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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 161/603 Medium Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

\(यदि (P={x:x\in\mathbb{N},x\) संख्या 18 और 30 दोनों का गुणनखंड है}), तो (P) क्या है?

\(If (P={x:x\in\mathbb{N},x\) is a factor of both 18 and 30}), what is (P)?

Explanation opens after your attempt

Correct Answer

A. ({1,2,3,6})

Step 1

Concept

(18) के गुणनखंड (1,2,3,6,9,18) हैं। / Factors of (18) are (1,2,3,6,9,18).

Step 2

Why this answer is correct

(30) के गुणनखंड (1,2,3,5,6,10,15,30) हैं। / Factors of (30) are (1,2,3,5,6,10,15,30).

Step 3

Exam Tip

दोनों में समान गुणनखंड (1,2,3,6) हैं। / The common factors are (1,2,3,6).

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Question 162/603 Medium Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

यदि \(A={x:x\in\mathbb{Z},-3\leq x<2}\), तो (A) में कितने तत्व हैं?

If \(A={x:x\in\mathbb{Z},-3\leq x<2}\), how many elements are in (A)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

शर्त के अनुसार (-3) शामिल है और (2) शामिल नहीं है। / The condition includes (-3) but does not include (2).

Step 2

Why this answer is correct

तत्व (-3,-2,-1,0,1) हैं। / The elements are (-3,-2,-1,0,1).

Step 3

Exam Tip

असमानता में बराबर का चिन्ह ध्यान से देखें। / Read the equality sign in inequalities carefully.

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Question 163/603 Medium Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

कौन सा समुच्चय \(A=\{4,8,12,16\}\) के बराबर है?

Which set is equal to \(A=\{4,8,12,16\}\)?

Explanation opens after your attempt

Correct Answer

A. \({x:x=4n,n\in\mathbb{N},1\leq n\leq4}\)

Step 1

Concept

पहले विकल्प में (n=1,2,3,4) रखने पर (4,8,12,16) मिलते हैं। / In the first option, putting (n=1,2,3,4) gives (4,8,12,16).

Step 2

Why this answer is correct

ये सभी (A) के तत्वों से मिलते हैं। / These exactly match the elements of (A).

Step 3

Exam Tip

नियम वाले समुच्चय को सूची में बदलकर समानता जाँचें। / Convert a rule-based set into a list to check equality.

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Question 164/603 Medium Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

\(यदि (A={x:x\in\mathbb{N},x\) सम है और x अभाज्य है}), तो (A) का सही रूप क्या है?

\(If (A={x:x\in\mathbb{N},x\) is even and prime}), what is the correct form of (A)?

Explanation opens after your attempt

Correct Answer

B. ({2})

Step 1

Concept

सम अभाज्य संख्या की शर्त बहुत विशेष है। / The condition of being even and prime is very specific.

Step 2

Why this answer is correct

(2) ही एकमात्र सम अभाज्य प्राकृतिक संख्या है। / (2) is the only even prime natural number.

Step 3

Exam Tip

अभाज्य संख्या में (1) को शामिल न करें। / Do not include (1) as a prime number.

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Question 165/603 Medium Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

निम्न में से कौन सा समुच्चय परिमित है पर रिक्त नहीं है?

Which of the following sets is finite but not empty?

Explanation opens after your attempt

Correct Answer

C. \(({x:x\in\mathbb{N},x\) संख्या 12 का गुणनखंड है})\(({x:x\in\mathbb{N},x\) is a factor of 12})

Step 1

Concept

(12) के गुणनखंडों की संख्या सीमित है। / The number of factors of (12) is limited.

Step 2

Why this answer is correct

उनमें (1,2,3,4,6,12) जैसे तत्व आते हैं, इसलिए समुच्चय रिक्त नहीं है। / It has elements such as (1,2,3,4,6,12), so it is not empty.

Step 3

Exam Tip

परिमित और रिक्त नहीं दोनों शर्तें साथ जाँचें। / Check both conditions: finite and non-empty.

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Question 166/603 Medium Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

यदि \(A={0,\varnothing,{0}}\), तो (A) में कितने तत्व हैं?

If \(A={0,\varnothing,{0}}\), how many elements are in (A)?

Explanation opens after your attempt

Correct Answer

C. (3)

Step 1

Concept

(0), \(\varnothing\), और ({0}) तीन अलग-अलग वस्तुएँ हैं। / (0), \(\varnothing\), and ({0}) are three different objects.

Step 2

Why this answer is correct

बाहरी कोष्ठक के अंदर ये तीन तत्व के रूप में लिखे हैं। / They are written inside the outer braces as three elements.

Step 3

Exam Tip

तत्व और समुच्चय के बीच का अंतर ध्यान से पहचानें। / Carefully distinguish between an element and a set.

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Question 167/603 Medium Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

\(समुच्चय (A={x:x\in\mathbb{N},x\) संख्या 5 से विभाज्य है और \(x<40}) में कितने तत्व हैं\)?

\(How many elements are in (A={x:x\in\mathbb{N},x\) is divisible by 5 and \(x<40})\)?

Explanation opens after your attempt

Correct Answer

A. (7)

Step 1

Concept

(40) से छोटी (5) से विभाज्य प्राकृतिक संख्याएँ (5,10,15,20,25,30,35) हैं। / Natural numbers divisible by (5) and less than (40) are (5,10,15,20,25,30,35).

Step 2

Why this answer is correct

कुल (7) तत्व मिलते हैं। / There are (7) elements.

Step 3

Exam Tip

अंतिम सीमा शामिल है या नहीं, यह अवश्य देखें। / Always check whether the endpoint is included.

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Question 168/603 Medium Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

\(यदि (A={x:x\in\mathbb{N},x\) संख्या 4 का गुणज है}), तो (A) किस प्रकार का समुच्चय है?

\(If (A={x:x\in\mathbb{N},x\) is a multiple of 4}), what type of set is (A)?

Explanation opens after your attempt

Correct Answer

C. अनंत समुच्चयInfinite set

Step 1

Concept

(4) के प्राकृतिक गुणज \(4,8,12,16,\ldots\) हैं। / Natural multiples of (4) are \(4,8,12,16,\ldots\).

Step 2

Why this answer is correct

यह सूची आगे बिना अंत के चलती है। / This list continues without ending.

Step 3

Exam Tip

बिना ऊपरी सीमा वाले गुणजों का समुच्चय अनंत होता है। / A set of multiples without an upper limit is infinite.

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Question 169/603 Medium Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

कौन सा कथन \(A=\{1,2,2,3,3,3\}\) के लिए सही है?

Which statement is correct for \(A=\{1,2,2,3,3,3\}\)?

Explanation opens after your attempt

Correct Answer

B. \(A=\{1,2,3\}\)

Step 1

Concept

समुच्चय में दोहराए गए तत्व अलग से नहीं गिने जाते। / Repeated elements are not counted separately in a set.

Step 2

Why this answer is correct

वास्तविक तत्व (1,2,3) हैं। / The actual elements are (1,2,3).

Step 3

Exam Tip

दोहराव हटाकर ही समुच्चय का सही रूप लिखें। / Remove repetition before writing the correct form of a set.

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Question 170/603 Medium Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

यदि \(A={x:x\in\mathbb{Z},x^2<4}\), तो (A) कौन सा है?

If \(A={x:x\in\mathbb{Z},x^2<4}\), which set is (A)?

Explanation opens after your attempt

Correct Answer

B. ({-1,0,1})

Step 1

Concept

\(x^2<4\) के लिए पूर्णांक मान जाँचें। / Check integer values for \(x^2<4\).

Step 2

Why this answer is correct

(-1,0,1) के वर्ग (4) से छोटे हैं, पर (-2) और (2) के वर्ग बराबर (4) हैं। / Squares of (-1,0,1) are less than (4), but squares of (-2) and (2) equal (4).

Step 3

Exam Tip

सख्त असमानता में बराबर मान शामिल नहीं होता। / Strict inequality does not include equal values.

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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

\(यदि (P={x:x\in\mathbb{N},x\) संख्या 18 और 30 दोनों का गुणनखंड है}), तो (P) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x:x\in\mathbb{Z},-3\leq x<2}\), तो (A) में कितने तत्व हैं?

Concept

Why this answer is correct

Exam Tip

कौन सा समुच्चय \(A=\{4,8,12,16\}\) के बराबर है?

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x:x\in\mathbb{N},x\) सम है और x अभाज्य है}), तो (A) का सही रूप क्या है?

Concept

Why this answer is correct

Exam Tip

निम्न में से कौन सा समुच्चय परिमित है पर रिक्त नहीं है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={0,\varnothing,{0}}\), तो (A) में कितने तत्व हैं?

Concept

Why this answer is correct

Exam Tip

\(समुच्चय (A={x:x\in\mathbb{N},x\) संख्या 5 से विभाज्य है और \(x<40}) में कितने तत्व हैं\)?

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x:x\in\mathbb{N},x\) संख्या 4 का गुणज है}), तो (A) किस प्रकार का समुच्चय है?

Concept

Why this answer is correct

Exam Tip

कौन सा कथन \(A=\{1,2,2,3,3,3\}\) के लिए सही है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x:x\in\mathbb{Z},x^2<4}\), तो (A) कौन सा है?

Concept

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Exam Tip

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