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

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

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Question 331/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

यदि \(E_1={x:x\in \mathbb{Z}, x^2+4=4}\) है, तो \(E_1\) कैसा है?

If \(E_1={x:x\in \mathbb{Z}, x^2+4=4}\), what type of set is \(E_1\)?

Explanation opens after your attempt

Correct Answer

B. एकलSingleton

Step 1

Concept

\(x^2+4=4\) से \(x^2=0\) मिलता है। / \(x^2+4=4\) gives \(x^2=0\).

Step 2

Why this answer is correct

इसका एकमात्र पूर्णांक हल (x=0) है। / Its only integer solution is (x=0).

Step 3

Exam Tip

\(x^2=0\) में धनात्मक और ऋणात्मक दो अलग हल नहीं होते। / For \(x^2=0\), there are not two different positive and negative roots.

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Question 332/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

यदि \(F_1={x:x\in \mathbb{R}, x^2+4=0}\) है, तो \(F_1\) क्या है?

If \(F_1={x:x\in \mathbb{R}, x^2+4=0}\), what is \(F_1\)?

Explanation opens after your attempt

Correct Answer

A. रिक्त समुच्चयEmpty set

Step 1

Concept

वास्तविक संख्या के लिए \(x^2\geq 0\) होता है। / For a real number, \(x^2\geq 0\).

Step 2

Why this answer is correct

इसलिए \(x^2+4=0\) किसी वास्तविक (x) के लिए संभव नहीं है। / Therefore, \(x^2+4=0\) is impossible for real (x).

Step 3

Exam Tip

वास्तविक वर्ग कभी ऋणात्मक नहीं होता, यह रिक्त समुच्चय पहचानने में मदद करता है। / A real square is never negative, which helps identify an empty set.

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Question 333/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

यदि \(G_1={x:x\in \mathbb{Q}, x^2=2}\) है, तो \(G_1\) किस प्रकार का समुच्चय है?

If \(G_1={x:x\in \mathbb{Q}, x^2=2}\), what type of set is \(G_1\)?

Explanation opens after your attempt

Correct Answer

C. रिक्तEmpty

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 परिमेय संख्याएँ नहीं हैं, इसलिए \(G_1\) में कोई अवयव नहीं होगा। / These are not rational numbers, so \(G_1\) has no element.

Step 3

Exam Tip

\(\mathbb{Q}\) की शर्त हो तो अपरिमेय हल स्वीकार नहीं करें। / When the domain is \(\mathbb{Q}\), do not accept irrational solutions.

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Question 334/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

यदि \(H_1={x:x\in \mathbb{R}, x^2=2}\) और \(I_1={-\sqrt{2},\sqrt{2}}\) हैं, तो सही कथन कौन-सा है?

If \(H_1={x:x\in \mathbb{R}, x^2=2}\) and \(I_1={-\sqrt{2},\sqrt{2}}\), which statement is correct?

Explanation opens after your attempt

Correct Answer

A. \(H_1=I_1\)

Step 1

Concept

वास्तविक संख्याओं में \(x^2=2\) के दो हल \(-\sqrt{2}\) और \(\sqrt{2}\) हैं। / In real numbers, \(x^2=2\) has two solutions, \(-\sqrt{2}\) and \(\sqrt{2}\).

Step 2

Why this answer is correct

यही दोनों अवयव \(I_1\) में हैं। / These are exactly the elements of \(I_1\).

Step 3

Exam Tip

मूल चिह्न वाले अवयव भी समुच्चय के वैध अवयव हो सकते हैं। / Elements involving radicals can also be valid set elements.

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Question 335/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

कौन-सा समुच्चय परिमित है लेकिन रिक्त नहीं है?

Which set is finite but not empty?

Explanation opens after your attempt

Correct Answer

C. \( {x:x\in \mathbb{N}, x\mid 24} \)

Step 1

Concept

\(x\mid 24\) का अर्थ है (x), (24) का गुणनखंड है। / \(x\mid 24\) means (x) is a factor of (24).

Step 2

Why this answer is correct

(24) के प्राकृतिक गुणनखंड सीमित और उपस्थित हैं, इसलिए समुच्चय परिमित और रिक्त नहीं है। / Natural factors of (24) exist and are limited, so the set is finite and non-empty.

Step 3

Exam Tip

निश्चित संख्या के गुणनखंडों का समुच्चय हमेशा सीमित होता है। / The set of factors of a fixed number is always finite.

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Question 336/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

कौन-सा समुच्चय अपरिमित है लेकिन सभी पूर्णांक नहीं है?

Which set is infinite but not the set of all integers?

Explanation opens after your attempt

Correct Answer

A. \( {x:x\in \mathbb{Z}, x>0} \)

Step 1

Concept

(x>0) वाले पूर्णांक \(1,2,3,\ldots\) हैं। / Integers with (x>0) are \(1,2,3,\ldots\).

Step 2

Why this answer is correct

यह सूची अपरिमित है, पर इसमें ऋणात्मक पूर्णांक नहीं हैं। / This list is infinite, but it does not include negative integers.

Step 3

Exam Tip

अपरिमित होना और सभी पूर्णांक होना एक ही बात नहीं है। / Being infinite is not the same as being the set of all integers.

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Question 337/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

यदि \(J_1={x:x\in \mathbb{N}, x\) (100) से छोटी पूर्ण घन संख्या है(}) है, तो \(J_1\) के अवयव कौन-से हैं?

If \(J_1={x:x\in \mathbb{N}, x\) is a perfect cube less than (100)(}), what are the elements of \(J_1\)?

Explanation opens after your attempt

Correct Answer

A. \(J_1={1,8,27,64}\)

Step 1

Concept

(100) से छोटे पूर्ण घन \(1^3,2^3,3^3,4^3\) से मिलते हैं। / Perfect cubes less than (100) come from \(1^3,2^3,3^3,4^3\).

Step 2

Why this answer is correct

इनके मान (1,8,27,64) हैं। / Their values are (1,8,27,64).

Step 3

Exam Tip

\(5^3=125\) सीमा से बाहर है, इसलिए उसे शामिल न करें। / \(5^3=125\) is outside the limit, so do not include it.

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Question 338/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

यदि \(K_1={x:x=n^3, n\in \mathbb{N}}\) है, तो \(K_1\) कैसा है?

If \(K_1={x:x=n^3, n\in \mathbb{N}}\), what type of set is \(K_1\)?

Explanation opens after your attempt

Correct Answer

C. अपरिमितInfinite

Step 1

Concept

\(n=1,2,3,\ldots\) रखने पर \(1,8,27,\ldots\) मिलते हैं। / Putting \(n=1,2,3,\ldots\) gives \(1,8,27,\ldots\).

Step 2

Why this answer is correct

(n) की कोई अंतिम सीमा नहीं है, इसलिए पूर्ण घनों की सूची भी समाप्त नहीं होती। / Since (n) has no final limit, the list of cubes does not end.

Step 3

Exam Tip

विशेष रूप वाली संख्याएँ भी बिना सीमा के अपरिमित हो सकती हैं। / Numbers of a special form can also form an infinite set when unbounded.

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Question 339/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

यदि \(L_1={x:x\in \mathbb{N}, x^2<10}\) और \(M_1={1,2,3}\) हैं, तो क्या \(L_1=M_1\) है?

If \(L_1={x:x\in \mathbb{N}, x^2<10}\) and \(M_1={1,2,3}\), is \(L_1=M_1\)?

Explanation opens after your attempt

Correct Answer

A. हाँ, क्योंकि दोनों में वही अवयव हैंYes, because both have the same elements

Step 1

Concept

प्राकृतिक संख्याओं में \(x^2<10\) के लिए (x=1,2,3) संभव हैं। / In natural numbers, \(x^2<10\) allows (x=1,2,3).

Step 2

Why this answer is correct

\(4^2=16\) होने से (4) शामिल नहीं होगा। / Since \(4^2=16\), (4) is not included.

Step 3

Exam Tip

वर्ग वाली असमानता में सीमा से पहले तक के मान सावधानी से गिनें। / In square inequalities, count values carefully up to the boundary.

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Question 340/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

यदि \(N_1={x:x\in \mathbb{N}, x^2\leq 10}\) और \(O_1={1,2,3}\) हैं, तो सही कथन कौन-सा है?

If \(N_1={x:x\in \mathbb{N}, x^2\leq 10}\) and \(O_1={1,2,3}\), which statement is correct?

Explanation opens after your attempt

Correct Answer

A. \(N_1=O_1\)

Step 1

Concept

\(1^2,2^2,3^2\) के मान (10) से कम या बराबर हैं। / \(1^2,2^2,3^2\) are less than or equal to (10).

Step 2

Why this answer is correct

\(4^2=16\) है, इसलिए (4) शामिल नहीं होगा। / \(4^2=16\), so (4) is not included.

Step 3

Exam Tip

\(\leq\) चिह्न होने पर भी सही वर्ग-सीमा जाँचनी पड़ती है। / Even with \(\leq\), the square boundary must be checked correctly.

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

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

यदि \(E_1={x:x\in \mathbb{Z}, x^2+4=4}\) है, तो \(E_1\) कैसा है?

Concept

Why this answer is correct

Exam Tip

यदि \(F_1={x:x\in \mathbb{R}, x^2+4=0}\) है, तो \(F_1\) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(G_1={x:x\in \mathbb{Q}, x^2=2}\) है, तो \(G_1\) किस प्रकार का समुच्चय है?

Concept

Why this answer is correct

Exam Tip

यदि \(H_1={x:x\in \mathbb{R}, x^2=2}\) और \(I_1={-\sqrt{2},\sqrt{2}}\) हैं, तो सही कथन कौन-सा है?

Concept

Why this answer is correct

Exam Tip

कौन-सा समुच्चय परिमित है लेकिन रिक्त नहीं है?

Concept

Why this answer is correct

Exam Tip

कौन-सा समुच्चय अपरिमित है लेकिन सभी पूर्णांक नहीं है?

Concept

Why this answer is correct

Exam Tip

यदि \(J_1={x:x\in \mathbb{N}, x\) (100) से छोटी पूर्ण घन संख्या है(}) है, तो \(J_1\) के अवयव कौन-से हैं?

Concept

Why this answer is correct

Exam Tip

यदि \(K_1={x:x=n^3, n\in \mathbb{N}}\) है, तो \(K_1\) कैसा है?

Concept

Why this answer is correct

Exam Tip

यदि \(L_1={x:x\in \mathbb{N}, x^2<10}\) और \(M_1={1,2,3}\) हैं, तो क्या \(L_1=M_1\) है?

Concept

Why this answer is correct

Exam Tip

यदि \(N_1={x:x\in \mathbb{N}, x^2\leq 10}\) और \(O_1={1,2,3}\) हैं, तो सही कथन कौन-सा है?

Concept

Why this answer is correct

Exam Tip

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