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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 381/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

समुच्चय \(A={x\in \mathbb{R}:x^2\geq 0}\) किस प्रकार का है?

What type of set is \(A={x\in \mathbb{R}:x^2\geq 0}\)?

Explanation opens after your attempt

Correct Answer

A. अनंत और \(\mathbb{R}\) के बराबरInfinite and equal to \(\mathbb{R}\)

Step 1

Concept

हर वास्तविक संख्या का वर्ग शून्य या धनात्मक होता है। / The square of every real number is zero or positive.

Step 2

Why this answer is correct

इसलिए हर वास्तविक संख्या (A) में आती है और \(A=\mathbb{R}\) है। / Hence every real number belongs to (A), so \(A=\mathbb{R}\).

Step 3

Exam Tip

सर्वसत्य शर्त वाला समुच्चय दिए हुए पूरे क्षेत्र के बराबर हो सकता है। / A condition true for all elements may make the set equal to the whole domain.

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Question 382/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

\(यदि (A={x\in \mathbb{N}:x\) is divisible by 2 and x is odd}) है, तो (A) क्या है?

\(If (A={x\in \mathbb{N}:x\) is divisible by 2 and x is odd}), what is (A)?

Explanation opens after your attempt

Correct Answer

A. \(\varnothing\)

Step 1

Concept

(2) से विभाज्य प्राकृतिक संख्या सम होती है। / A natural number divisible by (2) is even.

Step 2

Why this answer is correct

कोई संख्या एक साथ सम और विषम नहीं हो सकती। / No number can be both even and odd at the same time.

Step 3

Exam Tip

विरोधी शर्तें मिलें तो रिक्त समुच्चय की संभावना जाँचें। / When conditions conflict, check for the empty set.

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Question 383/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

यदि \(A={x\in \mathbb{Z}:x^2=25}\), \(B=\{5,-5\}\) और \(C=\{-5,5,5\}\) हैं, तो सही कथन क्या है?

If \(A={x\in \mathbb{Z}:x^2=25}\), \(B=\{5,-5\}\), and \(C=\{-5,5,5\}\), what is the correct statement?

Explanation opens after your attempt

Correct Answer

A. (A=B=C)

Step 1

Concept

\(x^2=25\) के पूर्णांक हल (5) और (-5) हैं। / The integer solutions of \(x^2=25\) are (5) and (-5).

Step 2

Why this answer is correct

Step 3

Exam Tip

बराबरी जाँचते समय सभी भिन्न अवयवों की तुलना करें। / Compare distinct elements when checking equality.

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Question 384/603 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 factor of every natural number}) क्या है?

\(What is the set (A={x\in \mathbb{N}:x\) is a factor of every natural number})?

Explanation opens after your attempt

Correct Answer

A. ({1})

Step 1

Concept

(1) हर प्राकृतिक संख्या का गुणनखंड होता है। / (1) is a factor of every natural number.

Step 2

Why this answer is correct

(2) हर प्राकृतिक संख्या को भाग नहीं देता, जैसे (3) को नहीं। / (2) does not divide every natural number, for example it does not divide (3).

Step 3

Exam Tip

सभी के लिए वाली शर्त में एक भी प्रतिवाद गलत विकल्प हटाने के लिए काफी है। / For an all-elements condition, one counterexample can eliminate a wrong option.

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Question 385/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

यदि \(A={x\in \mathbb{R}:1<x<2}\) है, तो सही कथन कौन सा है?

If \(A={x\in \mathbb{R}:1<x<2}\), which statement is correct?

Explanation opens after your attempt

Correct Answer

A. (A) अनंत है(A) is infinite

Step 1

Concept

(1) और (2) के बीच असंख्य वास्तविक संख्याएँ होती हैं, जैसे \(\frac{3}{2}\)। / There are infinitely many real numbers between (1) and (2), such as \(\frac{3}{2}\).

Step 2

Why this answer is correct

इसलिए यह समुच्चय रिक्त या परिमित नहीं है। / Therefore this set is neither empty nor finite.

Step 3

Exam Tip

वास्तविक संख्याओं के अंतराल सामान्यतः अनंत होते हैं। / Intervals of real numbers are usually infinite.

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Question 386/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

यदि \(A={x\in \mathbb{Q}:x^2=2}\) है, तो (A) के बारे में कौन सा कथन सही है?

If \(A={x\in \mathbb{Q}:x^2=2}\), which statement about (A) is correct?

Explanation opens after your attempt

Correct Answer

A. \(A=\varnothing\)

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 दोनों परिमेय नहीं हैं, इसलिए \(\mathbb{Q}\) में कोई हल नहीं। / Both are not rational, so there is no solution in \(\mathbb{Q}\).

Step 3

Exam Tip

हल मिलने के बाद यह भी देखें कि वह दिए क्षेत्र में है या नहीं। / After solving, check whether the solution belongs to the given domain.

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Question 387/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

समुच्चय \(A={x\in \mathbb{Z}:x^2\leq 4}\) और \(B=\{-2,-1,0,1,2\}\) के लिए सही कथन क्या है?

For \(A={x\in \mathbb{Z}:x^2\leq 4}\) and \(B=\{-2,-1,0,1,2\}\), what is the correct statement?

Explanation opens after your attempt

Correct Answer

A. (A=B)

Step 1

Concept

\(x^2\leq 4\) से \(-2\leq x\leq 2\) मिलता है। / \(x^2\leq 4\) gives \(-2\leq x\leq 2\).

Step 2

Why this answer is correct

इस सीमा के पूर्णांक (-2,-1,0,1,2) हैं। / The integers in this range are (-2,-1,0,1,2).

Step 3

Exam Tip

वर्ग वाली असमानता में बीच की संख्याएँ भी शामिल हो सकती हैं। / In square inequalities, include the intermediate values too.

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Question 388/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

\(यदि (A={x\in \mathbb{N}:x\) is a prime factor of \(18}) और (B={2,3}) है, तो सही कथन चुनिए\)।

\(If (A={x\in \mathbb{N}:x\) is a prime factor of \(18}) and (B={2,3}), choose the correct statement.\)

Explanation opens after your attempt

Correct Answer

A. (A=B)

Step 1

Concept

\(18=2\cdot 3^2\) है। / \(18=2\cdot 3^2\).

Step 2

Why this answer is correct

इसके अभाज्य गुणनखंड केवल (2) और (3) हैं। / Its prime factors are only (2) and (3).

Step 3

Exam Tip

गुणनखंड और अभाज्य गुणनखंड में अंतर समझना जरूरी है। / Understand the difference between factors and prime factors.

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Question 389/603 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 solution of \(x+2=x}) क्या है\)?

\(What is the set (A={x\in \mathbb{N}:x\) is a solution of \(x+2=x})\)?

Explanation opens after your attempt

Correct Answer

A. \(\varnothing\)

Step 1

Concept

(x+2=x) से (2=0) मिलता है, जो गलत है। / (x+2=x) gives (2=0), which is false.

Step 2

Why this answer is correct

कोई प्राकृतिक संख्या यह समीकरण पूरा नहीं करती। / No natural number satisfies this equation.

Step 3

Exam Tip

असंभव समानता देखकर सीधे रिक्त समुच्चय पहचानें। / An impossible equality leads directly to the empty set.

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Question 390/603 Hard Mathematics Sets The Empty Set, Finite and Infinite Sets, Equal Sets Class 11 Level 5

\(यदि (A={x\in \mathbb{Z}:x\) is even and \(-5<x<5}) है, तो (A) क्या है\)?

\(If (A={x\in \mathbb{Z}:x\) is even and \(-5<x<5}), what is (A)\)?

Explanation opens after your attempt

Correct Answer

A. ({-4,-2,0,2,4})

Step 1

Concept

(-5) और (5) के बीच पूर्णांक चुने जाते हैं। / Choose integers strictly between (-5) and (5).

Step 2

Why this answer is correct

उनमें सम पूर्णांक (-4,-2,0,2,4) हैं। / The even integers among them are (-4,-2,0,2,4).

Step 3

Exam Tip

(0) भी सम पूर्णांक है, इसे छोड़ना सामान्य गलती है। / (0) is also an even integer, so do not omit it.

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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

समुच्चय \(A={x\in \mathbb{R}:x^2\geq 0}\) किस प्रकार का है?

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x\in \mathbb{N}:x\) is divisible by 2 and x is odd}) है, तो (A) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x\in \mathbb{Z}:x^2=25}\), \(B=\{5,-5\}\) और \(C=\{-5,5,5\}\) हैं, तो सही कथन क्या है?

Concept

Why this answer is correct

Exam Tip

\(समुच्चय (A={x\in \mathbb{N}:x\) is a factor of every natural number}) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x\in \mathbb{R}:1<x<2}\) है, तो सही कथन कौन सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x\in \mathbb{Q}:x^2=2}\) है, तो (A) के बारे में कौन सा कथन सही है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(A={x\in \mathbb{Z}:x^2\leq 4}\) और \(B=\{-2,-1,0,1,2\}\) के लिए सही कथन क्या है?

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x\in \mathbb{N}:x\) is a prime factor of \(18}) और (B={2,3}) है, तो सही कथन चुनिए\)।

Concept

Why this answer is correct

Exam Tip

\(समुच्चय (A={x\in \mathbb{N}:x\) is a solution of \(x+2=x}) क्या है\)?

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x\in \mathbb{Z}:x\) is even and \(-5<x<5}) है, तो (A) क्या है\)?

Concept

Why this answer is correct

Exam Tip

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