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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 361/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

समुच्चय \(A={x\in \mathbb{R}:x^2=x}\) और \(B=\{0,1\}\) के लिए सही कथन कौन सा है?

For \(A={x\in \mathbb{R}:x^2=x}\) and \(B=\{0,1\}\), which statement is correct?

Explanation opens after your attempt

Correct Answer

A. (A=B)

Step 1

Concept

\(x^2=x\) को (x(x-1)=0) लिखा जा सकता है। / \(x^2=x\) can be written as (x(x-1)=0).

Step 2

Why this answer is correct

इसके हल (0) और (1) हैं, इसलिए \(A=\{0,1\}\)। / Its solutions are (0) and (1), so \(A=\{0,1\}\).

Step 3

Exam Tip

समीकरण को गुणनखंडित करना हल-समुच्चय पहचानने का तेज तरीका है। / Factoring an equation quickly identifies its solution set.

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Question 362/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

\(यदि (A={x:x\) is a letter in the word \(LEVEL}) और (B={L,E,V}) है, तो कौन सा कथन सही है\)?

\(If (A={x:x\) is a letter in the word \(LEVEL}) and (B={L,E,V}), which statement is correct\)?

Explanation opens after your attempt

Correct Answer

A. (A=B)

Step 1

Concept

शब्द में अक्षर दोहर सकते हैं, लेकिन समुच्चय में दोहराव नहीं गिना जाता। / Letters may repeat in a word, but repetitions are not counted in a set.

Step 2

Why this answer is correct

अलग-अलग अक्षर (L,E,V) हैं। / The distinct letters are (L,E,V).

Step 3

Exam Tip

अक्षर-समुच्चय बनाते समय केवल भिन्न अक्षरों को लिखें। / While forming a set of letters, list only distinct letters.

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Question 363/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

\(समुच्चय (A={x\in \mathbb{N}:x\) is a multiple of 3}) के बारे में सही कथन क्या है?

\(What is the correct statement about (A={x\in \mathbb{N}:x\) is a multiple of 3})?

Explanation opens after your attempt

Correct Answer

A. (A) अनंत समुच्चय है(A) is an infinite set

Step 1

Concept

\(3,6,9,12,\ldots\) जैसे गुणज लगातार मिलते रहते हैं। / Multiples such as \(3,6,9,12,\ldots\) continue without end.

Step 2

Why this answer is correct

इनके लिए कोई अंतिम प्राकृतिक गुणज नहीं है। / There is no last natural multiple of (3).

Step 3

Exam Tip

सूची में तीन बिंदु \(\ldots\) अक्सर अनंतता का संकेत देते हैं, पर शर्त से भी जाँचें। / Dots \(\ldots\) often indicate infinity, but confirm it from the rule.

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Question 364/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

यदि \(A={x\in \mathbb{N}:x<1}\) और \(B={x\in \mathbb{Z}:0<x<1}\) है, तो सही कथन कौन सा है?

If \(A={x\in \mathbb{N}:x<1}\) and \(B={x\in \mathbb{Z}:0<x<1}\), which statement is correct?

Explanation opens after your attempt

Correct Answer

A. \(A=B=\varnothing\)

Step 1

Concept

सामान्य स्कूल परिभाषा में प्राकृतिक संख्याएँ (1) से शुरू मानी जाती हैं। / In the usual school convention, natural numbers start from (1).

Step 2

Why this answer is correct

(1) से छोटी कोई प्राकृतिक संख्या नहीं और (0) तथा (1) के बीच कोई पूर्णांक नहीं। / There is no natural number less than (1), and no integer strictly between (0) and (1).

Step 3

Exam Tip

दिए गए संख्या-समूह के अनुसार अवयव चुनें। / Select elements according to the given number system.

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Question 365/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

समुच्चय \(A={x\in \mathbb{Z}:|x|<4}\) किसके बराबर है?

Which set is equal to \(A={x\in \mathbb{Z}:|x|<4}\)?

Explanation opens after your attempt

Correct Answer

A. ({-3,-2,-1,0,1,2,3})

Step 1

Concept

(|x|<4) का अर्थ (-4<x<4) है।

Step 2

Why this answer is correct

इस सीमा में पूर्णांक (-3) से (3) तक हैं। / The integers in this range are from (-3) to (3).

Step 3

Exam Tip

परिमाण वाले प्रश्नों में दोनों ओर की संख्याएँ जाँचें। / In absolute value questions, check both negative and positive sides.

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Question 366/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

यदि \(A={x\in \mathbb{R}:x^2=9}\) और \(B=\{-3,3\}\) है, तो (A) के बारे में सही कथन चुनिए।

If \(A={x\in \mathbb{R}:x^2=9}\) and \(B=\{-3,3\}\), choose the correct statement about (A).

Explanation opens after your attempt

Correct Answer

A. (A=B)

Step 1

Concept

\(x^2=9\) के दो वास्तविक हल (x=3) और (x=-3) हैं। / \(x^2=9\) has two real solutions, (x=3) and (x=-3).

Step 2

Why this answer is correct

इसलिए \(A=\{-3,3\}\), जो (B) के समान है। / Thus \(A=\{-3,3\}\), same as (B).

Step 3

Exam Tip

वर्ग समीकरण में धन और ऋण दोनों मूल याद रखें। / For square equations, remember both positive and negative roots.

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Question 367/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

\(समुच्चय (A={x\in \mathbb{N}:x\) divides 0}) के लिए सही कथन कौन सा है?

\(For the set (A={x\in \mathbb{N}:x\) divides 0}), which statement is correct?

Explanation opens after your attempt

Correct Answer

A. (A) अनंत है(A) is infinite

Step 1

Concept

हर प्राकृतिक संख्या (x) के लिए \(0=x\cdot 0\) लिखा जा सकता है। / For every natural number (x), \(0=x\cdot 0\).

Step 2

Why this answer is correct

इसलिए हर प्राकृतिक संख्या (0) को भाग देती है और अवयव समाप्त नहीं होते। / Hence every natural number divides (0), giving infinitely many elements.

Step 3

Exam Tip

शून्य को भाग देने और शून्य से भाग देने में अंतर याद रखें। / Remember the difference between dividing zero and division by zero.

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Question 368/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

यदि \(A={x\in \mathbb{Z}:x^2<0}\) है, तो (n(A)) कितना होगा?

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

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

किसी भी पूर्णांक का वर्ग कभी ऋणात्मक नहीं होता। / The square of any integer is never negative.

Step 2

Why this answer is correct

इसलिए \(x^2<0\) को कोई पूर्णांक पूरा नहीं करता। / So no integer satisfies \(x^2<0\).

Step 3

Exam Tip

असंभव शर्त वाला समुच्चय रिक्त होता है और उसका अवयव-मान (0) होता है। / A set with an impossible condition is empty and has cardinality (0).

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Question 369/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

समुच्चय \(A={x\in \mathbb{R}:x=x+1}\) के बारे में सही कथन क्या है?

What is the correct statement about \(A={x\in \mathbb{R}:x=x+1}\)?

Explanation opens after your attempt

Correct Answer

A. \(A=\varnothing\)

Step 1

Concept

समीकरण (x=x+1) से (0=1) मिलता है, जो असंभव है। / The equation (x=x+1) gives (0=1), which is impossible.

Step 2

Why this answer is correct

कोई वास्तविक संख्या इस शर्त को पूरा नहीं करती। / No real number satisfies the condition.

Step 3

Exam Tip

विरोधाभासी समीकरण का हल-समुच्चय रिक्त होता है। / A contradictory equation has the empty set as its solution set.

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Question 370/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

यदि \(A={x\in \mathbb{N}:x^2\leq 49}\) है, तो (A) किसके बराबर है?

If \(A={x\in \mathbb{N}:x^2\leq 49}\), which set is (A) equal to?

Explanation opens after your attempt

Correct Answer

A. ({1,2,3,4,5,6,7})

Step 1

Concept

प्राकृतिक संख्या (x) के लिए \(x^2\leq 49\) का अर्थ \(x\leq 7\) है। / For a natural number (x), \(x^2\leq 49\) means \(x\leq 7\).

Step 2

Why this answer is correct

प्राकृतिक संख्याएँ (1) से शुरू मानकर अवयव (1) से (7) तक होंगे। / Taking natural numbers from (1), the elements are (1) through (7).

Step 3

Exam Tip

क्षेत्र \(\mathbb{N}\) होने पर ऋणात्मक संख्याएँ न जोड़ें। / Since the domain is \(\mathbb{N}\), do not include negative numbers.

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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 \(A={x\in \mathbb{R}:x^2=x}\) और \(B=\{0,1\}\) के लिए सही कथन कौन सा है?

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x:x\) is a letter in the word \(LEVEL}) और (B={L,E,V}) है, तो कौन सा कथन सही है\)?

Concept

Why this answer is correct

Exam Tip

\(समुच्चय (A={x\in \mathbb{N}:x\) is a multiple of 3}) के बारे में सही कथन क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x\in \mathbb{N}:x<1}\) और \(B={x\in \mathbb{Z}:0<x<1}\) है, तो सही कथन कौन सा है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(A={x\in \mathbb{Z}:|x|<4}\) किसके बराबर है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x\in \mathbb{R}:x^2=9}\) और \(B=\{-3,3\}\) है, तो (A) के बारे में सही कथन चुनिए।

Concept

Why this answer is correct

Exam Tip

\(समुच्चय (A={x\in \mathbb{N}:x\) divides 0}) के लिए सही कथन कौन सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x\in \mathbb{Z}:x^2<0}\) है, तो (n(A)) कितना होगा?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(A={x\in \mathbb{R}:x=x+1}\) के बारे में सही कथन क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x\in \mathbb{N}:x^2\leq 49}\) है, तो (A) किसके बराबर है?

Concept

Why this answer is correct

Exam Tip

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