। इसलिए (n\(A\cap B\)=70-22-31=17)।

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Class 11 Science

Class 11 Mathematics - Sets - Operations on Sets (Union, Intersection, Difference) Hard Quiz

यदि \(A={x\in\mathbb{Z}: -2\le x<5}\) और \(B={x\in\mathbb{Z}: x^2\le 9}\) हैं, तो (A-B) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (n(A)=40), (n(B)=36), (n(C)=28), (n\(A\cap B\)=14), (n\(B\cap C\)=10), (n\(C\cap A\)=12) और (n\(A\cap B\cap C\)=5) है, तो (n(\(A\cup B\cup C\)-C)) कितना है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि \(A={x\in\mathbb{R}: -2<x\le 6}\), \(B={x\in\mathbb{R}: 1\le x<8}\) और \(C={x\in\mathbb{R}: 4<x\le 10}\), तो (\(A\cup C\)-B) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (n(A)=45), (n(B)=38) और (n\(A\cup B\)=63) है, तो (n\(A\cap B\)) ज्ञात कीजिए।

Concept

Why this answer is correct

Exam Tip

यदि (A), (B) और (C) समुच्चय हैं, तो \(A\cap(B-C)\) किसके बराबर है?

Concept

Why this answer is correct

Exam Tip

यदि \(A\subseteq B\) है, तो (\(A\cup B\)-\(A\cap B\)) किसके बराबर है?

Concept

Why this answer is correct

Exam Tip

यदि \(U={1,2,\ldots,12}\), \(A=\{2,4,6,8,10,12\}\) और \(B=\{3,6,9,12\}\) हैं, तो (\(A\cup B\)') क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(A=\{1,2,3,4,5\}\), \(B=\{2,4,6,8\}\) और \(C=\{1,4,7,8\}\) हैं, तो (A\cap\(B\cup C\)) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(A-B=\varnothing\) और \(B-A\ne\varnothing\) है, तो सही निष्कर्ष कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(A\triangle B=(A-B)\cup(B-A)\) है और \(A=\{a,b,c,d\}\), \(B=\{b,d,e,f\}\) हैं, तो \(A\triangle B\) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(A\cap B=A\cap C\) और \(A\cup B=A\cup C\) हैं, तो कौन-सा निष्कर्ष सही है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x\in\mathbb{R}: 0\le x<3}\) और \(B={x\in\mathbb{R}: 1<x\le 5}\), तो \(A\cup B\) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x\in\mathbb{R}: -3\le x\le 2}\) और \(B={x\in\mathbb{R}: -1<x<4}\), तो (A-B) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (n(A-B)=12), (n(B-A)=9) और (n\(A\cap B\)=7), तो (n\(A\cup B\)) क्या है?

Concept

Why this answer is correct

Exam Tip

Concept

Why this answer is correct

Exam Tip

यदि (n(A)=52), (n(B)=47), (n\(A\cap B\)=21) और (n(U)=80), तो (n(\(A\cup B\)')) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(A\cap B=\varnothing\), (n(A)=15) और (n(B)=19), तो (n\(A\cup B\)) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(A\cup B=A\) है, तो (B) के बारे में सही कथन क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(A\cap B=B\) है, तो कौन-सा निष्कर्ष सही है?

Concept

Why this answer is correct