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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 541/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

कौन सा समुच्चय \(\mathbb{Z}\) के बराबर नहीं है और फिर भी अपरिमित है?

Which set is not equal to \(\mathbb{Z}\) but is still infinite?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\({x\in\mathbb{Z}:x\ge 0}\) में \(0,1,2,\ldots\) आते हैं, इसलिए यह अपरिमित है। / The set \({x\in\mathbb{Z}:x\ge 0}\) contains \(0,1,2,\ldots\), so it is infinite.

Step 2

Why this answer is correct

इसमें ऋणात्मक पूर्णांक नहीं हैं, इसलिए यह \(\mathbb{Z}\) के बराबर नहीं है। / It does not contain negative integers, so it is not equal to \(\mathbb{Z}\).

Step 3

Exam Tip

अपरिमित समुच्चय हमेशा पूरे मूल समुच्चय के बराबर नहीं होता। / An infinite set need not be equal to the whole parent set.

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Question 542/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

समुच्चय \(A={x\in\mathbb{R}:x^2-4x+4=0}\) में कितने अवयव हैं?

How many elements are in \(A={x\in\mathbb{R}:x^2-4x+4=0}\)?

Explanation opens after your attempt

Correct Answer

B. (1)

Step 1

Concept

(x^-2-4x+4=(x-2)²) है। / (x^-2-4x+4=(x-2)²).

Step 2

Why this answer is correct

हल केवल (x=2) है, इसलिए समुच्चय में एक अवयव है। / The only solution is (x=2), so the set has one element.

Step 3

Exam Tip

दोहराए हुए मूल को समुच्चय में दो बार नहीं गिनते। / A repeated root is not counted twice in a set.

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Question 543/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

यदि \(A={x\in\mathbb{R}:|x|<0}\), तो (A) क्या है?

If \(A={x\in\mathbb{R}:|x|<0}\), what is (A)?

Explanation opens after your attempt

Correct Answer

A. \(\varnothing\)

Step 1

Concept

किसी भी वास्तविक संख्या का निरपेक्ष मान कभी ऋणात्मक नहीं होता। / The absolute value of any real number is never negative.

Step 2

Why this answer is correct

इसलिए (|x|<0) को कोई वास्तविक संख्या पूरा नहीं करती। / So no real number satisfies (|x|<0).

Step 3

Exam Tip

निरपेक्ष मान से बनी ऋणात्मक शर्त तुरंत असंभव समझें। / A negative condition on absolute value is immediately impossible.

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Question 544/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

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

If \(A={x\in\mathbb{Z}:x^2-1=0}\) and \(B={x\in\mathbb{N}:x^2-1=0}\), what is correct?

Explanation opens after your attempt

Correct Answer

B. \(A=\{-1,1\}\) और \(B=\{1\}\)\(A=\{-1,1\}\) and \(B=\{1\}\)

Step 1

Concept

पूर्णांक क्षेत्र में \(x^2-1=0\) के हल (-1) और (1) हैं। / In the integer domain, \(x^2-1=0\) gives (-1) and (1).

Step 2

Why this answer is correct

प्राकृतिक संख्या क्षेत्र में केवल (1) स्वीकार होगा। / In the natural-number domain, only (1) is allowed.

Step 3

Exam Tip

एक ही समीकरण के लिए क्षेत्र बदलने पर समुच्चय बदल सकता है। / The same equation can form different sets when the domain changes.

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Question 545/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

\(यदि (A={x\in\mathbb{N}:x\) 11 से विभाज्य है और \(x<11}), तो (A) क्या है\)?

\(If (A={x\in\mathbb{N}:x\) is divisible by 11 and \(x<11}), what is (A)\)?

Explanation opens after your attempt

Correct Answer

C. \(\varnothing\)

Step 1

Concept

(11) से विभाज्य पहली धनात्मक प्राकृतिक संख्या (11) है। / The first positive natural number divisible by (11) is (11).

Step 2

Why this answer is correct

(x<11) होने से (11) भी शामिल नहीं होगा। / Since (x<11), even (11) is not included.

Step 3

Exam Tip

विभाज्यता और सीमा को साथ-साथ लागू करें। / Apply divisibility and bounds together.

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Question 546/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

कौन सा विकल्प दिखाता है कि क्रम बदलने से समुच्चय नहीं बदलता?

Which option shows that changing order does not change a set?

Explanation opens after your attempt

Correct Answer

A. ({p,q,r}={r,p,q})

Step 1

Concept

समुच्चय में अवयवों का क्रम महत्व नहीं रखता। / The order of elements does not matter in a set.

Step 2

Why this answer is correct

({p,q,r}) और ({r,p,q}) में वही तीन अवयव हैं। / ({p,q,r}) and ({r,p,q}) contain the same three elements.

Step 3

Exam Tip

बराबरी जाँचते समय क्रम के बजाय अवयवों की सूची मिलाएँ। / While checking equality, match the element list instead of the order.

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Question 547/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

\(यदि (A={x\in\mathbb{N}:x\le 8\) और x अभाज्य नहीं है}), तो (A) किसके बराबर है?

\(If (A={x\in\mathbb{N}:x\le 8\) and x is not prime}), what is (A) equal to?

Explanation opens after your attempt

Correct Answer

A. ({1,4,6,8})

Step 1

Concept

(8) तक प्राकृतिक संख्याएँ (1,2,3,4,5,6,7,8) हैं। / Natural numbers up to (8) are (1,2,3,4,5,6,7,8).

Step 2

Why this answer is correct

अभाज्य संख्याएँ (2,3,5,7) हैं, इसलिए अभाज्य नहीं होने वाले (1,4,6,8) हैं। / The primes are (2,3,5,7), so the non-prime numbers are (1,4,6,8).

Step 3

Exam Tip

(1) न अभाज्य है न भाज्य, पर अभाज्य नहीं है। / (1) is neither prime nor composite, but it is not prime.

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Question 548/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

यदि \(A={x\in\mathbb{Z}:x^2+3x+2=0}\) और \(B=\{-2,-1\}\), तो सही संबंध कौन सा है?

If \(A={x\in\mathbb{Z}:x^2+3x+2=0}\) and \(B=\{-2,-1\}\), which relation is correct?

Explanation opens after your attempt

Correct Answer

A. (A=B)

Step 1

Concept

(x^-2+3x+2=(x+1)(x+2)) है। / (x^-2+3x+2=(x+1)(x+2)).

Step 2

Why this answer is correct

हल (-1) और (-2) हैं, इसलिए (A) और (B) में वही अवयव हैं। / The solutions are (-1) and (-2), so (A) and (B) contain the same elements.

Step 3

Exam Tip

ऋणात्मक मूलों के चिन्ह पर विशेष ध्यान दें। / Pay special attention to signs in negative roots.

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Question 549/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

समुच्चय \(A={x\in\mathbb{R}:x^2-2x+5=0}\) के बारे में सही कथन चुनिए।

Choose the correct statement about \(A={x\in\mathbb{R}:x^2-2x+5=0}\).

Explanation opens after your attempt

Correct Answer

C. \(A=\varnothing\)

Step 1

Concept

(x^-2-2x+5=(x-1)²+4) है। / (x^-2-2x+5=(x-1)²+4).

Step 2

Why this answer is correct

यह मान हमेशा धनात्मक रहेगा, इसलिए वास्तविक संख्या में शून्य नहीं बन सकता। / This value is always positive, so it cannot be zero for real numbers.

Step 3

Exam Tip

पूर्ण वर्ग में धनात्मक संख्या जुड़ी हो तो वास्तविक हल नहीं मिलता। / A completed square plus a positive number gives no real solution.

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Question 550/599 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

\(यदि (A={x\in\mathbb{N}:x\) 6 से विभाज्य है\(}) और (B={x\in\mathbb{N}:2\mid x\) और \(3\mid x}), तो कौन सा कथन सही है\)?

\(If (A={x\in\mathbb{N}:x\) is divisible by \(6}) and (B={x\in\mathbb{N}:2\mid x\) and \(3\mid x}), which statement is correct\)?

Explanation opens after your attempt

Correct Answer

A. (A=B), और दोनों अपरिमित हैं(A=B), and both are infinite

Step 1

Concept

कोई प्राकृतिक संख्या (2) और (3) दोनों से विभाज्य हो तो वह (6) से विभाज्य होती है। / A natural number divisible by both (2) and (3) is divisible by (6).

Step 2

Why this answer is correct

इसलिए (A) और (B) में \(6,12,18,\ldots\) जैसे वही अवयव हैं। / Thus both (A) and (B) contain the same elements such as \(6,12,18,\ldots\).

Step 3

Exam Tip

समान नियम अलग भाषा में लिखा हो तो वास्तविक अवयव मिलाकर देखें। / When the same rule is written differently, compare the actual elements.

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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

कौन सा समुच्चय \(\mathbb{Z}\) के बराबर नहीं है और फिर भी अपरिमित है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(A={x\in\mathbb{R}:x^2-4x+4=0}\) में कितने अवयव हैं?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x\in\mathbb{R}:|x|<0}\), तो (A) क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x\in\mathbb{N}:x\) 11 से विभाज्य है और \(x<11}), तो (A) क्या है\)?

Concept

Why this answer is correct

Exam Tip

कौन सा विकल्प दिखाता है कि क्रम बदलने से समुच्चय नहीं बदलता?

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x\in\mathbb{N}:x\le 8\) और x अभाज्य नहीं है}), तो (A) किसके बराबर है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x\in\mathbb{Z}:x^2+3x+2=0}\) और \(B=\{-2,-1\}\), तो सही संबंध कौन सा है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(A={x\in\mathbb{R}:x^2-2x+5=0}\) के बारे में सही कथन चुनिए।

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x\in\mathbb{N}:x\) 6 से विभाज्य है\(}) और (B={x\in\mathbb{N}:2\mid x\) और \(3\mid x}), तो कौन सा कथन सही है\)?

Concept

Why this answer is correct

Exam Tip

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