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Mathematics The Empty Set, Finite and Infinite Sets, Equal Sets MCQ Questions for Class 11 General

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

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Question 571/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

परिमेय संख्याओं का समुच्चय \({x \in \mathbb{Q}:0<x<1}\) किस प्रकार का है?

What type of set is \({x \in \mathbb{Q}:0<x<1}\)?

Explanation opens after your attempt

Correct Answer

D. अनंतInfinite

Step 1

Concept

(0) और (1) के बीच \(\frac{1}{2},\frac{1}{3},\frac{1}{4}\) जैसी अनेक परिमेय संख्याएँ हैं। / Between (0) and (1), there are rational numbers like \(\frac{1}{2},\frac{1}{3},\frac{1}{4}\), and so on.

Step 2

Why this answer is correct

यह सूची समाप्त नहीं होती। / This list never ends.

Step 3

Exam Tip

इसलिए यह अनंत समुच्चय है। / Therefore, the set is infinite.

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Question 572/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

यदि \(A={x \in \mathbb{N}:x^2=4}\) और \(B=\{2\}\), तो क्या (A) और (B) समान हैं?

If \(A={x \in \mathbb{N}:x^2=4}\) and \(B=\{2\}\), are (A) and (B) equal?

Explanation opens after your attempt

Correct Answer

A. हाँ, क्योंकि (A=B={2})Yes, because (A=B={2})

Step 1

Concept

प्राकृतिक संख्याओं में \(x^2=4\) का हल (x=2) है। / In natural numbers, the solution of \(x^2=4\) is (x=2).

Step 2

Why this answer is correct

(-2) प्राकृतिक संख्या नहीं है। / (-2) is not a natural number.

Step 3

Exam Tip

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

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Question 573/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

यदि \(A=\{1,2,3\}\) और \(B=\{a,b,c\}\), तो सही कथन कौन सा है?

If \(A=\{1,2,3\}\) and \(B=\{a,b,c\}\), which statement is correct?

Explanation opens after your attempt

Correct Answer

C. दोनों में तत्वों की संख्या समान है पर वे समान समुच्चय नहीं हैंThey have the same number of elements but are not equal sets

Step 1

Concept

(A) और (B) दोनों में (3) तत्व हैं। / Both (A) and (B) have (3) elements.

Step 2

Why this answer is correct

लेकिन उनके वास्तविक तत्व अलग-अलग हैं। / But their actual elements are different.

Step 3

Exam Tip

समान समुच्चय होने के लिए तत्व वही होने चाहिए, केवल संख्या समान होना पर्याप्त नहीं है। / Equal sets must have exactly the same elements, not just the same number of elements.

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Question 574/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

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

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

Explanation opens after your attempt

Correct Answer

A. (A=B)

Step 1

Concept

किसी भी पूर्णांक के लिए \(x^2\ge 0\) होता है। / For every integer, \(x^2\ge 0\).

Step 2

Why this answer is correct

इसलिए \(x^2+1=0\) का कोई पूर्णांक हल नहीं है। / So \(x^2+1=0\) has no integer solution.

Step 3

Exam Tip

(B) भी रिक्त है, अतः (A=B)। / Thus (B) is empty, and (A=B).

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Question 575/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

समुच्चय ({1,1,2,2,3,4,4}) के लिए सही (n(A)) क्या होगा?

For the set ({1,1,2,2,3,4,4}), what is the correct (n(A))?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

लिखे गए कुल चिन्ह (7) हैं पर समुच्चय में दोहराव नहीं गिना जाता। / Although (7) entries are written, repetitions are ignored in a set.

Step 2

Why this answer is correct

अलग तत्व (1,2,3,4) हैं। / The distinct elements are (1,2,3,4).

Step 3

Exam Tip

इसलिए (n(A)=4) है। / Therefore, (n(A)=4).

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Question 576/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

रिक्त समुच्चय के बारे में कौन सा कथन सबसे उचित है?

Which statement about the empty set is most appropriate?

Explanation opens after your attempt

Correct Answer

B. इसमें (0) तत्व होते हैंIt has (0) elements

Step 1

Concept

रिक्त समुच्चय का अर्थ है कोई तत्व नहीं। / Empty set means there is no element.

Step 2

Why this answer is correct

इसलिए इसकी तत्व संख्या (0) होती है। / So its number of elements is (0).

Step 3

Exam Tip

(0) तत्वों की संख्या है, स्वयं कोई तत्व नहीं। / Here (0) is the count of elements, not an element inside the set.

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Question 577/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

समुच्चय \({x \in \mathbb{R}:x^2-2x+1=0}\) किस प्रकार का है?

What type of set is \({x \in \mathbb{R}:x^2-2x+1=0}\)?

Explanation opens after your attempt

Correct Answer

B. एकांक समुच्चयSingleton set

Step 1

Concept

(x^-2-2x+1=(x-1)²) है। / (x^-2-2x+1=(x-1)²).

Step 2

Why this answer is correct

((x-1)²=0) से (x=1) मिलता है। / From ((x-1)²=0), we get (x=1).

Step 3

Exam Tip

केवल एक तत्व होने से यह एकांक समुच्चय है। / Since there is only one element, it is a singleton set.

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Question 578/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

समुच्चय \({2n:n \in \mathbb{N}}\) के लिए सही कथन चुनिए।

Choose the correct statement for the set \({2n:n \in \mathbb{N}}\).

Explanation opens after your attempt

Correct Answer

C. यह अनंत समुच्चय हैIt is an infinite set

Step 1

Concept

\(n=1,2,3,\ldots\) रखने पर \(2,4,6,\ldots\) मिलते हैं। / Substituting \(n=1,2,3,\ldots\) gives \(2,4,6,\ldots\).

Step 2

Why this answer is correct

सम संख्याएँ आगे चलती रहती हैं। / The even numbers continue without end.

Step 3

Exam Tip

इसलिए तत्वों की संख्या अनंत है। / Therefore, the set has infinitely many elements.

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Question 579/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

समुच्चय \({x \in \mathbb{N}:5<x<6}\) कैसा है?

What is the type of \({x \in \mathbb{N}:5<x<6}\)?

Explanation opens after your attempt

Correct Answer

A. रिक्त समुच्चयEmpty set

Step 1

Concept

(5) और (6) के बीच कोई प्राकृतिक संख्या नहीं होती। / There is no natural number between (5) and (6).

Step 2

Why this answer is correct

कोई तत्व शर्त पूरी नहीं करता। / No element satisfies the condition.

Step 3

Exam Tip

इसलिए यह रिक्त समुच्चय है। / Therefore, the set is empty.

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Question 580/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 6

समुच्चय \({x \in \mathbb{Z}:-2\le x\le 2}\) के लिए सही सूची कौन सी है?

Which is the correct roster form for \({x \in \mathbb{Z}:-2\le x\le 2}\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

शर्त में (-2) से (2) तक के सभी पूर्णांक शामिल हैं। / The condition includes all integers from (-2) to (2).

Step 2

Why this answer is correct

इसलिए तत्व (-2,-1,0,1,2) होंगे। / So the elements are (-2,-1,0,1,2).

Step 3

Exam Tip

सिरों पर बराबरी का चिन्ह हो तो सिरों को भी शामिल करें। / When equality signs are present, include the endpoints.

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Mathematics The Empty Set, Finite and Infinite Sets, Equal Sets MCQ Questions for Class 11 General

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

परिमेय संख्याओं का समुच्चय \({x \in \mathbb{Q}:0<x<1}\) किस प्रकार का है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x \in \mathbb{N}:x^2=4}\) और \(B=\{2\}\), तो क्या (A) और (B) समान हैं?

Concept

Why this answer is correct

Exam Tip

यदि \(A=\{1,2,3\}\) और \(B=\{a,b,c\}\), तो सही कथन कौन सा है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

समुच्चय ({1,1,2,2,3,4,4}) के लिए सही (n(A)) क्या होगा?

Concept

Why this answer is correct

Exam Tip

रिक्त समुच्चय के बारे में कौन सा कथन सबसे उचित है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \({x \in \mathbb{R}:x^2-2x+1=0}\) किस प्रकार का है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \({2n:n \in \mathbb{N}}\) के लिए सही कथन चुनिए।

Concept

Why this answer is correct

Exam Tip

समुच्चय \({x \in \mathbb{N}:5<x<6}\) कैसा है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \({x \in \mathbb{Z}:-2\le x\le 2}\) के लिए सही सूची कौन सी है?

Concept

Why this answer is correct

Exam Tip

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