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Mathematics The Empty Set, Finite and Infinite Sets, Equal Sets 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 Equal sets and Subsets 521 MCQs 03 Practice Topic Power Set and Universal Set 588 MCQs 04 Practice Topic Venn Diagrams 599 MCQs 05 Practice Topic Operations on Sets (Union, Intersection, Difference) 600 MCQs 06 Practice Topic Complement of a Set and its properties 600 MCQs 07 Practice Topic The Empty Set, many more. Step 3: Hence the set is infinite. 1 MCQs

The Empty Set, Finite and Infinite Sets, Equal Sets Practice Questions

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Question 581/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

समुच्चय \({x \in \mathbb{R}:x^2\le 0}\) किसके समान है?

The set \({x \in \mathbb{R}:x^2\le 0}\) is equal to which set?

Explanation opens after your attempt
Correct Answer

B. ({0})

Step 1

Concept

वास्तविक संख्या का वर्ग कभी ऋणात्मक नहीं होता। / The square of a real number is never negative.

Step 2

Why this answer is correct

\(x^2\le 0\) तभी संभव है जब \(x^2=0\)। / \(x^2\le 0\) is possible only when \(x^2=0\).

Step 3

Exam Tip

इससे (x=0), इसलिए समुच्चय ({0}) है। / Hence (x=0), so the set is ({0}).

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Question 582/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

समुच्चय \({x \in \mathbb{Z}:-3<x<3}\) में कितने तत्व हैं?

How many elements are in \({x \in \mathbb{Z}:-3<x<3}\)?

Explanation opens after your attempt
Correct Answer

B. (5)

Step 1

Concept

(-3) और (3) शामिल नहीं हैं क्योंकि चिह्न कठोर हैं। / (-3) and (3) are not included because the inequalities are strict.

Step 2

Why this answer is correct

पूर्णांक (-2,-1,0,1,2) मिलते हैं। / The integers are (-2,-1,0,1,2).

Step 3

Exam Tip

इसलिए कुल (5) तत्व हैं। / Thus there are (5) elements.

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Question 583/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

कौन सा समुच्चय रिक्त समुच्चय को सही दिखाता है?

Which notation correctly represents the empty set?

Explanation opens after your attempt
Correct Answer

C. \(\varnothing\)

Step 1

Concept

रिक्त समुच्चय में कोई तत्व नहीं होता। / The empty set has no element.

Step 2

Why this answer is correct

\(\varnothing\) उसका मानक संकेत है। / \(\varnothing\) is a standard notation for it.

Step 3

Exam Tip

({0}) और \({\varnothing}\) में एक-एक तत्व है, इसलिए वे रिक्त नहीं हैं। / ({0}) and \({\varnothing}\) each contain one element, so they are not empty.

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Question 584/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

यदि (A=B) और \(A=\{5,6,7,8\}\), तो (n(B)) क्या होगा?

If (A=B) and \(A=\{5,6,7,8\}\), what is (n(B))?

Explanation opens after your attempt
Correct Answer

C. (4)

Step 1

Concept

समान समुच्चयों में सभी तत्व समान होते हैं। / Equal sets have exactly the same elements.

Step 2

Why this answer is correct

इसलिए (B) में भी (5,6,7,8) होंगे। / Therefore, (B) also contains (5,6,7,8).

Step 3

Exam Tip

(B) में (4) तत्व हैं। / Hence (B) has (4) elements.

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Question 585/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

समुच्चय \(\left{\frac{1}{n}:n \in \mathbb{N}\right}\) के लिए सही कथन क्या है?

What is the correct statement for \(\left{\frac{1}{n}:n \in \mathbb{N}\right}\)?

Explanation opens after your attempt
Correct Answer

C. यह अनंत हैIt is infinite

Step 1

Concept

\(n=1,2,3,\ldots\) रखने पर \(1,\frac{1}{2},\frac{1}{3},\ldots\) मिलते हैं। / Substituting \(n=1,2,3,\ldots\) gives \(1,\frac{1}{2},\frac{1}{3},\ldots\).

Step 2

Why this answer is correct

हर नए (n) से नया भिन्न मिल सकता है। / Each new (n) can give a new fraction.

Step 3

Exam Tip

तत्वों की सूची समाप्त नहीं होती, इसलिए समुच्चय अनंत है। / The list does not end, so the set is infinite.

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Question 586/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

समुच्चय \({x \in \mathbb{N}:x\) (24) का गुणनखंड है(}) किस प्रकार का है?

What type of set is \({x \in \mathbb{N}:x\) is a factor of (24)(})?

Explanation opens after your attempt
Correct Answer

B. सांतFinite

Step 1

Concept

(24) के प्राकृतिक गुणनखंड सीमित हैं। / The natural factors of (24) are limited.

Step 2

Why this answer is correct

वे (1,2,3,4,6,8,12,24) हैं। / They are (1,2,3,4,6,8,12,24).

Step 3

Exam Tip

निश्चित संख्या के तत्व होने से यह सांत समुच्चय है। / Since the number of elements is definite, the set is finite.

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Question 587/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

यदि \(A=\{1,a,4\}\), \(B=\{1,3,4\}\) और (A=B), तो (a) का सही मान क्या है?

If \(A=\{1,a,4\}\), \(B=\{1,3,4\}\), and (A=B), what is the correct value of (a)?

Explanation opens after your attempt
Correct Answer

C. (3)

Step 1

Concept

(A) और (B) समान हैं तो उनके अलग तत्व समान होंगे। / If (A) and (B) are equal, their distinct elements must match.

Step 2

Why this answer is correct

(A) में (3) लाने के लिए (a=3) होना चाहिए। / To include (3) in (A), we need (a=3).

Step 3

Exam Tip

(a=1) या (a=4) रखने से (3) नहीं आएगा। / If (a=1) or (a=4), the element (3) would be missing.

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Question 588/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

समुच्चय \({x \in \mathbb{Z}:x^2=2}\) कैसा है?

What is the type of \({x \in \mathbb{Z}:x^2=2}\)?

Explanation opens after your attempt
Correct Answer

A. रिक्त समुच्चयEmpty set

Step 1

Concept

\(x^2=2\) के वास्तविक हल \(\sqrt{2}\) और \(-\sqrt{2}\) हैं। / The real solutions of \(x^2=2\) are \(\sqrt{2}\) and \(-\sqrt{2}\).

Step 2

Why this answer is correct

ये पूर्णांक नहीं हैं। / These are not integers.

Step 3

Exam Tip

पूर्णांकों में कोई हल न होने से समुच्चय रिक्त है। / Since there is no integer solution, the set is empty.

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Question 589/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

समुच्चय \({x \in \mathbb{N}:x\) (36) का गुणनखंड है(}) में कितने तत्व हैं?

How many elements are in \({x \in \mathbb{N}:x\) is a factor of (36)(})?

Explanation opens after your attempt
Correct Answer

B. (9)

Step 1

Concept

(36) के गुणनखंड (1,2,3,4,6,9,12,18,36) हैं। / The factors of (36) are (1,2,3,4,6,9,12,18,36).

Step 2

Why this answer is correct

ये सभी प्राकृतिक संख्याएँ हैं। / All of them are natural numbers.

Step 3

Exam Tip

कुल (9) तत्व हैं, इसलिए उत्तर (9) है। / There are (9) elements in total.

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Question 590/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

यदि \(A={x \in \mathbb{R}:x^2-4=0}\), तो (A) किसके समान है?

If \(A={x \in \mathbb{R}:x^2-4=0}\), which set is equal to (A)?

Explanation opens after your attempt
Correct Answer

A. ({-2,2})

Step 1

Concept

\(x^2-4=0\) से \(x^2=4\) मिलता है। / From \(x^2-4=0\), we get \(x^2=4\).

Step 2

Why this answer is correct

वास्तविक हल (x=-2) और (x=2) हैं। / The real solutions are (x=-2) and (x=2).

Step 3

Exam Tip

इसलिए \(A=\{-2,2\}\)। / Hence \(A=\{-2,2\}\).

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