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

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

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Question 341/626 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 342/626 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 343/626 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 344/626 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 345/626 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 346/626 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 347/626 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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Question 348/626 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

यदि \(P_1={x:x\in \mathbb{Z}, x^2<10}\) है, तो \(P_1\) में कितने अवयव हैं?

If \(P_1={x:x\in \mathbb{Z}, x^2<10}\), how many elements are in \(P_1\)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

\(x^2<10\) के लिए पूर्णांक (-3,-2,-1,0,1,2,3) संभव हैं। / For \(x^2<10\), the possible integers are (-3,-2,-1,0,1,2,3).

Step 2

Why this answer is correct

कुल (7) अवयव मिलते हैं। / There are (7) elements in total.

Step 3

Exam Tip

पूर्णांकों में ऋणात्मक, शून्य और धनात्मक तीनों भागों को गिनें। / For integer sets, count negative values, zero, and positive values.

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Question 349/626 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

यदि \(Q_1={x:x\in \mathbb{Z}, 2x+1=0}\) है, तो \(Q_1\) क्या है?

If \(Q_1={x:x\in \mathbb{Z}, 2x+1=0}\), what is \(Q_1\)?

Explanation opens after your attempt

Correct Answer

C. \(Q_1=\varnothing\)

Step 1

Concept

(2x+1=0) से \(x=-\frac{1}{2}\) मिलता है। / (2x+1=0) gives \(x=-\frac{1}{2}\).

Step 2

Why this answer is correct

\(-\frac{1}{2}\) पूर्णांक नहीं है, इसलिए कोई स्वीकार्य अवयव नहीं है। / \(-\frac{1}{2}\) is not an integer, so there is no acceptable element.

Step 3

Exam Tip

रैखिक समीकरण का हल भी क्षेत्र की शर्त पूरी करे, तभी समुच्चय में आएगा। / A linear equation solution must also satisfy the domain condition.

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Question 350/626 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 4

यदि \(R_1={x:x\in \mathbb{Q}, 2x+1=0}\) है, तो \(R_1\) कैसा समुच्चय है?

If \(R_1={x:x\in \mathbb{Q}, 2x+1=0}\), what type of set is \(R_1\)?

Explanation opens after your attempt

Correct Answer

B. एकलSingleton

Step 1

Concept

(2x+1=0) से \(x=-\frac{1}{2}\) मिलता है। / (2x+1=0) gives \(x=-\frac{1}{2}\).

Step 2

Why this answer is correct

यह परिमेय संख्या है, इसलिए समुच्चय में एक ही अवयव होगा। / This is a rational number, so the set has exactly one element.

Step 3

Exam Tip

क्षेत्र \(\mathbb{Q}\) हो तो भिन्न रूप के हल स्वीकार हो सकते हैं। / When the domain is \(\mathbb{Q}\), fractional solutions may be accepted.

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

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

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

यदि \(P_1={x:x\in \mathbb{Z}, x^2<10}\) है, तो \(P_1\) में कितने अवयव हैं?

Concept

Why this answer is correct

Exam Tip

यदि \(Q_1={x:x\in \mathbb{Z}, 2x+1=0}\) है, तो \(Q_1\) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(R_1={x:x\in \mathbb{Q}, 2x+1=0}\) है, तो \(R_1\) कैसा समुच्चय है?

Concept

Why this answer is correct

Exam Tip

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