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Mathematics Complement of a Set and its properties MCQ Questions for Class 11 General

Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.

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Same chapter ke nearby topics ko revise jarur karein. Exam preparation ke liye yeh topics important hain. jisme niche ke ye 7 Topics hain.

7 topics
01 Practice Topic Sets and their representations 614 MCQs 02 Practice Topic The Empty Set, Finite and Infinite Sets, Equal Sets 599 MCQs 03 Practice Topic Equal sets and Subsets 491 MCQs 04 Practice Topic Power Set and Universal Set 588 MCQs 05 Practice Topic Venn Diagrams 599 MCQs 06 Practice Topic Operations on Sets (Union, Intersection, Difference) 600 MCQs 07 Practice Topic The Empty Set, many more. Step 3: Hence the set is infinite. 1 MCQs

Complement of a Set and its properties Practice Questions

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Question 451/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 19

\(यदि सार्वत्रिक समुच्चय (U={1,2,3,\ldots,20}) और (A={x:x \in U\) तथा x अभाज्य है}) है, तो (A') क्या होगा?

\(If the universal set is (U={1,2,3,\ldots,20}) and (A={x:x \in U\) and x is prime}), then what is (A')?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

(A') में (U) के वे सदस्य आते हैं जो (A) में नहीं हैं। परीक्षा में (1) को अभाज्य न मानें। / (A') contains the elements of (U) that are not in (A). In exams remember that (1) is not prime.

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Question 452/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 19

यदि \(U={x:x \in \mathbb{N},x\le 48}\), \(A={x:x \in U,4\mid x}\) और \(B={x:x \in U,6\mid x}\) हैं, तो (n(\(A\cup B\)')) क्या है?

If \(U={x:x \in \mathbb{N},x\le 48}\), \(A={x:x \in U,4\mid x}\), and \(B={x:x \in U,6\mid x}\), what is (n(\(A\cup B\)'))?

Explanation opens after your attempt
Correct Answer

A. (32)

Explanation

Simple Explanation

(4) या (6) से विभाज्य संख्याएं (12+8-4=16) हैं। इसलिए पूरक में (48-16=32) सदस्य होंगे। / Numbers divisible by (4) or (6) are (12+8-4=16). So the complement has (48-16=32) elements.

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Question 453/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 19

\(यदि (U={x:x \in \mathbb{Z}, -5 \le x \le 5}) और (A={x:x \in U\) तथा \(x^2<10}) है, तो (A') ज्ञात कीजिए\)।

\(If (U={x:x \in \mathbb{Z}, -5 \le x \le 5}) and (A={x:x \in U\) and \(x^2<10}), find (A').\)

Explanation opens after your attempt
Correct Answer

A. (A'={-5,-4,4,5})

Explanation

Simple Explanation

\(x^2<10\) के लिए \(A=\{-3,-2,-1,0,1,2,3\}\) होगा। इसलिए (U) से इनको हटाने पर (A') मिलता है। / For \(x^2<10\), \(A=\{-3,-2,-1,0,1,2,3\}\). Removing these from (U) gives (A').

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Question 454/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 19

यदि \(U={x:x \in \mathbb{Z},-8\le x\le 8}\) और \(A={x:x \in U,x^2-2x-15\le 0}\), तो (A') में कितने सदस्य हैं?

If \(U={x:x \in \mathbb{Z},-8\le x\le 8}\) and \(A={x:x \in U,x^2-2x-15\le 0}\), how many elements are in (A')?

Explanation opens after your attempt
Correct Answer

A. (7)

Explanation

Simple Explanation

\(x^2-2x-15\le 0\) से \(-3\le x\le 5\) मिलता है, इसलिए (A) में (9) पूर्णांक हैं। (U) में (17) सदस्य हैं, पर यहां पूरक (8) नहीं बल्कि (-8) से (-4) और (6) से (8) मिलाकर (8) होना चाहिए। / The inequality \(x^2-2x-15\le 0\) gives \(-3\le x\le 5\), so (A) has (9) integers. Since (U) has (17) elements, the complement has (17-9=8) elements.

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Question 455/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 19

यदि \(U=\mathbb{R}\), (A=\(-\infty,-2\)\cup[3,7]) है, तो (A') क्या होगा?

If \(U=\mathbb{R}\) and (A=\(-\infty,-2\)\cup[3,7]), what is (A')?

Explanation opens after your attempt
Correct Answer

A. ([-2,3)\cup\(7,\infty\))

Explanation

Simple Explanation

(-2) समुच्चय (A) में नहीं है, इसलिए पूरक में आएगा। (3) और (7) (A) में हैं, इसलिए पूरक में (3) नहीं और (7) के बाद के मान आएंगे। / The point (-2) is not in (A), so it is included in the complement. The points (3) and (7) are in (A), so (3) is excluded and values after (7) are included.

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Question 456/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 19

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

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

Explanation opens after your attempt
Correct Answer

A. (A'=(2,5])

Explanation

Simple Explanation

(2) समुच्चय (A) में है और (5) समुच्चय (A) में नहीं है। इसलिए पूरक (A'=(2,5]) है। / The point (2) is in (A), while (5) is not in (A). Therefore the complement is (A'=(2,5]).

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Question 457/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 19

यदि \(A\subseteq B\subseteq U\) और (n(U)=90), (n(B)=54), (n(A)=31), तो (n\(A'\cap B\)) क्या है?

If \(A\subseteq B\subseteq U\), (n(U)=90), (n(B)=54), and (n(A)=31), what is (n\(A'\cap B\))?

Explanation opens after your attempt
Correct Answer

A. (23)

Explanation

Simple Explanation

\(A'\cap B\) का अर्थ (B-A) है क्योंकि \(A\subseteq B\)। इसलिए (n\(A'\cap B\)=54-31=23) है। / \(A'\cap B\) means (B-A) because \(A\subseteq B\). Therefore (n\(A'\cap B\)=54-31=23).

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Question 458/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 19

\(यदि (U={1,2,\ldots,30}), (A={x:x \in U\) तथा \(2 \mid x}) और (B={x:x \in U\) तथा \(3 \mid x}) हैं, तो ((A \cup B)') में कितने सदस्य हैं\)?

\(If (U={1,2,\ldots,30}), (A={x:x \in U\) and \(2 \mid x}), and (B={x:x \in U\) and \(3 \mid x}), how many elements are in ((A \cup B)')\)?

Explanation opens after your attempt
Correct Answer

A. (10)

Explanation

Simple Explanation

(2) या (3) से विभाज्य संख्याएं (20) हैं, इसलिए पूरक में (30-20=10) सदस्य हैं। समावेशन-बहिष्करण जल्दी लगाएं। / There are (20) numbers divisible by (2) or (3), so the complement has (30-20=10) elements. Use inclusion-exclusion quickly.

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Question 459/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 19

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

\(If (U={1,2,\ldots,20}), (A={x:x \in U,x\) 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})

Explanation

Simple Explanation

(A') विषम संख्याओं का समुच्चय है और (B) अभाज्य संख्याओं का। इसलिए \(A'\cap B\) में (2) को छोड़कर सभी विषम अभाज्य आएंगे। / (A') is the set of odd numbers and (B) is the set of primes. Thus \(A'\cap B\) contains all odd primes except (2).

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Question 460/600 Expert Mathematics Sets Complement of a Set and its properties Class 11 Level 19

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

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

Explanation opens after your attempt
Correct Answer

A. ({d})

Explanation

Simple Explanation

(A'={b,d,f}) और (B'={a,d,e}) हैं। उनका प्रतिच्छेद केवल ({d}) है। / Here (A'={b,d,f}) and (B'={a,d,e}). Their intersection is only ({d}).

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