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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 531/603 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

\(समुच्चय (A={x\in\mathbb{R}:x^2=0\) और \(x>0}) के लिए सही विकल्प कौन सा है\)?

\(Which option is correct for (A={x\in\mathbb{R}:x^2=0\) and \(x>0})\)?

Explanation opens after your attempt

Correct Answer

B. \(A=\varnothing\)

Step 1

Concept

\(x^2=0\) से केवल (x=0) मिलता है। / \(x^2=0\) gives only (x=0).

Step 2

Why this answer is correct

लेकिन (x>0) में (0) शामिल नहीं होता, इसलिए कोई अवयव नहीं बचता। / But (x>0) does not include (0), so no element remains.

Step 3

Exam Tip

संयुक्त शर्तों में दोनों शर्तें साथ पूरी होनी चाहिए। / In combined conditions, both conditions must hold together.

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Question 532/603 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

\(यदि (A={x\in\mathbb{N}:x\) पूर्ण वर्ग है}), तो (A) कैसा है?

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

Explanation opens after your attempt

Correct Answer

C. अपरिमित समुच्चयinfinite set

Step 1

Concept

\(1,4,9,16,\ldots\) जैसे पूर्ण वर्ग लगातार मिलते हैं। / Perfect squares such as \(1,4,9,16,\ldots\) continue endlessly.

Step 2

Why this answer is correct

\(n^2\) हर प्राकृतिक (n) के लिए नया या आगे का पूर्ण वर्ग देता रहता है। / For every natural (n), \(n^2\) keeps giving further perfect squares.

Step 3

Exam Tip

यदि (n) पर कोई ऊपरी सीमा न हो, तो पूर्ण वर्गों का समुच्चय अपरिमित है। / Without an upper bound on (n), the set of perfect squares is infinite.

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Question 533/603 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

\(यदि (A={x\in\mathbb{N}:x\) पूर्ण वर्ग है और \(x<50}), तो (A) में कितने अवयव हैं\)?

\(If (A={x\in\mathbb{N}:x\) is a perfect square and \(x<50}), how many elements are in (A)\)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

(50) से छोटे पूर्ण वर्ग (1,4,9,16,25,36,49) हैं। / Perfect squares less than (50) are (1,4,9,16,25,36,49).

Step 2

Why this answer is correct

इनकी संख्या (7) है। / There are (7) such elements.

Step 3

Exam Tip

सीमा लगते ही अपरिमित जैसी दिखने वाली सूची परिमित हो सकती है। / Once a bound is given, an infinite-looking pattern may become finite.

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Question 534/603 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

\(यदि (A={x\in\mathbb{Z}:x^2=16\) और \(x<0}), तो (A) क्या है\)?

\(If (A={x\in\mathbb{Z}:x^2=16\) and \(x<0}), what is (A)\)?

Explanation opens after your attempt

Correct Answer

A. ({-4})

Step 1

Concept

\(x^2=16\) के पूर्णांक हल (-4) और (4) हैं। / The integer solutions of \(x^2=16\) are (-4) and (4).

Step 2

Why this answer is correct

(x<0) शर्त के कारण केवल (-4) बचेगा। / The condition (x<0) leaves only (-4).

Step 3

Exam Tip

अतिरिक्त शर्त समाधान-समुच्चय को छोटा कर सकती है। / An extra condition can reduce the solution set.

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Question 535/603 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

\(यदि (A={x\in\mathbb{N}:x\) 1 से बड़ा और 2 से छोटा है}), तो (A) कैसा है?

\(If (A={x\in\mathbb{N}:x\) is greater than 1 and less than 2}), what type of set is (A)?

Explanation opens after your attempt

Correct Answer

A. रिक्त समुच्चयempty set

Step 1

Concept

(1) और (2) के बीच कोई प्राकृतिक संख्या नहीं होती। / There is no natural number between (1) and (2).

Step 2

Why this answer is correct

इसलिए दी गई शर्त को कोई अवयव पूरा नहीं करता। / So no element satisfies the condition.

Step 3

Exam Tip

प्राकृतिक संख्या और वास्तविक संख्या के बीच का अंतर याद रखें। / Remember the difference between natural numbers and real numbers.

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Question 536/603 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

यदि \(A={x\in\mathbb{Z}:x^3=x}\), तो (A) किसके बराबर है?

If \(A={x\in\mathbb{Z}:x^3=x}\), what is (A) equal to?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(x^3=x\) को (x(x-1)(x+1)=0) लिखा जा सकता है। / \(x^3=x\) can be written as (x(x-1)(x+1)=0).

Step 2

Why this answer is correct

पूर्णांक हल (-1,0,1) हैं। / The integer solutions are (-1,0,1).

Step 3

Exam Tip

गुणनखंड बनने पर हर गुणनखंड को शून्य के बराबर रखें। / After factorising, set each factor equal to zero.

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Question 537/603 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

किस विकल्प में समुच्चय ({0,1}) के बराबर है?

Which option gives a set equal to ({0,1})?

Explanation opens after your attempt

Correct Answer

A. \({x\in\mathbb{Z}:x^2=x}\)

Step 1

Concept

\(x^2=x\) से (x(x-1)=0) मिलता है। / \(x^2=x\) gives (x(x-1)=0).

Step 2

Why this answer is correct

पूर्णांक क्षेत्र में हल (0) और (1) हैं, इसलिए समुच्चय ({0,1}) है। / In the integer domain, the solutions are (0) and (1), so the set is ({0,1}).

Step 3

Exam Tip

यदि क्षेत्र \(\mathbb{N}\) हो और (0) शामिल न माना जाए, तो उत्तर बदल सकता है। / If the domain is \(\mathbb{N}\) and (0) is not included, the answer may change.

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Question 538/603 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

\(यदि (A={x\in\mathbb{N}:x\) अभाज्य है और \(x<2}), तो (A) क्या है\)?

\(If (A={x\in\mathbb{N}:x\) is prime and \(x<2}), what is (A)\)?

Explanation opens after your attempt

Correct Answer

C. \(\varnothing\)

Step 1

Concept

(2) से छोटी प्राकृतिक संख्या (1) है। / The natural number less than (2) is (1).

Step 2

Why this answer is correct

(1) अभाज्य संख्या नहीं है, इसलिए कोई अवयव नहीं मिलेगा। / Since (1) is not prime, no element is obtained.

Step 3

Exam Tip

अभाज्य संख्या की परिभाषा में (1) को शामिल न करें। / Do not include (1) in the set of prime numbers.

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Question 539/603 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

\(यदि (A={x\in\mathbb{N}:x\) अभाज्य है और x सम है और \(x<10}), तो (A) किसके बराबर है\)?

\(If (A={x\in\mathbb{N}:x\) is prime and x is even and \(x<10}), what is (A) equal to\)?

Explanation opens after your attempt

Correct Answer

A. ({2})

Step 1

Concept

(10) से छोटे सम प्राकृतिक मान (2,4,6,8) हैं। / The even natural numbers less than (10) are (2,4,6,8).

Step 2

Why this answer is correct

इनमें केवल (2) अभाज्य है। / Only (2) among them is prime.

Step 3

Exam Tip

सम और अभाज्य साथ दिखें तो (2) को विशेष रूप से जाँचें। / When even and prime appear together, check (2) specially.

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Question 540/603 Expert Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

कौन सा कथन बराबर समुच्चयों के लिए पर्याप्त और आवश्यक है?

Which statement is necessary and sufficient for equal sets?

Explanation opens after your attempt

Correct Answer

B. दोनों में ठीक वही अवयव होंthey have exactly the same elements

Step 1

Concept

बराबर समुच्चय का अर्थ है कि एक समुच्चय का हर अवयव दूसरे में भी हो और उल्टा भी हो। / Equal sets mean every element of one set is in the other and conversely.

Step 2

Why this answer is correct

केवल संख्या समान होना पर्याप्त नहीं है। / Having only the same number of elements is not enough.

Step 3

Exam Tip

बराबरी में क्रम और नाम नहीं, अवयव निर्णायक होते हैं। / Equality depends on elements, not order or names.

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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

\(समुच्चय (A={x\in\mathbb{R}:x^2=0\) और \(x>0}) के लिए सही विकल्प कौन सा है\)?

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x\in\mathbb{N}:x\) पूर्ण वर्ग है}), तो (A) कैसा है?

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x\in\mathbb{N}:x\) पूर्ण वर्ग है और \(x<50}), तो (A) में कितने अवयव हैं\)?

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x\in\mathbb{Z}:x^2=16\) और \(x<0}), तो (A) क्या है\)?

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x\in\mathbb{N}:x\) 1 से बड़ा और 2 से छोटा है}), तो (A) कैसा है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x\in\mathbb{Z}:x^3=x}\), तो (A) किसके बराबर है?

Concept

Why this answer is correct

Exam Tip

किस विकल्प में समुच्चय ({0,1}) के बराबर है?

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x\in\mathbb{N}:x\) अभाज्य है और \(x<2}), तो (A) क्या है\)?

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x\in\mathbb{N}:x\) अभाज्य है और x सम है और \(x<10}), तो (A) किसके बराबर है\)?

Concept

Why this answer is correct

Exam Tip

कौन सा कथन बराबर समुच्चयों के लिए पर्याप्त और आवश्यक है?

Concept

Why this answer is correct

Exam Tip

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