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Mathematics Quiz - Class 11 Mathematics Expert Level 20 Quiz

Question 1/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={x:x \in \mathbb{N},x\le 60}\), \(A={x:x \in U,4\mid x}\) और \(B={x:x \in U,9\mid x}\), तो (n(\(A\cup B\)')) क्या है?

If \(U={x:x \in \mathbb{N},x\le 60}\), \(A={x:x \in U,4\mid x}\), and \(B={x:x \in U,9\mid x}\), what is (n(\(A\cup B\)'))?

Explanation opens after your attempt

Correct Answer

A. (40)

Step 1

Concept

Numbers divisible by (4) or (9) are (15+6-1=20). So the complement has (60-20=40) elements.

Step 2

Why this answer is correct

The correct answer is A. (40). Numbers divisible by (4) or (9) are (15+6-1=20). So the complement has (60-20=40) elements.

Step 3

Exam Tip

(4) या (9) से विभाज्य संख्याएं (15+6-1=20) हैं। इसलिए पूरक में (60-20=40) सदस्य हैं।

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Question 2/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={x:x\in\mathbb{N},x\le 84}\), \(A={x:x\in U,6\mid x}\) और \(B={x:x\in U,14\mid x}\), तो (n\(A'\cap B'\)) क्या है?

If \(U={x:x\in\mathbb{N},x\le 84}\), \(A={x:x\in U,6\mid x}\), and \(B={x:x\in U,14\mid x}\), what is (n\(A'\cap B'\))?

Explanation opens after your attempt

Correct Answer

A. (66)

Step 1

Concept

By De Morgan's law, (A'\cap B'=\(A\cup B\)'). Since (n\(A\cup B\)=14+6-2=18), (n\(A'\cap B'\)=84-18=66).

Step 2

Why this answer is correct

The correct answer is A. (66). By De Morgan's law, (A'\cap B'=\(A\cup B\)'). Since (n\(A\cup B\)=14+6-2=18), (n\(A'\cap B'\)=84-18=66).

Step 3

Exam Tip

डी मॉर्गन से (A'\cap B'=\(A\cup B\)') है। (n\(A\cup B\)=14+6-2=18), इसलिए (n\(A'\cap B'\)=84-18=66) है।

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Question 3/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={x:x \in \mathbb{Z},-10\le x\le 10}\) और \(A={x:x \in U,x^2\le 16}\), तो (n(A')) क्या है?

If \(U={x:x \in \mathbb{Z},-10\le x\le 10}\) and \(A={x:x \in U,x^2\le 16}\), what is (n(A'))?

Explanation opens after your attempt

Correct Answer

A. (12)

Step 1

Concept

\(x^2\le 16\) gives \(-4\le x\le 4\), so (A) has (9) elements. Since (U) has (21) elements, (n(A')=12).

Step 2

Why this answer is correct

The correct answer is A. (12). \(x^2\le 16\) gives \(-4\le x\le 4\), so (A) has (9) elements. Since (U) has (21) elements, (n(A')=12).

Step 3

Exam Tip

\(x^2\le 16\) से \(-4\le x\le 4\) मिलता है, इसलिए (A) में (9) सदस्य हैं। (U) में (21) सदस्य हैं, अतः (n(A')=12) है।

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Question 4/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U=\mathbb{R}\) और (A=\(-\infty,-4]\cup(2,6)\) है, तो (A') क्या होगा?

If \(U=\mathbb{R}\) and (A=\(-\infty,-4]\cup(2,6)\), what is (A')?

Explanation opens after your attempt

Correct Answer

A. (\(-4,2]\cup[6,\infty\))

Step 1

Concept

The complement contains real values outside (A). The point (-4) is excluded, while (2) and (6) are included.

Step 2

Why this answer is correct

The correct answer is A. (\(-4,2]\cup[6,\infty\)). The complement contains real values outside (A). The point (-4) is excluded, while (2) and (6) are included.

Step 3

Exam Tip

पूरक में (A) से बाहर के वास्तविक मान आते हैं। (-4) हटेगा, पर (2) और (6) शामिल होंगे।

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Question 5/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(A\subseteq B\subseteq U\), (n(U)=150), (n(A)=64) और (n(B)=97), तो (n\(A'\cap B\)) क्या है?

If \(A\subseteq B\subseteq U\), (n(U)=150), (n(A)=64), and (n(B)=97), what is (n\(A'\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (33)

Step 1

Concept

Since \(A\subseteq B\), \(A'\cap B=B-A\). Therefore the count is (97-64=33).

Step 2

Why this answer is correct

The correct answer is A. (33). Since \(A\subseteq B\), \(A'\cap B=B-A\). Therefore the count is (97-64=33).

Step 3

Exam Tip

क्योंकि \(A\subseteq B\), \(A'\cap B=B-A\) होगा। इसलिए संख्या (97-64=33) है।

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Question 6/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

\(यदि (U={1,2,\ldots,30}), (A={x:x \in U,x\) सम है\(}) और (B={x:x \in U,x\) अभाज्य है\(}), तो (A'\cap B) क्या है\)?

\(If (U={1,2,\ldots,30}), (A={x:x \in U,x\) is even\(}), and (B={x:x \in U,x\) is prime\(}), what is (A'\cap B)\)?

Explanation opens after your attempt

Correct Answer

A. ({3,5,7,11,13,17,19,23,29})

Step 1

Concept

(A') is the set of odd numbers. Thus \(A'\cap B\) contains odd prime numbers except (2).

Step 2

Why this answer is correct

The correct answer is A. ({3,5,7,11,13,17,19,23,29}). (A') is the set of odd numbers. Thus \(A'\cap B\) contains odd prime numbers except (2).

Step 3

Exam Tip

(A') विषम संख्याओं का समुच्चय है। इसलिए \(A'\cap B\) में (2) को छोड़कर विषम अभाज्य संख्याएं होंगी।

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Question 7/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

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

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

Explanation opens after your attempt

Correct Answer

A. ({c,f})

Step 1

Concept

\(A'\cap B'\) contains elements not in \(A\cup B\). Since \(A\cup B={a,b,d,e,g,h}\), the answer is ({c,f}).

Step 2

Why this answer is correct

The correct answer is A. ({c,f}). \(A'\cap B'\) contains elements not in \(A\cup B\). Since \(A\cup B={a,b,d,e,g,h}\), the answer is ({c,f}).

Step 3

Exam Tip

\(A'\cap B'\) वही सदस्य हैं जो \(A\cup B\) में नहीं हैं। \(A\cup B={a,b,d,e,g,h}\), इसलिए उत्तर ({c,f}) है।

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Question 8/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={1,2,\ldots,45}\), \(A={x:x \in U,3\mid x}\), \(B={x:x \in U,5\mid x}\), तो (n\(A'\cup B'\)) क्या है?

If \(U={1,2,\ldots,45}\), \(A={x:x \in U,3\mid x}\), \(B={x:x \in U,5\mid x}\), what is (n\(A'\cup B'\))?

Explanation opens after your attempt

Correct Answer

A. (42)

Step 1

Concept

By De Morgan, (A'\cup B'=\(A\cap B\)'). \(A\cap B\) has (3) multiples of (15), so the complement has (45-3=42) elements.

Step 2

Why this answer is correct

The correct answer is A. (42). By De Morgan, (A'\cup B'=\(A\cap B\)'). \(A\cap B\) has (3) multiples of (15), so the complement has (45-3=42) elements.

Step 3

Exam Tip

डी मॉर्गन से (A'\cup B'=\(A\cap B\)') है। \(A\cap B\) में (15) के (3) गुणज हैं, इसलिए पूरक (45-3=42) है।

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Question 9/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U=\mathbb{R}\), (A=[-5,1)) और (B=(3,8]), तो (\(A\cup B\)') क्या है?

If \(U=\mathbb{R}\), (A=[-5,1)), and (B=(3,8]), what is (\(A\cup B\)')?

Explanation opens after your attempt

Correct Answer

A. (\(-\infty,-5\)\cup[1,3]\cup\(8,\infty\))

Step 1

Concept

Removing \(A\cup B\) from the real line leaves three parts. Watch the open and closed endpoints carefully.

Step 2

Why this answer is correct

The correct answer is A. (\(-\infty,-5\)\cup[1,3]\cup\(8,\infty\)). Removing \(A\cup B\) from the real line leaves three parts. Watch the open and closed endpoints carefully.

Step 3

Exam Tip

\(A\cup B\) को वास्तविक रेखा से हटाने पर तीन भाग बचते हैं। सिरों की खुली-बंद स्थिति ध्यान से देखें।

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Question 10/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

\(यदि (U={1,2,\ldots,16}), (A={x:x \in U,x\) वर्ग संख्या है\(}) और (B={x:x \in U,x\) विषम है\(}), तो (A'\cap B) क्या है\)?

\(If (U={1,2,\ldots,16}), (A={x:x \in U,x\) is a square number\(}), and (B={x:x \in U,x\) is odd\(}), what is (A'\cap B)\)?

Explanation opens after your attempt

Correct Answer

A. ({3,5,7,11,13,15})

Step 1

Concept

From the odd numbers, the square numbers (1) and (9) are removed. Hence \(A'\cap B={3,5,7,11,13,15}\).

Step 2

Why this answer is correct

The correct answer is A. ({3,5,7,11,13,15}). From the odd numbers, the square numbers (1) and (9) are removed. Hence \(A'\cap B={3,5,7,11,13,15}\).

Step 3

Exam Tip

विषम संख्याओं में से वर्ग संख्याएं (1) और (9) हटेंगी। इसलिए \(A'\cap B={3,5,7,11,13,15}\) है।

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Question 11/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={x:x \in \mathbb{Z},-6\le x\le 12}\) और \(A={x:x \in U,2x-3<7}\), तो (A') क्या है?

If \(U={x:x \in \mathbb{Z},-6\le x\le 12}\) and \(A={x:x \in U,2x-3<7}\), what is (A')?

Explanation opens after your attempt

Correct Answer

A. ({5,6,7,8,9,10,11,12})

Step 1

Concept

(2x-3<7) gives (x<5). Therefore the complement contains elements with \(x\ge 5\).

Step 2

Why this answer is correct

The correct answer is A. ({5,6,7,8,9,10,11,12}). (2x-3<7) gives (x<5). Therefore the complement contains elements with \(x\ge 5\).

Step 3

Exam Tip

(2x-3<7) से (x<5) मिलता है। इसलिए पूरक में \(x\ge 5\) वाले सदस्य आएंगे।

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Question 12/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

\(यदि (U={1,2,\ldots,25}), (A={x:x \in U,x\) का कोई भाजक 5 है}), तो (A') में अभाज्य संख्याओं की संख्या कितनी है?

\(If (U={1,2,\ldots,25}), (A={x:x \in U,5\) is a divisor of x}), how many prime numbers are in (A')?

Explanation opens after your attempt

Correct Answer

A. (7)

Step 1

Concept

There are (9) primes up to (25), and (5) must be removed. Multiples of (5) are not in (A'), so (7) primes remain.

Step 2

Why this answer is correct

The correct answer is A. (7). There are (9) primes up to (25), and (5) must be removed. Multiples of (5) are not in (A'), so (7) primes remain.

Step 3

Exam Tip

(25) तक अभाज्य संख्याएं (9) हैं और उनमें (5) को हटाना होगा। (A') में (5) के गुणज नहीं आते, इसलिए (7) अभाज्य बचते हैं।

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Question 13/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(A\cap B'=A\), तो कौन सा निष्कर्ष अवश्य सत्य है?

If \(A\cap B'=A\), which conclusion must be true?

Explanation opens after your attempt

Correct Answer

A. \(A\subseteq B'\)

Step 1

Concept

\(A\cap B'=A\) occurs only when every element of (A) is in (B'). Hence \(A\subseteq B'\).

Step 2

Why this answer is correct

The correct answer is A. \(A\subseteq B'\). \(A\cap B'=A\) occurs only when every element of (A) is in (B'). Hence \(A\subseteq B'\).

Step 3

Exam Tip

\(A\cap B'=A\) तभी होता है जब (A) का हर सदस्य (B') में हो। अतः \(A\subseteq B'\) है।

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Question 14/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={1,2,\ldots,70}\), \(A={x:x \in U,2\mid x}\), \(B={x:x \in U,7\mid x}\), तो (n((A-B)')) क्या है?

If \(U={1,2,\ldots,70}\), \(A={x:x \in U,2\mid x}\), \(B={x:x \in U,7\mid x}\), what is (n((A-B)'))?

Explanation opens after your attempt

Correct Answer

A. (40)

Step 1

Concept

(A-B) contains even numbers not divisible by (7), and their count is (35-5=30). Therefore the complement has (70-30=40) elements.

Step 2

Why this answer is correct

The correct answer is A. (40). (A-B) contains even numbers not divisible by (7), and their count is (35-5=30). Therefore the complement has (70-30=40) elements.

Step 3

Exam Tip

(A-B) में वे सम संख्याएं हैं जो (7) से विभाज्य नहीं हैं, उनकी संख्या (35-5=30) है। इसलिए पूरक (70-30=40) है।

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Question 15/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U=\mathbb{R}\) और \(A={x:x \in \mathbb{R},x^2-6x+8>0}\), तो (A') क्या है?

If \(U=\mathbb{R}\) and \(A={x:x \in \mathbb{R},x^2-6x+8>0}\), what is (A')?

Explanation opens after your attempt

Correct Answer

A. ([2,4])

Step 1

Concept

The solution of \(x^2-6x+8>0\) is (x<2) or (x>4). Thus the complement is \(2\le x\le 4\).

Step 2

Why this answer is correct

The correct answer is A. ([2,4]). The solution of \(x^2-6x+8>0\) is (x<2) or (x>4). Thus the complement is \(2\le x\le 4\).

Step 3

Exam Tip

\(x^2-6x+8>0\) का हल (x<2) या (x>4) है। इसलिए पूरक में \(2\le x\le 4\) आएगा।

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Question 16/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={1,2,\ldots,18}\), \(A=\{2,4,6,8,10,12,14,16,18\}\) और \(B=\{3,6,9,12,15,18\}\), तो \(A'\cup B'\) क्या है?

If \(U={1,2,\ldots,18}\), \(A=\{2,4,6,8,10,12,14,16,18\}\), and \(B=\{3,6,9,12,15,18\}\), what is \(A'\cup B'\)?

Explanation opens after your attempt

Correct Answer

A. ({1,2,3,4,5,7,8,9,10,11,13,14,15,16,17})

Step 1

Concept

(A'\cup B'=\(A\cap B\)'). Since \(A\cap B={6,12,18}\), remove these from (U).

Step 2

Why this answer is correct

The correct answer is A. ({1,2,3,4,5,7,8,9,10,11,13,14,15,16,17}). (A'\cup B'=\(A\cap B\)'). Since \(A\cap B={6,12,18}\), remove these from (U).

Step 3

Exam Tip

(A'\cup B'=\(A\cap B\)') है। \(A\cap B={6,12,18}\), इसलिए इन्हें (U) से हटाएं।

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Question 17/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

\(यदि (U={x:x \in \mathbb{N},x\le 40}), (A={x:x \in U,x\) सम है\(}), (B={x:x \in U,x\) वर्ग संख्या है\(}), तो (n(A'\cap B')) क्या है\)?

\(If (U={x:x \in \mathbb{N},x\le 40}), (A={x:x \in U,x\) is even\(}), and (B={x:x \in U,x\) is a square number\(}), what is (n(A'\cap B'))\)?

Explanation opens after your attempt

Correct Answer

A. (17)

Step 1

Concept

\(A'\cap B'\) means odd and non-square numbers. Among (20) odd numbers up to (40), (1,9,25) are squares, so (17) remain.

Step 2

Why this answer is correct

The correct answer is A. (17). \(A'\cap B'\) means odd and non-square numbers. Among (20) odd numbers up to (40), (1,9,25) are squares, so (17) remain.

Step 3

Exam Tip

\(A'\cap B'\) का अर्थ विषम और वर्ग नहीं संख्याएं हैं। (40) तक (20) विषम संख्याओं में (1,9,25) वर्ग हैं, इसलिए (17) बचते हैं।

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Question 18/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U=\{p,q,r,s,t,u,v\}\), (A'={q,s,u}) और \(B=\{p,q,t,v\}\), तो \(A\cap B\) क्या है?

If \(U=\{p,q,r,s,t,u,v\}\), (A'={q,s,u}), and \(B=\{p,q,t,v\}\), what is \(A\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ({p,t,v})

Step 1

Concept

First write (A=U-A'={p,r,t,v}). Intersecting with (B) gives ({p,t,v}).

Step 2

Why this answer is correct

The correct answer is A. ({p,t,v}). First write (A=U-A'={p,r,t,v}). Intersecting with (B) gives ({p,t,v}).

Step 3

Exam Tip

पहले (A=U-A'={p,r,t,v}) लिखें। फिर (B) से प्रतिच्छेद लेने पर ({p,t,v}) मिलता है।

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Question 19/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U=\mathbb{R}\), (A=\(-3,\infty\)) और (B=\(-\infty,5]\), तो (\(A\cap B\)') क्या है?

If \(U=\mathbb{R}\), (A=\(-3,\infty\)), and (B=\(-\infty,5]\), what is (\(A\cap B\)')?

Explanation opens after your attempt

Correct Answer

A. ((-\infty,-3]\cup\(5,\infty\))

Step 1

Concept

(A\cap B=(-3,5]). Its complement is ((-\infty,-3]\cup\(5,\infty\)).

Step 2

Why this answer is correct

The correct answer is A. ((-\infty,-3]\cup\(5,\infty\)). (A\cap B=(-3,5]). Its complement is ((-\infty,-3]\cup\(5,\infty\)).

Step 3

Exam Tip

(A\cap B=(-3,5]) है। इसका पूरक ((-\infty,-3]\cup\(5,\infty\)) होगा।

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Question 20/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={1,2,\ldots,90}\), \(A={x:x \in U,6\mid x}\), \(B={x:x \in U,10\mid x}\), तो (n(\(A\cap B\)')) क्या है?

If \(U={1,2,\ldots,90}\), \(A={x:x \in U,6\mid x}\), and \(B={x:x \in U,10\mid x}\), what is (n(\(A\cap B\)'))?

Explanation opens after your attempt

Correct Answer

A. (87)

Step 1

Concept

\(A\cap B\) contains multiples of (30), and there are (3) up to (90). So the complement has (90-3=87) elements.

Step 2

Why this answer is correct

The correct answer is A. (87). \(A\cap B\) contains multiples of (30), and there are (3) up to (90). So the complement has (90-3=87) elements.

Step 3

Exam Tip

\(A\cap B\) में (30) के गुणज होंगे, जो (90) तक (3) हैं। इसलिए पूरक में (90-3=87) सदस्य हैं।

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Question 21/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={1,2,\ldots,12}\), \(A=\{1,4,7,10\}\), तो \(A'\cap {2,4,6,8,10,12}\) क्या है?

If \(U={1,2,\ldots,12}\), \(A=\{1,4,7,10\}\), what is \(A'\cap {2,4,6,8,10,12}\)?

Explanation opens after your attempt

Correct Answer

A. ({2,6,8,12})

Step 1

Concept

(A') does not contain (1,4,7,10). Removing (4) and (10) from the given set leaves ({2,6,8,12}).

Step 2

Why this answer is correct

The correct answer is A. ({2,6,8,12}). (A') does not contain (1,4,7,10). Removing (4) and (10) from the given set leaves ({2,6,8,12}).

Step 3

Exam Tip

(A') में (1,4,7,10) नहीं होंगे। दिए गए समुच्चय में से (4) और (10) हटाने पर ({2,6,8,12}) बचता है।

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Question 22/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि (A'=U) और \(B'\ne U\), तो \(A\cup B\) के बारे में कौन सा कथन सही है?

If (A'=U) and \(B'\ne U\), which statement about \(A\cup B\) is correct?

Explanation opens after your attempt

Correct Answer

A. \(A\cup B=B\)

Step 1

Concept

(A'=U) gives \(A=\varnothing\). Hence \(A\cup B=\varnothing\cup B=B\).

Step 2

Why this answer is correct

The correct answer is A. \(A\cup B=B\). (A'=U) gives \(A=\varnothing\). Hence \(A\cup B=\varnothing\cup B=B\).

Step 3

Exam Tip

(A'=U) से \(A=\varnothing\) मिलता है। इसलिए \(A\cup B=\varnothing\cup B=B\) है।

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Question 23/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={x:x \in \mathbb{Z},0\le x\le 20}\) और \(A={x:x \in U,x^2-9x+20=0}\), तो (A') में (5) से छोटे सदस्यों की संख्या कितनी है?

If \(U={x:x \in \mathbb{Z},0\le x\le 20}\) and \(A={x:x \in U,x^2-9x+20=0}\), how many elements of (A') are less than (5)?

Explanation opens after your attempt

Correct Answer

A. (5)

Step 1

Concept

The equation gives \(A=\{4,5\}\). Elements less than (5) are (0,1,2,3,4), and (4) is removed, so (4) elements remain.

Step 2

Why this answer is correct

The correct answer is A. (5). The equation gives \(A=\{4,5\}\). Elements less than (5) are (0,1,2,3,4), and (4) is removed, so (4) elements remain.

Step 3

Exam Tip

समीकरण से \(A=\{4,5\}\) है। (5) से छोटे सदस्य (0,1,2,3,4) हैं, इनमें (4) हटेगा, इसलिए (4) नहीं बल्कि (4) सदस्य बचते हैं।

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Question 24/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={1,2,\ldots,100}\), \(A={x:x \in U,8\mid x}\), तो (n(A')) क्या है?

If \(U={1,2,\ldots,100}\), \(A={x:x \in U,8\mid x}\), what is (n(A'))?

Explanation opens after your attempt

Correct Answer

A. (88)

Step 1

Concept

There are (12) multiples of (8) up to (100). Hence (n(A')=100-12=88).

Step 2

Why this answer is correct

The correct answer is A. (88). There are (12) multiples of (8) up to (100). Hence (n(A')=100-12=88).

Step 3

Exam Tip

(100) तक (8) के (12) गुणज हैं। इसलिए (n(A')=100-12=88) है।

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Question 25/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U=\mathbb{R}\) और \(A={x:x \in \mathbb{R},|x-2|<5}\), तो (A') क्या है?

If \(U=\mathbb{R}\) and \(A={x:x \in \mathbb{R},|x-2|<5}\), what is (A')?

Explanation opens after your attempt

Correct Answer

A. (\(-\infty,-3]\cup[7,\infty\))

Step 1

Concept

(|x-2|<5) gives (-3<x<7). Its complement is (\(-\infty,-3]\cup[7,\infty\)).

Step 2

Why this answer is correct

The correct answer is A. (\(-\infty,-3]\cup[7,\infty\)). (|x-2|<5) gives (-3<x<7). Its complement is (\(-\infty,-3]\cup[7,\infty\)).

Step 3

Exam Tip

(|x-2|<5) से (-3<x<7) मिलता है। इसका पूरक (\(-\infty,-3]\cup[7,\infty\)) है।

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Question 26/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

\(यदि (U={1,2,\ldots,50}), (A={x:x \in U,x\) सम नहीं है}), तो (A') क्या है?

\(If (U={1,2,\ldots,50}), (A={x:x \in U,x\) is not even}), what is (A')?

Explanation opens after your attempt

Correct Answer

A. (U) में सम संख्याओं का समुच्चयThe set of even numbers in (U)

Step 1

Concept

(A) contains numbers that are not even, meaning odd numbers. Therefore (A') contains the even numbers of (U).

Step 2

Why this answer is correct

The correct answer is A. (U) में सम संख्याओं का समुच्चय / The set of even numbers in (U). (A) contains numbers that are not even, meaning odd numbers. Therefore (A') contains the even numbers of (U).

Step 3

Exam Tip

(A) में सम नहीं यानी विषम संख्याएं हैं। इसलिए (A') में (U) की सम संख्याएं होंगी।

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Question 27/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={1,2,\ldots,36}\), \(A={x:x \in U,2\mid x}\), \(B={x:x \in U,3\mid x}\), तो (n\(A'\cap B\)) क्या है?

If \(U={1,2,\ldots,36}\), \(A={x:x \in U,2\mid x}\), and \(B={x:x \in U,3\mid x}\), what is (n\(A'\cap B\))?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

\(A'\cap B\) means multiples of (3) that are not even. Up to (36), there are (12) multiples of (3), (6) of them are even, so (6) remain.

Step 2

Why this answer is correct

The correct answer is A. (6). \(A'\cap B\) means multiples of (3) that are not even. Up to (36), there are (12) multiples of (3), (6) of them are even, so (6) remain.

Step 3

Exam Tip

\(A'\cap B\) का अर्थ (3) के वे गुणज हैं जो सम नहीं हैं। (36) तक (3) के (12) गुणज हैं, उनमें (6) सम हैं, इसलिए (6) बचते हैं।

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Question 28/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

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

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

Explanation opens after your attempt

Correct Answer

A. (A')

Step 1

Concept

If two sets together form (U) and are disjoint, they are complements of each other. Hence (B=A').

Step 2

Why this answer is correct

The correct answer is A. (A'). If two sets together form (U) and are disjoint, they are complements of each other. Hence (B=A').

Step 3

Exam Tip

यदि दो समुच्चय मिलकर (U) बनाते हैं और अलग-अलग हैं, तो वे एक-दूसरे के पूरक होते हैं। इसलिए (B=A') है।

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Question 29/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={1,2,\ldots,15}\), \(A=\{1,5,9,13\}\), \(B=\{2,5,8,11,14\}\), तो (\(A\cap B\)') क्या है?

If \(U={1,2,\ldots,15}\), \(A=\{1,5,9,13\}\), and \(B=\{2,5,8,11,14\}\), what is (\(A\cap B\)')?

Explanation opens after your attempt

Correct Answer

A. ({1,2,3,4,6,7,8,9,10,11,12,13,14,15})

Step 1

Concept

\(A\cap B={5}\). Therefore (\(A\cap B\)') contains all elements of (U) except (5).

Step 2

Why this answer is correct

The correct answer is A. ({1,2,3,4,6,7,8,9,10,11,12,13,14,15}). \(A\cap B={5}\). Therefore (\(A\cap B\)') contains all elements of (U) except (5).

Step 3

Exam Tip

\(A\cap B={5}\) है। इसलिए (\(A\cap B\)') में (5) को छोड़कर (U) के सभी सदस्य होंगे।

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Question 30/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U=\mathbb{R}\), (A=\(-\infty,0\)\cup\(4,\infty\)) और (B=[-2,6]), तो \(A'\cap B\) क्या है?

If \(U=\mathbb{R}\), (A=\(-\infty,0\)\cup\(4,\infty\)), and (B=[-2,6]), what is \(A'\cap B\)?

Explanation opens after your attempt

Correct Answer

A. ([0,4])

Step 1

Concept

(A') contains all real values from (0) to (4). Intersecting with (B) still gives ([0,4]).

Step 2

Why this answer is correct

The correct answer is A. ([0,4]). (A') contains all real values from (0) to (4). Intersecting with (B) still gives ([0,4]).

Step 3

Exam Tip

(A') में (0) से (4) तक सभी वास्तविक मान आते हैं। इसे (B) से काटने पर ([0,4]) ही मिलता है।

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Question 31/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

\(यदि (U={x:x \in \mathbb{N},x\le 32}) और (A={x:x \in U,x=2^k\) किसी \(k\in\mathbb{N}_0\) के लिए}), तो (n(A')) क्या है?

\(If (U={x:x \in \mathbb{N},x\le 32}) and (A={x:x \in U,x=2^k\) for some \(k\in\mathbb{N}_0}), what is (n(A'))\)?

Explanation opens after your attempt

Correct Answer

A. (26)

Step 1

Concept

Powers of (2) up to (32) are (1,2,4,8,16,32), so (A) has (6) elements. The complement has (32-6=26) elements.

Step 2

Why this answer is correct

The correct answer is A. (26). Powers of (2) up to (32) are (1,2,4,8,16,32), so (A) has (6) elements. The complement has (32-6=26) elements.

Step 3

Exam Tip

(32) तक (2) की घातें (1,2,4,8,16,32) हैं, इसलिए (A) में (6) सदस्य हैं। पूरक में (32-6=26) सदस्य हैं।

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Question 32/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={1,2,\ldots,20}\), (A'={2,3,5,7,11,13,17,19}), तो (A) क्या है?

If \(U={1,2,\ldots,20}\) and (A'={2,3,5,7,11,13,17,19}), what is (A)?

Explanation opens after your attempt

Correct Answer

A. ({1,4,6,8,9,10,12,14,15,16,18,20})

Step 1

Concept

(A=U-A'). Removing the given prime elements from (U) gives the answer.

Step 2

Why this answer is correct

The correct answer is A. ({1,4,6,8,9,10,12,14,15,16,18,20}). (A=U-A'). Removing the given prime elements from (U) gives the answer.

Step 3

Exam Tip

(A=U-A') होता है। दिए गए अभाज्य सदस्यों को (U) से हटाने पर उत्तर मिलता है।

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Question 33/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(A-B=\varnothing\), तो निम्न में से कौन सा कथन अवश्य सत्य है?

If \(A-B=\varnothing\), which of the following statements must be true?

Explanation opens after your attempt

Correct Answer

A. \(A\subseteq B\)

Step 1

Concept

\(A-B=\varnothing\) means no element of (A) lies outside (B). Hence \(A\subseteq B\).

Step 2

Why this answer is correct

The correct answer is A. \(A\subseteq B\). \(A-B=\varnothing\) means no element of (A) lies outside (B). Hence \(A\subseteq B\).

Step 3

Exam Tip

\(A-B=\varnothing\) का अर्थ है कि (A) का कोई सदस्य (B) से बाहर नहीं है। इसलिए \(A\subseteq B\) है।

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Question 34/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={1,2,\ldots,54}\), \(A={x:x \in U,9\mid x}\), \(B={x:x \in U,6\mid x}\), तो (n\(A'\cap B'\)) क्या है?

If \(U={1,2,\ldots,54}\), \(A={x:x \in U,9\mid x}\), and \(B={x:x \in U,6\mid x}\), what is (n\(A'\cap B'\))?

Explanation opens after your attempt

Correct Answer

A. (42)

Step 1

Concept

(A'\cap B'=\(A\cup B\)'). Numbers divisible by (9) or (6) are (6+9-3=12), so the complement is (42).

Step 2

Why this answer is correct

The correct answer is A. (42). (A'\cap B'=\(A\cup B\)'). Numbers divisible by (9) or (6) are (6+9-3=12), so the complement is (42).

Step 3

Exam Tip

(A'\cap B'=\(A\cup B\)') है। (9) या (6) से विभाज्य संख्याएं (6+9-3=12) हैं, इसलिए पूरक (42) है।

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Question 35/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

\(यदि (U=\mathbb{R}) और (A={x:x \in \mathbb{R},x\le -1\) या \(x>3}), तो (A') क्या है\)?

\(If (U=\mathbb{R}) and (A={x:x \in \mathbb{R},x\le -1\) or \(x>3}), what is (A')\)?

Explanation opens after your attempt

Correct Answer

A. ((-1,3])

Step 1

Concept

(A) includes (-1), so it is not in the complement. The point (3) is not in (A), so it is included in the complement.

Step 2

Why this answer is correct

The correct answer is A. ((-1,3]). (A) includes (-1), so it is not in the complement. The point (3) is not in (A), so it is included in the complement.

Step 3

Exam Tip

(A) में (-1) शामिल है, इसलिए पूरक में नहीं आएगा। (3) (A) में नहीं है, इसलिए पूरक में शामिल होगा।

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Question 36/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

\(यदि (U={1,2,\ldots,28}), (A={x:x \in U,x\) विषम है\(}) और (B={x:x \in U,7\mid x}), तो (A'\cap B) क्या है\)?

\(If (U={1,2,\ldots,28}), (A={x:x \in U,x\) is odd\(}), and (B={x:x \in U,7\mid x}), what is (A'\cap B)\)?

Explanation opens after your attempt

Correct Answer

A. ({14,28})

Step 1

Concept

(A') is the set of even numbers. Among multiples of (7), the even members are (14) and (28).

Step 2

Why this answer is correct

The correct answer is A. ({14,28}). (A') is the set of even numbers. Among multiples of (7), the even members are (14) and (28).

Step 3

Exam Tip

(A') सम संख्याओं का समुच्चय है। (7) के गुणजों में सम सदस्य (14) और (28) हैं।

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Question 37/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

\(यदि (U={1,2,\ldots,22}), (A={x:x \in U,x\) अभाज्य है}), तो (A') में कितनी विषम संख्याएं हैं?

\(If (U={1,2,\ldots,22}), (A={x:x \in U,x\) is prime}), how many odd numbers are in (A')?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

There are (11) odd numbers up to (22). Removing odd primes (3,5,7,11,13,17,19) leaves (4) odd non-prime numbers including (1).

Step 2

Why this answer is correct

The correct answer is A. (4). There are (11) odd numbers up to (22). Removing odd primes (3,5,7,11,13,17,19) leaves (4) odd non-prime numbers including (1).

Step 3

Exam Tip

(22) तक विषम संख्याएं (11) हैं। उनमें अभाज्य विषम (3,5,7,11,13,17,19) हटेंगे, इसलिए (4) विषम मिश्रित या (1) बचते हैं।

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Question 38/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={1,2,\ldots,14}\), \(A=\{2,4,6,8,10,12,14\}\), तो \(A'\times A\) में कितने क्रमित युग्म होंगे?

If \(U={1,2,\ldots,14}\), \(A=\{2,4,6,8,10,12,14\}\), how many ordered pairs are in \(A'\times A\)?

Explanation opens after your attempt

Correct Answer

A. (49)

Step 1

Concept

(A') has (7) odd elements and (A) has (7) even elements. Hence (n\(A'\times A\)=7\times 7=49).

Step 2

Why this answer is correct

The correct answer is A. (49). (A') has (7) odd elements and (A) has (7) even elements. Hence (n\(A'\times A\)=7\times 7=49).

Step 3

Exam Tip

(A') में (7) विषम सदस्य और (A) में (7) सम सदस्य हैं। इसलिए (n\(A'\times A\)=7\times 7=49) है।

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Question 39/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={x:x \in \mathbb{Z},-4\le x\le 6}\) और \(A=\{x:x \in U,(x-1)(x+2)\ge 0\}\), तो (A') क्या है?

If \(U={x:x \in \mathbb{Z},-4\le x\le 6}\) and \(A=\{x:x \in U,(x-1)(x+2)\ge 0\}\), what is (A')?

Explanation opens after your attempt

Correct Answer

A. ({-1,0})

Step 1

Concept

The solution of ((x-1)(x+2)\ge 0) is \(x\le -2\) or \(x\ge 1\). Thus the middle integers (-1,0) are in the complement.

Step 2

Why this answer is correct

The correct answer is A. ({-1,0}). The solution of ((x-1)(x+2)\ge 0) is \(x\le -2\) or \(x\ge 1\). Thus the middle integers (-1,0) are in the complement.

Step 3

Exam Tip

((x-1)(x+2)\ge 0) का हल \(x\le -2\) या \(x\ge 1\) है। इसलिए बीच के पूर्णांक (-1,0) पूरक में आते हैं।

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Question 40/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि (n(U)=200), (n(A')=76), (n(B')=89) और (n\(A'\cap B'\)=31), तो (n(\(A\cap B\)')) क्या है?

If (n(U)=200), (n(A')=76), (n(B')=89), and (n\(A'\cap B'\)=31), what is (n(\(A\cap B\)'))?

Explanation opens after your attempt

Correct Answer

A. (134)

Step 1

Concept

By De Morgan, (\(A\cap B\)'=A'\cup B'). Thus (n\(A'\cup B'\)=76+89-31=134).

Step 2

Why this answer is correct

The correct answer is A. (134). By De Morgan, (\(A\cap B\)'=A'\cup B'). Thus (n\(A'\cup B'\)=76+89-31=134).

Step 3

Exam Tip

डी मॉर्गन से (\(A\cap B\)'=A'\cup B')। इसलिए (n\(A'\cup B'\)=76+89-31=134) है।

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Question 41/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={1,2,\ldots,10}\), \(A=\{1,2,3\}\), \(B=\{3,4,5\}\), तो (\(A'\cap B\)') क्या है?

If \(U={1,2,\ldots,10}\), \(A=\{1,2,3\}\), and \(B=\{3,4,5\}\), what is (\(A'\cap B\)')?

Explanation opens after your attempt

Correct Answer

A. ({1,2,3,6,7,8,9,10})

Step 1

Concept

(A'={4,5,6,7,8,9,10}) and \(A'\cap B={4,5}\). Its complement is ({1,2,3,6,7,8,9,10}).

Step 2

Why this answer is correct

The correct answer is A. ({1,2,3,6,7,8,9,10}). (A'={4,5,6,7,8,9,10}) and \(A'\cap B={4,5}\). Its complement is ({1,2,3,6,7,8,9,10}).

Step 3

Exam Tip

(A'={4,5,6,7,8,9,10}) और \(A'\cap B={4,5}\) है। इसका पूरक ({1,2,3,6,7,8,9,10}) है।

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Question 42/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U=\mathbb{R}\), \(A=[1,\infty\)) और (B=\(-\infty,4\)), तो \(A'\cup B'\) क्या है?

If \(U=\mathbb{R}\), \(A=[1,\infty\)), and (B=\(-\infty,4\)), what is \(A'\cup B'\)?

Explanation opens after your attempt

Correct Answer

A. (\(-\infty,1\)\cup[4,\infty))

Step 1

Concept

(A'=\(-\infty,1\)) and \(B'=[4,\infty\)). Their union is (\(-\infty,1\)\cup[4,\infty)).

Step 2

Why this answer is correct

The correct answer is A. (\(-\infty,1\)\cup[4,\infty)). (A'=\(-\infty,1\)) and \(B'=[4,\infty\)). Their union is (\(-\infty,1\)\cup[4,\infty)).

Step 3

Exam Tip

(A'=\(-\infty,1\)) और \(B'=[4,\infty\)) हैं। उनका संघ (\(-\infty,1\)\cup[4,\infty)) है।

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Question 43/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

\(यदि (U={1,2,\ldots,81}), (A={x:x \in U,x\) पूर्ण वर्ग है}), तो (A') में (9) से विभाज्य संख्याओं की संख्या कितनी है?

\(If (U={1,2,\ldots,81}), (A={x:x \in U,x\) is a perfect square}), how many numbers divisible by (9) are in (A')?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

Numbers divisible by (9) are (9,18,27,36,45,54,63,72,81). Removing squares (9,36,81) leaves (6) members.

Step 2

Why this answer is correct

The correct answer is A. (4). Numbers divisible by (9) are (9,18,27,36,45,54,63,72,81). Removing squares (9,36,81) leaves (6) members.

Step 3

Exam Tip

(9) से विभाज्य संख्याएं (9,18,27,36,45,54,63,72,81) हैं। इनमें वर्ग (9,36,81) हटेंगे, इसलिए (6) नहीं बल्कि (6) सदस्य बचते हैं।

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Question 44/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

\(यदि (U={1,2,\ldots,18}), (A={x:x \in U,x\) अभाज्य है}), तो (A') में (3) के गुणजों का समुच्चय कौन सा है?

\(If (U={1,2,\ldots,18}), (A={x:x \in U,x\) is prime}), which set of multiples of (3) lies in (A')?

Explanation opens after your attempt

Correct Answer

A. ({6,9,12,15,18})

Step 1

Concept

(3) is prime, so it is not in (A'). The remaining multiples (6,9,12,15,18) are in the complement.

Step 2

Why this answer is correct

The correct answer is A. ({6,9,12,15,18}). (3) is prime, so it is not in (A'). The remaining multiples (6,9,12,15,18) are in the complement.

Step 3

Exam Tip

(3) अभाज्य है, इसलिए वह (A') में नहीं होगा। बाकी (3) के गुणज (6,9,12,15,18) पूरक में हैं।

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Question 45/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={x:x \in \mathbb{Z},1\le x\le 30}\) और \(A={x:x \in U,x \equiv 1 \pmod{4}}\), तो (n(A')) क्या है?

If \(U={x:x \in \mathbb{Z},1\le x\le 30}\) and \(A={x:x \in U,x \equiv 1 \pmod{4}}\), what is (n(A'))?

Explanation opens after your attempt

Correct Answer

A. (22)

Step 1

Concept

The elements (1,5,9,13,17,21,25,29), so (8) elements, are in (A). Hence (n(A')=30-8=22).

Step 2

Why this answer is correct

The correct answer is A. (22). The elements (1,5,9,13,17,21,25,29), so (8) elements, are in (A). Hence (n(A')=30-8=22).

Step 3

Exam Tip

(1,5,9,13,17,21,25,29) यानी (8) सदस्य (A) में हैं। इसलिए (n(A')=30-8=22) है।

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Question 46/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(A\subseteq U\), तो (\(A'\cup A\)') किसके बराबर है?

If \(A\subseteq U\), what is (\(A'\cup A\)') equal to?

Explanation opens after your attempt

Correct Answer

A. \(\varnothing\)

Step 1

Concept

\(A'\cup A=U\). Therefore (\(A'\cup A\)'=U'=\varnothing).

Step 2

Why this answer is correct

The correct answer is A. \(\varnothing\). \(A'\cup A=U\). Therefore (\(A'\cup A\)'=U'=\varnothing).

Step 3

Exam Tip

\(A'\cup A=U\) होता है। इसलिए (\(A'\cup A\)'=U'=\varnothing) है।

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Question 47/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={1,2,\ldots,24}\), \(A={x:x \in U,4\mid x}\), \(B={x:x \in U,8\mid x}\), तो \(B'\cap A\) क्या है?

If \(U={1,2,\ldots,24}\), \(A={x:x \in U,4\mid x}\), and \(B={x:x \in U,8\mid x}\), what is \(B'\cap A\)?

Explanation opens after your attempt

Correct Answer

A. ({4,12,20})

Step 1

Concept

(A) contains multiples of (4), and (B) contains multiples of (8). \(B'\cap A\) contains multiples of (4) that are not multiples of (8).

Step 2

Why this answer is correct

The correct answer is A. ({4,12,20}). (A) contains multiples of (4), and (B) contains multiples of (8). \(B'\cap A\) contains multiples of (4) that are not multiples of (8).

Step 3

Exam Tip

(A) में (4) के गुणज हैं और (B) में (8) के गुणज हैं। \(B'\cap A\) में (4) के वे गुणज आएंगे जो (8) के गुणज नहीं हैं।

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Question 48/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

\(यदि (U=\mathbb{R}), (A={x:x \in \mathbb{R},x\ne -2\) और \(x\ne 5}), तो (A') क्या है\)?

\(If (U=\mathbb{R}), (A={x:x \in \mathbb{R},x\ne -2\) and \(x\ne 5}), what is (A')\)?

Explanation opens after your attempt

Correct Answer

A. ({-2,5})

Step 1

Concept

(A) contains all real numbers except (-2) and (5). Therefore the complement is only ({-2,5}).

Step 2

Why this answer is correct

The correct answer is A. ({-2,5}). (A) contains all real numbers except (-2) and (5). Therefore the complement is only ({-2,5}).

Step 3

Exam Tip

(A) में सभी वास्तविक संख्याएं हैं, पर (-2) और (5) नहीं हैं। इसलिए पूरक केवल ({-2,5}) है।

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Question 49/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

यदि \(U={1,2,\ldots,27}\), \(A={x:x \in U,3\mid x}\), तो (A') में (2) से विभाज्य सदस्यों की संख्या कितनी है?

If \(U={1,2,\ldots,27}\), \(A={x:x \in U,3\mid x}\), how many elements divisible by (2) are in (A')?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

There are (13) even numbers up to (27). Among them (6,12,18,24) are also divisible by (3), so (13-4=9) remain.

Step 2

Why this answer is correct

The correct answer is A. (9). There are (13) even numbers up to (27). Among them (6,12,18,24) are also divisible by (3), so (13-4=9) remain.

Step 3

Exam Tip

(27) तक सम संख्याएं (13) हैं। इनमें (6,12,18,24) (3) से भी विभाज्य हैं, इसलिए (13-4=9) बचते हैं।

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Question 50/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 20

\(यदि (U={1,2,\ldots,12}), (A={x:x \in U,x\) सम है\(}) और (B={x:x \in U,x>8}), तो ((A'\cup B')') क्या है\)?

\(If (U={1,2,\ldots,12}), (A={x:x \in U,x\) is even\(}), and (B={x:x \in U,x>8}), what is ((A'\cup B')')\)?

Explanation opens after your attempt

Correct Answer

A. ({10,12})

Step 1

Concept

By De Morgan, (\(A'\cup B'\)'=A\cap B). The even elements greater than (8) are (10) and (12).

Step 2

Why this answer is correct

The correct answer is A. ({10,12}). By De Morgan, (\(A'\cup B'\)'=A\cap B). The even elements greater than (8) are (10) and (12).

Step 3

Exam Tip

डी मॉर्गन से (\(A'\cup B'\)'=A\cap B) है। सम और (8) से बड़े सदस्य (10) और (12) हैं।

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Class 11 Mathematics Expert Quiz

यदि \(U={x:x \in \mathbb{N},x\le 60}\), \(A={x:x \in U,4\mid x}\) और \(B={x:x \in U,9\mid x}\), तो (n(\(A\cup B\)')) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(U={x:x\in\mathbb{N},x\le 84}\), \(A={x:x\in U,6\mid x}\) और \(B={x:x\in U,14\mid x}\), तो (n\(A'\cap B'\)) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(U={x:x \in \mathbb{Z},-10\le x\le 10}\) और \(A={x:x \in U,x^2\le 16}\), तो (n(A')) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(U=\mathbb{R}\) और (A=\(-\infty,-4]\cup(2,6)\) है, तो (A') क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(A\subseteq B\subseteq U\), (n(U)=150), (n(A)=64) और (n(B)=97), तो (n\(A'\cap B\)) क्या है?

Concept

Why this answer is correct

Exam Tip

\(यदि (U={1,2,\ldots,30}), (A={x:x \in U,x\) सम है\(}) और (B={x:x \in U,x\) अभाज्य है\(}), तो (A'\cap B) क्या है\)?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि \(U={1,2,\ldots,45}\), \(A={x:x \in U,3\mid x}\), \(B={x:x \in U,5\mid x}\), तो (n\(A'\cup B'\)) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(U=\mathbb{R}\), (A=[-5,1)) और (B=(3,8]), तो (\(A\cup B\)') क्या है?

Concept

Why this answer is correct

Exam Tip

\(यदि (U={1,2,\ldots,16}), (A={x:x \in U,x\) वर्ग संख्या है\(}) और (B={x:x \in U,x\) विषम है\(}), तो (A'\cap B) क्या है\)?

Concept

Why this answer is correct

Exam Tip

यदि \(U={x:x \in \mathbb{Z},-6\le x\le 12}\) और \(A={x:x \in U,2x-3<7}\), तो (A') क्या है?

Concept

Why this answer is correct

Exam Tip

\(यदि (U={1,2,\ldots,25}), (A={x:x \in U,x\) का कोई भाजक 5 है}), तो (A') में अभाज्य संख्याओं की संख्या कितनी है?

Concept

Why this answer is correct

Exam Tip

यदि \(A\cap B'=A\), तो कौन सा निष्कर्ष अवश्य सत्य है?

Concept

Why this answer is correct

Exam Tip

यदि \(U={1,2,\ldots,70}\), \(A={x:x \in U,2\mid x}\), \(B={x:x \in U,7\mid x}\), तो (n((A-B)')) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(U=\mathbb{R}\) और \(A={x:x \in \mathbb{R},x^2-6x+8>0}\), तो (A') क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(U={1,2,\ldots,18}\), \(A=\{2,4,6,8,10,12,14,16,18\}\) और \(B=\{3,6,9,12,15,18\}\), तो \(A'\cup B'\) क्या है?

Concept

Why this answer is correct

Exam Tip

\(यदि (U={x:x \in \mathbb{N},x\le 40}), (A={x:x \in U,x\) सम है\(}), (B={x:x \in U,x\) वर्ग संख्या है\(}), तो (n(A'\cap B')) क्या है\)?

Concept

Why this answer is correct

Exam Tip

यदि \(U=\{p,q,r,s,t,u,v\}\), (A'={q,s,u}) और \(B=\{p,q,t,v\}\), तो \(A\cap B\) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(U=\mathbb{R}\), (A=\(-3,\infty\)) और (B=\(-\infty,5]\), तो (\(A\cap B\)') क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(U={1,2,\ldots,90}\), \(A={x:x \in U,6\mid x}\), \(B={x:x \in U,10\mid x}\), तो (n(\(A\cap B\)')) क्या है?

Concept

Why this answer is correct