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

Question 1/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={x:x\in\mathbb{N},x\le 96}\), \(A={x:x\in U,8\mid x}\) और \(B={x:x\in U,12\mid x}\), तो (n\(A'\cap B'\)) क्या है?

If \(U={x:x\in\mathbb{N},x\le 96}\), \(A={x:x\in U,8\mid x}\), and \(B={x:x\in U,12\mid x}\), what is (n\(A'\cap B'\))?

Explanation opens after your attempt

Correct Answer

A. (80)

Step 1

Concept

By De Morgan's law, (A'\cap B'=\(A\cup B\)'). Since (n\(A\cup B\)=12+8-4=16), the complement has (96-16=80) elements.

Step 2

Why this answer is correct

The correct answer is A. (80). By De Morgan's law, (A'\cap B'=\(A\cup B\)'). Since (n\(A\cup B\)=12+8-4=16), the complement has (96-16=80) elements.

Step 3

Exam Tip

डी मॉर्गन से (A'\cap B'=\(A\cup B\)') है। (n\(A\cup B\)=12+8-4=16), इसलिए पूरक में (96-16=80) सदस्य हैं।

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Question 2/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={x:x\in\mathbb{N},x\le 120}\), \(A={x:x\in U,8\mid x}\), \(B={x:x\in U,15\mid x}\) और \(C={x:x\in U,20\mid x}\), तो (n(\(A\cup B\cup C\)')) क्या है?

If \(U={x:x\in\mathbb{N},x\le 120}\), \(A={x:x\in U,8\mid x}\), \(B={x:x\in U,15\mid x}\), and \(C={x:x\in U,20\mid x}\), what is (n(\(A\cup B\cup C\)'))?

Explanation opens after your attempt

Correct Answer

A. (96)

Step 1

Concept

By inclusion-exclusion, (n\(A\cup B\cup C\)=15+8+6-1-3-2+1=24). Therefore the complement has (120-24=96) elements.

Step 2

Why this answer is correct

The correct answer is A. (96). By inclusion-exclusion, (n\(A\cup B\cup C\)=15+8+6-1-3-2+1=24). Therefore the complement has (120-24=96) elements.

Step 3

Exam Tip

समावेशन-बहिष्करण से (n\(A\cup B\cup C\)=15+8+6-1-3-2+1=24) है। इसलिए पूरक में (120-24=96) सदस्य होंगे।

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Question 3/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={x:x\in\mathbb{Z},-12\le x\le 12}\) और \(A={x:x\in U,x^2-9x+18\le 0}\), तो (n(A')) क्या है?

If \(U={x:x\in\mathbb{Z},-12\le x\le 12}\) and \(A={x:x\in U,x^2-9x+18\le 0}\), what is (n(A'))?

Explanation opens after your attempt

Correct Answer

A. (20)

Step 1

Concept

The inequality gives \(3\le x\le 6\), so (A) has (4) elements. Since (U) has (25) elements, (n(A')=25-4=21).

Step 2

Why this answer is correct

The correct answer is A. (20). The inequality gives \(3\le x\le 6\), so (A) has (4) elements. Since (U) has (25) elements, (n(A')=25-4=21).

Step 3

Exam Tip

असमानता से \(3\le x\le 6\) मिलता है, इसलिए (A) में (4) सदस्य हैं। (U) में (25) सदस्य हैं, अतः (n(A')=25-4=21) नहीं बल्कि (21) होता है।

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Question 4/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U=\mathbb{R}\), \(A=\{x:x\in\mathbb{R},(x-2)(x+5)\le 0\}\) और \(B={x:x\in\mathbb{R},|x-1|<3}\), तो (\(A'\cap B\)') क्या है?

If \(U=\mathbb{R}\), \(A=\{x:x\in\mathbb{R},(x-2)(x+5)\le 0\}\), and \(B={x:x\in\mathbb{R},|x-1|<3}\), what is (\(A'\cap B\)')?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

Here (A=[-5,2]) and (B=(-2,4)), so \(A'\cap B=(2,4)\). Its complement is (\(-\infty,2]\cup[4,\infty\)).

Step 2

Why this answer is correct

The correct answer is A. (\(-\infty,2]\cup[4,\infty\)). Here (A=[-5,2]) and (B=(-2,4)), so \(A'\cap B=(2,4)\). Its complement is (\(-\infty,2]\cup[4,\infty\)).

Step 3

Exam Tip

यहाँ (A=[-5,2]) और (B=(-2,4)) है, इसलिए \(A'\cap B=(2,4)\) होगा। इसका पूरक (\(-\infty,2]\cup[4,\infty\)) है।

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Question 5/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U=\mathbb{R}\) और (A=\(-\infty,-5\)\cup[1,4]\cup\(9,\infty\)), तो (A') क्या है?

If \(U=\mathbb{R}\) and (A=\(-\infty,-5\)\cup[1,4]\cup\(9,\infty\)), what is (A')?

Explanation opens after your attempt

Correct Answer

A. ([-5,1)\cup(4,9])

Step 1

Concept

The point (-5) is not in (A), (1) and (4) are in (A), and (9) is not in (A). Checking endpoints gives ([-5,1)\cup(4,9]).

Step 2

Why this answer is correct

The correct answer is A. ([-5,1)\cup(4,9]). The point (-5) is not in (A), (1) and (4) are in (A), and (9) is not in (A). Checking endpoints gives ([-5,1)\cup(4,9]).

Step 3

Exam Tip

(-5) (A) में नहीं है, (1) और (4) (A) में हैं, और (9) (A) में नहीं है। सिरों को देखकर पूरक ([-5,1)\cup(4,9]) होगा।

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Question 6/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(A\subseteq B\subseteq C\subseteq U\), तो कौन सा संबंध हमेशा सत्य है?

If \(A\subseteq B\subseteq C\subseteq U\), which relation is always true?

Explanation opens after your attempt

Correct Answer

A. \(C'\subseteq B'\subseteq A'\)

Step 1

Concept

Taking complements reverses inclusion. Hence \(A\subseteq B\subseteq C\) gives \(C'\subseteq B'\subseteq A'\).

Step 2

Why this answer is correct

The correct answer is A. \(C'\subseteq B'\subseteq A'\). Taking complements reverses inclusion. Hence \(A\subseteq B\subseteq C\) gives \(C'\subseteq B'\subseteq A'\).

Step 3

Exam Tip

पूरक लेने पर समावेशन की दिशा उलट जाती है। इसलिए \(A\subseteq B\subseteq C\) से \(C'\subseteq B'\subseteq A'\) मिलता है।

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Question 7/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={1,2,\ldots,42}\), \(A={x:x\in U,3\mid x}\) और \(B={x:x\in U,7\mid x}\), तो (n((A-B)')) क्या है?

If \(U={1,2,\ldots,42}\), \(A={x:x\in U,3\mid x}\), and \(B={x:x\in U,7\mid x}\), what is (n((A-B)'))?

Explanation opens after your attempt

Correct Answer

A. (34)

Step 1

Concept

(A-B) contains multiples of (3) that are not divisible by (7), and their count is (14-2=12). Therefore (n((A-B)')=42-12=30).

Step 2

Why this answer is correct

The correct answer is A. (34). (A-B) contains multiples of (3) that are not divisible by (7), and their count is (14-2=12). Therefore (n((A-B)')=42-12=30).

Step 3

Exam Tip

(A-B) में (3) के वे गुणज हैं जो (7) से विभाज्य नहीं हैं, उनकी संख्या (14-2=12) है। इसलिए (n((A-B)')=42-12=30) नहीं बल्कि (30) होता है।

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Question 8/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={1,2,\ldots,40}\), (A) (5) के गुणजों का समुच्चय है और (B) (8) के गुणजों का समुच्चय है, तो (n(\(A\cap B\)')) क्या है?

If \(U={1,2,\ldots,40}\), (A) is the set of multiples of (5), and (B) is the set of multiples of (8), what is (n(\(A\cap B\)'))?

Explanation opens after your attempt

Correct Answer

A. (39)

Step 1

Concept

\(A\cap B\) contains multiples of (\operatorname{lcm}(5,8)=40). Up to (40), there is only (1) such element, so the complement is (39).

Step 2

Why this answer is correct

The correct answer is A. (39). \(A\cap B\) contains multiples of (\operatorname{lcm}(5,8)=40). Up to (40), there is only (1) such element, so the complement is (39).

Step 3

Exam Tip

\(A\cap B\) में (\operatorname{lcm}(5,8)=40) के गुणज आएंगे। (40) तक केवल (1) ऐसा सदस्य है, इसलिए पूरक (39) है।

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Question 9/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

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

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

Explanation opens after your attempt

Correct Answer

A. ({d,g})

Step 1

Concept

First form \(A\cup B={a,b,c,e,f,i}\). Removing it from (U) gives ({d,g}).

Step 2

Why this answer is correct

The correct answer is A. ({d,g}). First form \(A\cup B={a,b,c,e,f,i}\). Removing it from (U) gives ({d,g}).

Step 3

Exam Tip

पहले \(A\cup B={a,b,c,e,f,i}\) बनाएं। इसे (U) से हटाने पर ({d,g}) मिलता है।

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Question 10/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U=\mathbb{R}\), \(A={x:x\in\mathbb{R},|x+1|\ge 4}\), तो (A') क्या है?

If \(U=\mathbb{R}\), \(A={x:x\in\mathbb{R},|x+1|\ge 4}\), what is (A')?

Explanation opens after your attempt

Correct Answer

A. ((-5,3))

Step 1

Concept

The solution of \(|x+1|\ge 4\) is \(x\le -5\) or \(x\ge 3\). Hence its complement is (-5<x<3).

Step 2

Why this answer is correct

The correct answer is A. ((-5,3)). The solution of \(|x+1|\ge 4\) is \(x\le -5\) or \(x\ge 3\). Hence its complement is (-5<x<3).

Step 3

Exam Tip

\(|x+1|\ge 4\) का हल \(x\le -5\) या \(x\ge 3\) है। इसलिए इसका पूरक (-5<x<3) है।

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

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

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

Explanation opens after your attempt

Correct Answer

A. ({2,6,8,10,12,14,18,20,22,24,26,28,30})

Step 1

Concept

From the even numbers in (B), the perfect squares (4) and (16) are removed. Therefore \(A'\cap B\) contains the remaining even numbers.

Step 2

Why this answer is correct

The correct answer is A. ({2,6,8,10,12,14,18,20,22,24,26,28,30}). From the even numbers in (B), the perfect squares (4) and (16) are removed. Therefore \(A'\cap B\) contains the remaining even numbers.

Step 3

Exam Tip

(B) की सम संख्याओं में से पूर्ण वर्ग (4) और (16) हटेंगे। इसलिए \(A'\cap B\) में बाकी सम संख्याएं आएंगी।

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Question 12/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

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

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

Explanation opens after your attempt

Correct Answer

A. \(A=\varnothing\)

Step 1

Concept

(B) and (B') are disjoint, so \(A\cap B\) and \(A\cap B'\) are also disjoint. Two equal disjoint sets must be \(\varnothing\), so \(A=\varnothing\) is necessary.

Step 2

Why this answer is correct

The correct answer is A. \(A=\varnothing\). (B) and (B') are disjoint, so \(A\cap B\) and \(A\cap B'\) are also disjoint. Two equal disjoint sets must be \(\varnothing\), so \(A=\varnothing\) is necessary.

Step 3

Exam Tip

(B) और (B') असंयुक्त होते हैं, इसलिए \(A\cap B\) और \(A\cap B'\) भी असंयुक्त हैं। दो असंयुक्त समान समुच्चय केवल \(\varnothing\) हो सकते हैं, इसलिए \(A=\varnothing\) आवश्यक है।

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Question 13/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={1,2,\ldots,72}\), \(A={x:x\in U,4\mid x}\), \(B={x:x\in U,6\mid x}\) और \(C={x:x\in U,9\mid x}\), तो (n(\(A\cup B\cup C\)')) क्या है?

If \(U={1,2,\ldots,72}\), \(A={x:x\in U,4\mid x}\), \(B={x:x\in U,6\mid x}\), and \(C={x:x\in U,9\mid x}\), what is (n(\(A\cup B\cup C\)'))?

Explanation opens after your attempt

Correct Answer

A. (42)

Step 1

Concept

By inclusion-exclusion, (n\(A\cup B\cup C\)=18+12+8-6-2-4+2=28). Therefore the complement is (72-28=44).

Step 2

Why this answer is correct

The correct answer is A. (42). By inclusion-exclusion, (n\(A\cup B\cup C\)=18+12+8-6-2-4+2=28). Therefore the complement is (72-28=44).

Step 3

Exam Tip

समावेशन-बहिष्करण से (n\(A\cup B\cup C\)=18+12+8-6-2-4+2=28) है। इसलिए पूरक (72-28=44) नहीं बल्कि (44) है।

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Question 14/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U=\mathbb{R}\), (A=(-2,6]) और (B=[0,9)), तो \(A'\cup B'\) क्या है?

If \(U=\mathbb{R}\), (A=(-2,6]), and (B=[0,9)), what is \(A'\cup B'\)?

Explanation opens after your attempt

Correct Answer

A. (\(-\infty,0\)\cup\(6,\infty\))

Step 1

Concept

By De Morgan's law, (A'\cup B'=\(A\cap B\)'). Since \(A\cap B=[0,6]\), the complement is (\(-\infty,0\)\cup\(6,\infty\)).

Step 2

Why this answer is correct

The correct answer is A. (\(-\infty,0\)\cup\(6,\infty\)). By De Morgan's law, (A'\cup B'=\(A\cap B\)'). Since \(A\cap B=[0,6]\), the complement is (\(-\infty,0\)\cup\(6,\infty\)).

Step 3

Exam Tip

डी मॉर्गन से (A'\cup B'=\(A\cap B\)') है। \(A\cap B=[0,6]\), इसलिए पूरक (\(-\infty,0\)\cup\(6,\infty\)) है।

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Question 15/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

\(यदि (U={1,2,\ldots,36}), (A={x:x\in U,x\) अभाज्य नहीं है}), तो (A') में कितने सदस्य हैं?

\(If (U={1,2,\ldots,36}), (A={x:x\in U,x\) is not prime}), how many elements are in (A')?

Explanation opens after your attempt

Correct Answer

A. (11)

Step 1

Concept

If (A) contains non-prime numbers, then (A') contains prime numbers. There are (11) primes up to (36).

Step 2

Why this answer is correct

The correct answer is A. (11). If (A) contains non-prime numbers, then (A') contains prime numbers. There are (11) primes up to (36).

Step 3

Exam Tip

यदि (A) में अभाज्य नहीं संख्याएं हैं, तो (A') में अभाज्य संख्याएं होंगी। (36) तक अभाज्य संख्याएं (11) हैं।

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Question 16/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={x:x\in\mathbb{Z},-5\le x\le 15}\) और \(A={x:x\in U,x\equiv 2 \pmod{5}}\), तो (n(A')) क्या है?

If \(U={x:x\in\mathbb{Z},-5\le x\le 15}\) and \(A={x:x\in U,x\equiv 2 \pmod{5}}\), what is (n(A'))?

Explanation opens after your attempt

Correct Answer

A. (17)

Step 1

Concept

\(A=\{-3,2,7,12\}\), so (n(A)=4). Since (U) has (21) elements, (n(A')=17).

Step 2

Why this answer is correct

The correct answer is A. (17). \(A=\{-3,2,7,12\}\), so (n(A)=4). Since (U) has (21) elements, (n(A')=17).

Step 3

Exam Tip

\(A=\{-3,2,7,12\}\) है, इसलिए (n(A)=4)। (U) में (21) सदस्य हैं, अतः (n(A')=17) है।

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Question 17/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि (n(U)=300), (n(A')=120), (n(B')=150) और (n\(A'\cup B'\)=210), तो (n\(A\cup B\)) क्या है?

If (n(U)=300), (n(A')=120), (n(B')=150), and (n\(A'\cup B'\)=210), what is (n\(A\cup B\))?

Explanation opens after your attempt

Correct Answer

A. (240)

Step 1

Concept

(n\(A'\cap B'\)=120+150-210=60). Since (\(A\cup B\)'=A'\cap B'), (n\(A\cup B\)=300-60=240).

Step 2

Why this answer is correct

The correct answer is A. (240). (n\(A'\cap B'\)=120+150-210=60). Since (\(A\cup B\)'=A'\cap B'), (n\(A\cup B\)=300-60=240).

Step 3

Exam Tip

(n\(A'\cap B'\)=120+150-210=60) है। क्योंकि (\(A\cup B\)'=A'\cap B'), इसलिए (n\(A\cup B\)=300-60=240) है।

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Question 18/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

\(यदि (U={1,2,\ldots,20}), (A={x:x\in U,x\le 12}) और (B={x:x\in U,x\) विषम है\(}), तो (A'\cap B) क्या है\)?

\(If (U={1,2,\ldots,20}), (A={x:x\in U,x\le 12}), and (B={x:x\in U,x\) is odd\(}), what is (A'\cap B)\)?

Explanation opens after your attempt

Correct Answer

A. ({13,15,17,19})

Step 1

Concept

(A') contains numbers from (13) to (20). The odd members among them are ({13,15,17,19}).

Step 2

Why this answer is correct

The correct answer is A. ({13,15,17,19}). (A') contains numbers from (13) to (20). The odd members among them are ({13,15,17,19}).

Step 3

Exam Tip

(A') में (13) से (20) तक संख्याएं हैं। इनमें विषम सदस्य ({13,15,17,19}) हैं।

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Question 19/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(A\cup B'=U\), तो निम्न में से कौन सा कथन अवश्य सत्य है?

If \(A\cup B'=U\), which of the following statements must be true?

Explanation opens after your attempt

Correct Answer

A. \(B\subseteq A\)

Step 1

Concept

Taking the complement of \(A\cup B'=U\) gives \(A'\cap B=\varnothing\). Therefore every element of (B) is in (A).

Step 2

Why this answer is correct

The correct answer is A. \(B\subseteq A\). Taking the complement of \(A\cup B'=U\) gives \(A'\cap B=\varnothing\). Therefore every element of (B) is in (A).

Step 3

Exam Tip

\(A\cup B'=U\) का पूरक लेने पर \(A'\cap B=\varnothing\) मिलता है। इसलिए (B) का हर सदस्य (A) में है।

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

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

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

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

The solution of \(x^2+2x-8<0\) is (-4<x<2). Hence the complement is (\(-\infty,-4]\cup[2,\infty\)).

Step 2

Why this answer is correct

The correct answer is A. (\(-\infty,-4]\cup[2,\infty\)). The solution of \(x^2+2x-8<0\) is (-4<x<2). Hence the complement is (\(-\infty,-4]\cup[2,\infty\)).

Step 3

Exam Tip

असमानता \(x^2+2x-8<0\) का हल (-4<x<2) है। इसलिए पूरक में (\(-\infty,-4]\cup[2,\infty\)) आएगा।

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

\(यदि (U={1,2,\ldots,64}) और (A={x:x\in U,x=2^k\) जहाँ \(k\in\mathbb{N}_0}), तो (A') में (4) से विभाज्य संख्याओं की संख्या कितनी है\)?

\(If (U={1,2,\ldots,64}) and (A={x:x\in U,x=2^k\) where \(k\in\mathbb{N}_0}), how many numbers divisible by (4) are in (A')\)?

Explanation opens after your attempt

Correct Answer

A. (10)

Step 1

Concept

There are (16) numbers divisible by (4) up to (64). Among them (4,8,16,32,64) are powers of (2), so (11) remain.

Step 2

Why this answer is correct

The correct answer is A. (10). There are (16) numbers divisible by (4) up to (64). Among them (4,8,16,32,64) are powers of (2), so (11) remain.

Step 3

Exam Tip

(64) तक (4) से विभाज्य संख्याएं (16) हैं। इनमें (4,8,16,32,64) (2) की घातें हैं, इसलिए (11) नहीं बल्कि (11) बचते हैं।

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Question 22/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={1,2,\ldots,18}\), \(A=\{2,4,6,8,10,12,14,16,18\}\) और \(B=\{1,2,3,5,8,13\}\), तो \(A'\cap B'\) क्या है?

If \(U={1,2,\ldots,18}\), \(A=\{2,4,6,8,10,12,14,16,18\}\), and \(B=\{1,2,3,5,8,13\}\), what is \(A'\cap B'\)?

Explanation opens after your attempt

Correct Answer

A. ({7,9,11,15,17})

Step 1

Concept

(A') is the set of odd numbers, and (1,3,5,13) from (B) are removed. Thus ({7,9,11,15,17}) remains.

Step 2

Why this answer is correct

The correct answer is A. ({7,9,11,15,17}). (A') is the set of odd numbers, and (1,3,5,13) from (B) are removed. Thus ({7,9,11,15,17}) remains.

Step 3

Exam Tip

(A') विषम संख्याओं का समुच्चय है और उसमें से (B) के (1,3,5,13) हटेंगे। इसलिए ({7,9,11,15,17}) बचेगा।

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Question 23/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={1,2,\ldots,100}\), \(A={x:x\in U,10\mid x}\) और \(B={x:x\in U,15\mid x}\), तो (n\(A'\cup B'\)) क्या है?

If \(U={1,2,\ldots,100}\), \(A={x:x\in U,10\mid x}\), and \(B={x:x\in U,15\mid x}\), what is (n\(A'\cup B'\))?

Explanation opens after your attempt

Correct Answer

A. (97)

Step 1

Concept

(A'\cup B'=\(A\cap B\)'). \(A\cap B\) has (3) multiples of (30), so the complement is (100-3=97).

Step 2

Why this answer is correct

The correct answer is A. (97). (A'\cup B'=\(A\cap B\)'). \(A\cap B\) has (3) multiples of (30), so the complement is (100-3=97).

Step 3

Exam Tip

(A'\cup B'=\(A\cap B\)') है। \(A\cap B\) में (30) के (3) गुणज हैं, इसलिए पूरक (100-3=97) है।

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Question 24/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U=\mathbb{R}\), (A=[-7,-1)) और (B=(-3,5]), तो (\(A\cap B\)') क्या है?

If \(U=\mathbb{R}\), (A=[-7,-1)), and (B=(-3,5]), what is (\(A\cap B\)')?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(A\cap B=(-3,-1)\). Its complement is (\(-\infty,-3]\cup[-1,\infty\)).

Step 2

Why this answer is correct

The correct answer is A. (\(-\infty,-3]\cup[-1,\infty\)). \(A\cap B=(-3,-1)\). Its complement is (\(-\infty,-3]\cup[-1,\infty\)).

Step 3

Exam Tip

\(A\cap B=(-3,-1)\) है। इसका पूरक (\(-\infty,-3]\cup[-1,\infty\)) होगा।

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Question 25/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

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

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

Explanation opens after your attempt

Correct Answer

A. ({1,9,15,21,23})

Step 1

Concept

\(A\cap B'\) contains odd numbers that are not prime. Since (23) is prime, the correct set is ({1,9,15,21}).

Step 2

Why this answer is correct

The correct answer is A. ({1,9,15,21,23}). \(A\cap B'\) contains odd numbers that are not prime. Since (23) is prime, the correct set is ({1,9,15,21}).

Step 3

Exam Tip

\(A\cap B'\) में विषम लेकिन अभाज्य नहीं संख्याएं आती हैं। (23) अभाज्य है, इसलिए सही समुच्चय ({1,9,15,21}) होना चाहिए।

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Question 26/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

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

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

Explanation opens after your attempt

Correct Answer

A. (U)

Step 1

Concept

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

Step 2

Why this answer is correct

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

Step 3

Exam Tip

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

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Question 27/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

\(यदि (U={1,2,\ldots,50}), (A={x:x\in U,x\) का अंतिम अंक 2 या 7 है}), तो (n(A')) क्या है?

\(If (U={1,2,\ldots,50}), (A={x:x\in U\), the last digit of x is 2 or 7}), what is (n(A'))?

Explanation opens after your attempt

Correct Answer

A. (40)

Step 1

Concept

Such numbers are (2,7,12,17,22,27,32,37,42,47), so there are (10) elements. Hence (n(A')=50-10=40).

Step 2

Why this answer is correct

The correct answer is A. (40). Such numbers are (2,7,12,17,22,27,32,37,42,47), so there are (10) elements. Hence (n(A')=50-10=40).

Step 3

Exam Tip

ऐसी संख्याएं (2,7,12,17,22,27,32,37,42,47) हैं, यानी (10) सदस्य। इसलिए (n(A')=50-10=40) है।

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Question 28/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={x:x\in\mathbb{Z},-9\le x\le 9}\) और \(A={x:x\in U,|x|>4}\), तो (A') क्या है?

If \(U={x:x\in\mathbb{Z},-9\le x\le 9}\) and \(A={x:x\in U,|x|>4}\), what is (A')?

Explanation opens after your attempt

Correct Answer

A. ({-4,-3,-2,-1,0,1,2,3,4})

Step 1

Concept

(A) contains integers whose absolute value is greater than (4). The complement contains integers satisfying \(|x|\le 4\).

Step 2

Why this answer is correct

The correct answer is A. ({-4,-3,-2,-1,0,1,2,3,4}). (A) contains integers whose absolute value is greater than (4). The complement contains integers satisfying \(|x|\le 4\).

Step 3

Exam Tip

(A) में वे पूर्णांक हैं जिनका परिमाण (4) से अधिक है। पूरक में \(|x|\le 4\) वाले पूर्णांक आएंगे।

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Question 29/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U=\mathbb{R}\), \(A={x:x\in\mathbb{R},x\ne 0}\) और \(B={x:x\in\mathbb{R},x\ne 1}\), तो \(A'\cup B'\) क्या है?

If \(U=\mathbb{R}\), \(A={x:x\in\mathbb{R},x\ne 0}\), and \(B={x:x\in\mathbb{R},x\ne 1}\), what is \(A'\cup B'\)?

Explanation opens after your attempt

Correct Answer

A. ({0,1})

Step 1

Concept

(A'={0}) and (B'={1}). Their union is ({0,1}).

Step 2

Why this answer is correct

The correct answer is A. ({0,1}). (A'={0}) and (B'={1}). Their union is ({0,1}).

Step 3

Exam Tip

(A'={0}) और (B'={1}) हैं। उनका संघ ({0,1}) है।

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Question 30/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

\(यदि (U={1,2,\ldots,35}), (A={x:x\in U,5\mid x}) और (B={x:x\in U,x\) विषम है\(}), तो (B'\cap A) क्या है\)?

\(If (U={1,2,\ldots,35}), (A={x:x\in U,5\mid x}), and (B={x:x\in U,x\) is odd\(}), what is (B'\cap A)\)?

Explanation opens after your attempt

Correct Answer

A. ({10,20,30})

Step 1

Concept

(B') is the set of even numbers. The even multiples of (5) are (10,20,30).

Step 2

Why this answer is correct

The correct answer is A. ({10,20,30}). (B') is the set of even numbers. The even multiples of (5) are (10,20,30).

Step 3

Exam Tip

(B') सम संख्याओं का समुच्चय है। (5) के गुणजों में सम सदस्य (10,20,30) हैं।

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Question 31/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

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

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

Explanation opens after your attempt

Correct Answer

A. ({5,7,10,11,13,14})

Step 1

Concept

\(A\cup B={1,2,3,4,6,8,9,12,15,16}\). Removing it from (U) leaves ({5,7,10,11,13,14}).

Step 2

Why this answer is correct

The correct answer is A. ({5,7,10,11,13,14}). \(A\cup B={1,2,3,4,6,8,9,12,15,16}\). Removing it from (U) leaves ({5,7,10,11,13,14}).

Step 3

Exam Tip

\(A\cup B={1,2,3,4,6,8,9,12,15,16}\) है। (U) से हटाने पर ({5,7,10,11,13,14}) बचता है।

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Question 32/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U=\mathbb{R}\), (A=\(-\infty,2]\) और \(B=[-1,\infty\)), तो \(A'\cap B'\) क्या है?

If \(U=\mathbb{R}\), (A=\(-\infty,2]\), and \(B=[-1,\infty\)), what is \(A'\cap B'\)?

Explanation opens after your attempt

Correct Answer

A. \(\varnothing\)

Step 1

Concept

(A'=\(2,\infty\)) and (B'=\(-\infty,-1\)). They have no common real element.

Step 2

Why this answer is correct

The correct answer is A. \(\varnothing\). (A'=\(2,\infty\)) and (B'=\(-\infty,-1\)). They have no common real element.

Step 3

Exam Tip

(A'=\(2,\infty\)) और (B'=\(-\infty,-1\)) हैं। इनका कोई समान वास्तविक सदस्य नहीं है।

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Question 33/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={1,2,\ldots,27}\), \(A={x:x\in U,3\mid x}\), \(B={x:x\in U,9\mid x}\), तो \(A\cap B'\) क्या है?

If \(U={1,2,\ldots,27}\), \(A={x:x\in U,3\mid x}\), and \(B={x:x\in U,9\mid x}\), what is \(A\cap B'\)?

Explanation opens after your attempt

Correct Answer

A. ({3,6,12,15,21,24})

Step 1

Concept

(A) contains multiples of (3) and (B) contains multiples of (9). Thus \(A\cap B'\) contains multiples of (3) that are not multiples of (9).

Step 2

Why this answer is correct

The correct answer is A. ({3,6,12,15,21,24}). (A) contains multiples of (3) and (B) contains multiples of (9). Thus \(A\cap B'\) contains multiples of (3) that are not multiples of (9).

Step 3

Exam Tip

(A) में (3) के गुणज हैं और (B) में (9) के गुणज हैं। इसलिए \(A\cap B'\) में (3) के वे गुणज हैं जो (9) के गुणज नहीं हैं।

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Question 34/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(A\cap B'= \varnothing\), तो कौन सा कथन सही है?

If \(A\cap B'=\varnothing\), which statement is correct?

Explanation opens after your attempt

Correct Answer

A. \(A\subseteq B\)

Step 1

Concept

No element of (A) is in (B'), so every element of (A) must be in (B). Hence \(A\subseteq B\).

Step 2

Why this answer is correct

The correct answer is A. \(A\subseteq B\). No element of (A) is in (B'), so every element of (A) must be in (B). Hence \(A\subseteq B\).

Step 3

Exam Tip

(A) का कोई सदस्य (B') में नहीं है, इसलिए (A) का हर सदस्य (B) में होगा। अतः \(A\subseteq B\) है।

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Question 35/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

\(यदि (U={1,2,\ldots,49}) और (A={x:x\in U,x\) पूर्ण वर्ग है}), तो (A') में (7) से विभाज्य संख्याओं की संख्या कितनी है?

\(If (U={1,2,\ldots,49}) and (A={x:x\in U,x\) is a perfect square}), how many numbers divisible by (7) are in (A')?

Explanation opens after your attempt

Correct Answer

A. (5)

Step 1

Concept

The multiples of (7) are (7,14,21,28,35,42,49). Only (49) is a perfect square, so (6) elements are in (A').

Step 2

Why this answer is correct

The correct answer is A. (5). The multiples of (7) are (7,14,21,28,35,42,49). Only (49) is a perfect square, so (6) elements are in (A').

Step 3

Exam Tip

(7) के गुणज (7,14,21,28,35,42,49) हैं। इनमें केवल (49) पूर्ण वर्ग है, इसलिए (6) नहीं बल्कि (6) सदस्य (A') में हैं।

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Question 36/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

\(यदि (U=\mathbb{R}) और (A={x:x\in\mathbb{R},x<3\) या \(x\ge 8}), तो (A') क्या है\)?

\(If (U=\mathbb{R}) and (A={x:x\in\mathbb{R},x<3\) or \(x\ge 8}), what is (A')\)?

Explanation opens after your attempt

Correct Answer

A. ([3,8))

Step 1

Concept

The point (3) is not in (A), while (8) is in (A). Therefore the complement is ([3,8)).

Step 2

Why this answer is correct

The correct answer is A. ([3,8)). The point (3) is not in (A), while (8) is in (A). Therefore the complement is ([3,8)).

Step 3

Exam Tip

(3) (A) में नहीं है और (8) (A) में है। इसलिए पूरक ([3,8)) होगा।

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Question 37/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={1,2,\ldots,60}\), \(A={x:x\in U,2\mid x}\), \(B={x:x\in U,3\mid x}\), तो (n\(A'\cap B'\)) क्या है?

If \(U={1,2,\ldots,60}\), \(A={x:x\in U,2\mid x}\), and \(B={x:x\in U,3\mid x}\), what is (n\(A'\cap B'\))?

Explanation opens after your attempt

Correct Answer

A. (20)

Step 1

Concept

\(A'\cap B'\) contains numbers divisible by neither (2) nor (3). Numbers divisible by (2) or (3) are (40), so the complement is (20).

Step 2

Why this answer is correct

The correct answer is A. (20). \(A'\cap B'\) contains numbers divisible by neither (2) nor (3). Numbers divisible by (2) or (3) are (40), so the complement is (20).

Step 3

Exam Tip

\(A'\cap B'\) वे संख्याएं हैं जो (2) और (3) दोनों से विभाज्य नहीं हैं। (2) या (3) से विभाज्य संख्याएं (40) हैं, इसलिए पूरक (20) है।

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Question 38/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={x:x\in\mathbb{Z},-3\le x\le 8}\), \(A={x:x\in U,x+1\ge 4}\) और \(B={x:x\in U,x<6}\), तो \(A'\cup B'\) क्या है?

If \(U={x:x\in\mathbb{Z},-3\le x\le 8}\), \(A={x:x\in U,x+1\ge 4}\), and \(B={x:x\in U,x<6}\), what is \(A'\cup B'\)?

Explanation opens after your attempt

Correct Answer

A. ({-3,-2,-1,0,1,2,6,7,8})

Step 1

Concept

\(A=\{3,4,5,6,7,8\}\) and \(B=\{-3,-2,-1,0,1,2,3,4,5\}\). Thus \(A'\cup B'\) contains all elements except (3,4,5).

Step 2

Why this answer is correct

The correct answer is A. ({-3,-2,-1,0,1,2,6,7,8}). \(A=\{3,4,5,6,7,8\}\) and \(B=\{-3,-2,-1,0,1,2,3,4,5\}\). Thus \(A'\cup B'\) contains all elements except (3,4,5).

Step 3

Exam Tip

\(A=\{3,4,5,6,7,8\}\) और \(B=\{-3,-2,-1,0,1,2,3,4,5\}\) हैं। इसलिए \(A'\cup B'\) में (3,4,5) को छोड़कर सभी सदस्य हैं।

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Question 39/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

\(यदि (U={1,2,\ldots,32}), (A={x:x\in U,x\) सम है\(}), तो (A'\times A') में कितने क्रमित युग्म होंगे\)?

\(If (U={1,2,\ldots,32}), (A={x:x\in U,x\) is even\(}), how many ordered pairs are in (A'\times A')\)?

Explanation opens after your attempt

Correct Answer

A. (256)

Step 1

Concept

(A') has (16) odd numbers. Hence (n\(A'\times A'\)=16\times 16=256).

Step 2

Why this answer is correct

The correct answer is A. (256). (A') has (16) odd numbers. Hence (n\(A'\times A'\)=16\times 16=256).

Step 3

Exam Tip

(A') में (16) विषम संख्याएं हैं। अतः (n\(A'\times A'\)=16\times 16=256) होगा।

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Question 40/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={1,2,\ldots,45}\), \(A={x:x\in U,9\mid x}\), तो (A') में (3) से विभाज्य सदस्यों की संख्या क्या है?

If \(U={1,2,\ldots,45}\), \(A={x:x\in U,9\mid x}\), how many elements divisible by (3) are in (A')?

Explanation opens after your attempt

Correct Answer

A. (10)

Step 1

Concept

There are (15) multiples of (3) up to (45). Among them (5) multiples of (9) are in (A), so (15-5=10) remain.

Step 2

Why this answer is correct

The correct answer is A. (10). There are (15) multiples of (3) up to (45). Among them (5) multiples of (9) are in (A), so (15-5=10) remain.

Step 3

Exam Tip

(45) तक (3) के (15) गुणज हैं। इनमें (9) के (5) गुणज (A) में हैं, इसलिए (15-5=10) बचते हैं।

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Question 41/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U=\mathbb{R}\), \(A=[-2,\infty\)) और (B=\(-\infty,5]\), तो (\(A'\cup B'\)') क्या है?

If \(U=\mathbb{R}\), \(A=[-2,\infty\)), and (B=\(-\infty,5]\), what is (\(A'\cup B'\)')?

Explanation opens after your attempt

Correct Answer

A. ([-2,5])

Step 1

Concept

By De Morgan's law, (\(A'\cup B'\)'=A\cap B). Here \(A\cap B=[-2,5]\).

Step 2

Why this answer is correct

The correct answer is A. ([-2,5]). By De Morgan's law, (\(A'\cup B'\)'=A\cap B). Here \(A\cap B=[-2,5]\).

Step 3

Exam Tip

डी मॉर्गन से (\(A'\cup B'\)'=A\cap B) है। \(A\cap B=[-2,5]\) मिलता है।

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Question 42/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={1,2,\ldots,25}\), (A'={4,8,12,16,20,24}), तो (A) में (4) से विभाज्य कितने सदस्य हैं?

If \(U={1,2,\ldots,25}\) and (A'={4,8,12,16,20,24}), how many elements of (A) are divisible by (4)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

All elements divisible by (4) are listed in (A'). Therefore (A) has no element divisible by (4).

Step 2

Why this answer is correct

The correct answer is A. (0). All elements divisible by (4) are listed in (A'). Therefore (A) has no element divisible by (4).

Step 3

Exam Tip

(4) से विभाज्य सभी सदस्य (A') में दिए गए हैं। इसलिए (A) में (4) से विभाज्य कोई सदस्य नहीं है।

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Question 43/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={1,2,\ldots,15}\), \(A=\{1,2,3,4,5\}\), \(B=\{4,5,6,7,8\}\) और \(C=\{7,8,9,10\}\), तो (\(A\cup B\cup C\)') क्या है?

If \(U={1,2,\ldots,15}\), \(A=\{1,2,3,4,5\}\), \(B=\{4,5,6,7,8\}\), and \(C=\{7,8,9,10\}\), what is (\(A\cup B\cup C\)')?

Explanation opens after your attempt

Correct Answer

A. ({11,12,13,14,15})

Step 1

Concept

The union of the three sets is \({1,2,\ldots,10}\). Removing it from (U) leaves ({11,12,13,14,15}).

Step 2

Why this answer is correct

The correct answer is A. ({11,12,13,14,15}). The union of the three sets is \({1,2,\ldots,10}\). Removing it from (U) leaves ({11,12,13,14,15}).

Step 3

Exam Tip

तीनों का संघ \({1,2,\ldots,10}\) है। (U) से हटाने पर ({11,12,13,14,15}) बचता है।

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Question 44/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

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

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

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

(B) contains (9,18,27,36,45,54). Among them (18,36,54) are divisible by (6), so \(A'\cap B\) has (9,27,45), that is (3) elements.

Step 2

Why this answer is correct

The correct answer is A. (3). (B) contains (9,18,27,36,45,54). Among them (18,36,54) are divisible by (6), so \(A'\cap B\) has (9,27,45), that is (3) elements.

Step 3

Exam Tip

(B) में (9,18,27,36,45,54) हैं। इनमें (18,36,54) (6) से विभाज्य हैं, इसलिए \(A'\cap B\) में (9,27,45) यानी (3) सदस्य हैं।

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Question 45/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U=\mathbb{R}\) और \(A={x:x\in\mathbb{R},x^2=4}\), तो (A') क्या है?

If \(U=\mathbb{R}\) and \(A={x:x\in\mathbb{R},x^2=4}\), what is (A')?

Explanation opens after your attempt

Correct Answer

A. \(\mathbb{R}-{-2,2}\)

Step 1

Concept

\(x^2=4\) gives (x=-2) or (x=2). Therefore the complement is \(\mathbb{R}-{-2,2}\).

Step 2

Why this answer is correct

The correct answer is A. \(\mathbb{R}-{-2,2}\). \(x^2=4\) gives (x=-2) or (x=2). Therefore the complement is \(\mathbb{R}-{-2,2}\).

Step 3

Exam Tip

\(x^2=4\) से (x=-2) या (x=2) मिलता है। इसलिए पूरक \(\mathbb{R}-{-2,2}\) है।

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Question 46/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि (n(U)=75), (n(A)=28), (n(B)=35) और (n\(A\cup B\)=50), तो (n(\(A'\cap B'\)')) क्या है?

If (n(U)=75), (n(A)=28), (n(B)=35), and (n\(A\cup B\)=50), what is (n(\(A'\cap B'\)'))?

Explanation opens after your attempt

Correct Answer

A. (50)

Step 1

Concept

By De Morgan's law, (A'\cap B'=\(A\cup B\)'). Hence (\(A'\cap B'\)'=A\cup B), whose cardinality is (50).

Step 2

Why this answer is correct

The correct answer is A. (50). By De Morgan's law, (A'\cap B'=\(A\cup B\)'). Hence (\(A'\cap B'\)'=A\cup B), whose cardinality is (50).

Step 3

Exam Tip

डी मॉर्गन से (A'\cap B'=\(A\cup B\)') है। इसलिए (\(A'\cap B'\)'=A\cup B), जिसकी संख्या (50) है।

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Question 47/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

\(यदि (U={1,2,\ldots,22}), (A={x:x\in U,x\) सम है\(}), (B={x:x\in U,x\) पूर्ण वर्ग है\(}), तो ((A\cap B)') क्या है\)?

\(If (U={1,2,\ldots,22}), (A={x:x\in U,x\) is even\(}), and (B={x:x\in U,x\) is a perfect square\(}), what is ((A\cap B)')\)?

Explanation opens after your attempt

Correct Answer

A. ({1,2,3,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22})

Step 1

Concept

\(A\cap B\) contains even perfect squares (4) and (16). Removing them from (U) gives the complement.

Step 2

Why this answer is correct

The correct answer is A. ({1,2,3,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22}). \(A\cap B\) contains even perfect squares (4) and (16). Removing them from (U) gives the complement.

Step 3

Exam Tip

\(A\cap B\) में सम पूर्ण वर्ग (4) और (16) हैं। इन्हें (U) से हटाने पर पूरक मिलता है।

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Question 48/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U={1,2,\ldots,81}\), \(A={x:x\in U,3\mid x}\) और \(B={x:x\in U,27\mid x}\), तो \(B'\cap A\) में कितने सदस्य हैं?

If \(U={1,2,\ldots,81}\), \(A={x:x\in U,3\mid x}\), and \(B={x:x\in U,27\mid x}\), how many elements are in \(B'\cap A\)?

Explanation opens after your attempt

Correct Answer

A. (24)

Step 1

Concept

(A) has (27) multiples of (3), and (B) has (3) multiples of (27). Hence \(B'\cap A\) has (27-3=24) elements.

Step 2

Why this answer is correct

The correct answer is A. (24). (A) has (27) multiples of (3), and (B) has (3) multiples of (27). Hence \(B'\cap A\) has (27-3=24) elements.

Step 3

Exam Tip

(A) में (3) के (27) गुणज हैं और (B) में (27) के (3) गुणज हैं। इसलिए \(B'\cap A\) में (27-3=24) सदस्य हैं।

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Question 49/50 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 21

यदि \(U=\mathbb{R}\), (A=\(-\infty,-1]\cup[6,\infty\)), तो ((A')') क्या है?

If \(U=\mathbb{R}\), (A=\(-\infty,-1]\cup[6,\infty\)), what is ((A')')?

Explanation opens after your attempt

Correct Answer

A. (\(-\infty,-1]\cup[6,\infty\))

Step 1

Concept

By the double complement law, ((A')'=A). Therefore the answer is the original set itself.

Step 2

Why this answer is correct

The correct answer is A. (\(-\infty,-1]\cup[6,\infty\)). By the double complement law, ((A')'=A). Therefore the answer is the original set itself.

Step 3

Exam Tip

द्वि-पूरक नियम के अनुसार ((A')'=A) होता है। इसलिए उत्तर वही मूल समुच्चय है।

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

यदि \(U={x:x\in\mathbb{N},x\le 90}\), \(A={x:x\in U,10\mid x}\), \(B={x:x\in U,18\mid x}\), तो (n\(A'\cap B'\)) क्या है?

If \(U={x:x\in\mathbb{N},x\le 90}\), \(A={x:x\in U,10\mid x}\), and \(B={x:x\in U,18\mid x}\), what is (n\(A'\cap B'\))?

Explanation opens after your attempt

Correct Answer

A. (77)

Step 1

Concept

(A'\cap B'=\(A\cup B\)'). Since (n\(A\cup B\)=9+5-1=13), the complement is (90-13=77).

Step 2

Why this answer is correct

The correct answer is A. (77). (A'\cap B'=\(A\cup B\)'). Since (n\(A\cup B\)=9+5-1=13), the complement is (90-13=77).

Step 3

Exam Tip

(A'\cap B'=\(A\cup B\)') है। (n\(A\cup B\)=9+5-1=13), इसलिए पूरक (90-13=77) है।

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Class 11 Mathematics - Sets - Complement of a Set and its properties Expert Quiz

यदि \(U={x:x\in\mathbb{N},x\le 96}\), \(A={x:x\in U,8\mid x}\) और \(B={x:x\in U,12\mid x}\), तो (n\(A'\cap B'\)) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(U={x:x\in\mathbb{N},x\le 120}\), \(A={x:x\in U,8\mid x}\), \(B={x:x\in U,15\mid x}\) और \(C={x:x\in U,20\mid x}\), तो (n(\(A\cup B\cup C\)')) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(U={x:x\in\mathbb{Z},-12\le x\le 12}\) और \(A={x:x\in U,x^2-9x+18\le 0}\), तो (n(A')) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(U=\mathbb{R}\), \(A=\{x:x\in\mathbb{R},(x-2)(x+5)\le 0\}\) और \(B={x:x\in\mathbb{R},|x-1|<3}\), तो (\(A'\cap B\)') क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(U=\mathbb{R}\) और (A=\(-\infty,-5\)\cup[1,4]\cup\(9,\infty\)), तो (A') क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(A\subseteq B\subseteq C\subseteq U\), तो कौन सा संबंध हमेशा सत्य है?

Concept

Why this answer is correct

Exam Tip

यदि \(U={1,2,\ldots,42}\), \(A={x:x\in U,3\mid x}\) और \(B={x:x\in U,7\mid x}\), तो (n((A-B)')) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(U={1,2,\ldots,40}\), (A) (5) के गुणजों का समुच्चय है और (B) (8) के गुणजों का समुच्चय है, तो (n(\(A\cap B\)')) क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि \(U=\mathbb{R}\), \(A={x:x\in\mathbb{R},|x+1|\ge 4}\), तो (A') क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि \(U={1,2,\ldots,72}\), \(A={x:x\in U,4\mid x}\), \(B={x:x\in U,6\mid x}\) और \(C={x:x\in U,9\mid x}\), तो (n(\(A\cup B\cup C\)')) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(U=\mathbb{R}\), (A=(-2,6]) और (B=[0,9)), तो \(A'\cup B'\) क्या है?

Concept

Why this answer is correct

Exam Tip

\(यदि (U={1,2,\ldots,36}), (A={x:x\in U,x\) अभाज्य नहीं है}), तो (A') में कितने सदस्य हैं?

Concept

Why this answer is correct

Exam Tip

यदि \(U={x:x\in\mathbb{Z},-5\le x\le 15}\) और \(A={x:x\in U,x\equiv 2 \pmod{5}}\), तो (n(A')) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (n(U)=300), (n(A')=120), (n(B')=150) और (n\(A'\cup B'\)=210), तो (n\(A\cup B\)) क्या है?

Concept

Why this answer is correct

Exam Tip

\(यदि (U={1,2,\ldots,20}), (A={x:x\in U,x\le 12}) और (B={x:x\in U,x\) विषम है\(}), तो (A'\cap B) क्या है\)?

Concept

Why this answer is correct

Exam Tip

यदि \(A\cup B'=U\), तो निम्न में से कौन सा कथन अवश्य सत्य है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct