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Mathematics Sets and their representations MCQ Questions for Class 11

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Sets and their representations Practice Questions

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Question 411/615 Hard Mathematics Sets Sets and their representations Class 11 Level 3

समुच्चय \(F={x:x=2n+1,,n\in \mathbb{Z},,-2\leq n\leq2}\) का सूची रूप क्या होगा?

What is the roster form of \(F={x:x=2n+1,,n\in \mathbb{Z},,-2\leq n\leq2}\)?

Explanation opens after your attempt

Correct Answer

A. \(F=\{-3,-1,1,3,5\}\)

Step 1

Concept

(n=-2,-1,0,1,2) रखिए। / Put (n=-2,-1,0,1,2).

Step 2

Why this answer is correct

(x=2n+1) से मान (-3,-1,1,3,5) मिलते हैं। / Using (x=2n+1), we get (-3,-1,1,3,5).

Step 3

Exam Tip

ऐसे प्रश्नों में पहले छिपे हुए चर के सभी मान लिखें। / In such questions, first list all allowed values of the hidden variable.

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Question 412/615 Hard Mathematics Sets Sets and their representations Class 11 Level 3

कौन-सा विवरण \(G=\{4,9,16,25\}\) को सही समुच्चय-निर्माण रूप में दर्शाता है?

Which description correctly represents \(G=\{4,9,16,25\}\) in set-builder form?

Explanation opens after your attempt

Correct Answer

A. \(G={x:x=n^2,,n\in \mathbb{N},,2\leq n\leq5}\)

Step 1

Concept

(4,9,16,25) क्रमशः \(2^2,3^2,4^2,5^2\) हैं। / (4,9,16,25) are \(2^2,3^2,4^2,5^2\).

Step 2

Why this answer is correct

इसलिए \(x=n^2\) और \(2\leq n\leq5\) सही है। / Hence \(x=n^2\) with \(2\leq n\leq5\) is correct.

Step 3

Exam Tip

केवल पैटर्न नहीं, आरंभ और अंत की सीमा भी जांचें। / Check both the pattern and the starting and ending limits.

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Question 413/615 Hard Mathematics Sets Sets and their representations Class 11 Level 3

\(यदि (H={x:x\in \mathbb{N},,12<x<30,,x\) is divisible by 6}), तो (H) क्या है?

\(If (H={x:x\in \mathbb{N},,12<x<30,,x\) is divisible by 6}), what is (H)?

Explanation opens after your attempt

Correct Answer

B. \(H=\{18,24\}\)

Step 1

Concept

(12) और (30) के बीच (6) से विभाज्य संख्याएं देखें। / Look for multiples of (6) between (12) and (30).

Step 2

Why this answer is correct

(18) और (24) ही खुली सीमा के अंदर आते हैं। / Only (18) and (24) lie strictly inside the open interval.

Step 3

Exam Tip

(<) वाली सीमा में किनारे के मान शामिल नहीं होते। / With (<), boundary values are not included.

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Question 414/615 Hard Mathematics Sets Sets and their representations Class 11 Level 3

समुच्चय \(I={x:x\in \mathbb{R},,x^2+1=0}\) के बारे में सही कथन कौन-सा है?

Which statement is correct about the set \(I={x:x\in \mathbb{R},,x^2+1=0}\)?

Explanation opens after your attempt

Correct Answer

D. \(I=\varnothing\)

Step 1

Concept

वास्तविक संख्या के लिए \(x^2\geq0\) होता है। / For any real number, \(x^2\geq0\).

Step 2

Why this answer is correct

इसलिए \(x^2+1\) कभी (0) नहीं हो सकता। / Therefore \(x^2+1\) can never be (0) in real numbers.

Step 3

Exam Tip

संख्या-समूह वास्तविक है या सम्मिश्र, यह पहले देखना चाहिए। / Always check whether the domain is real or complex before solving.

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Question 415/615 Hard Mathematics Sets Sets and their representations Class 11 Level 3

\(यदि (J={x:x\) is a letter in the word STATISTICS}), तो सूची रूप में सही समुच्चय कौन-सा है?

\(If (J={x:x\) is a letter in the word STATISTICS}), which is the correct roster form?

Explanation opens after your attempt

Correct Answer

A. \(J=\{S,T,A,I,C\}\)

Step 1

Concept

शब्द में आने वाले अलग-अलग अक्षर पहचानें। / Identify the distinct letters in the word.

Step 2

Why this answer is correct

समुच्चय में दोहराए गए अक्षर फिर से नहीं लिखे जाते, इसलिए (S,T,A,I,C) मिलते हैं। / Repeated letters are not written again in a set, so we get (S,T,A,I,C).

Step 3

Exam Tip

सूची रूप में क्रम और पुनरावृत्ति दोनों महत्वपूर्ण नहीं माने जाते। / In roster form, order and repetition do not matter.

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Question 416/615 Hard Mathematics Sets Sets and their representations Class 11 Level 3

कौन-सा समुच्चय \(K=\{0,1,4,9,16\}\) के बराबर है?

Which set is equal to \(K=\{0,1,4,9,16\}\)?

Explanation opens after your attempt

Correct Answer

B. \({x:x=n^2,,n\in \mathbb{Z},,0\leq n\leq4}\)

Step 1

Concept

(0,1,4,9,16) ये \(0^2,1^2,2^2,3^2,4^2\) हैं। / (0,1,4,9,16) are \(0^2,1^2,2^2,3^2,4^2\).

Step 2

Why this answer is correct

\(0\leq n\leq4\) रखने पर ठीक यही वर्ग मिलते हैं। / Taking \(0\leq n\leq4\) gives exactly these squares.

Step 3

Exam Tip

ऋणात्मक (n) लेने पर भी नए वर्ग नहीं मिलते, पर सरल सही रूप विकल्प B है। / Negative (n) may repeat values, but option B is the clean exact representation.

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Question 417/615 Hard Mathematics Sets Sets and their representations Class 11 Level 3

\(यदि (L={x:x\in \mathbb{N},,x\leq20,,x\) is not divisible by 2 but divisible by 3}), तो (L) का सूची रूप है?

\(If (L={x:x\in \mathbb{N},,x\leq20,,x\) is not divisible by 2 but divisible by 3}), what is the roster form of (L)?

Explanation opens after your attempt

Correct Answer

B. \(L=\{3,9,15\}\)

Step 1

Concept

(20) तक (3) के गुणज (3,6,9,12,15,18) हैं। / Multiples of (3) up to (20) are (3,6,9,12,15,18).

Step 2

Why this answer is correct

इनमें (2) से विभाज्य संख्याएं हटाने पर (3,9,15) बचते हैं। / Removing numbers divisible by (2), we get (3,9,15).

Step 3

Exam Tip

मिली-जुली शर्तों में पहले बड़ी सूची बनाकर छांटना आसान रहता है। / For combined conditions, first make a broad list and then filter it.

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Question 418/615 Hard Mathematics Sets Sets and their representations Class 11 Level 3

समुच्चय \(M={x:x\in \mathbb{Z},,|x-2|\leq3}\) का सूची रूप क्या होगा?

What is the roster form of \(M={x:x\in \mathbb{Z},,|x-2|\leq3}\)?

Explanation opens after your attempt

Correct Answer

A. \(M=\{-1,0,1,2,3,4,5\}\)

Step 1

Concept

\(|x-2|\leq3\) से \(-3\leq x-2\leq3\) मिलता है। / \(|x-2|\leq3\) gives \(-3\leq x-2\leq3\).

Step 2

Why this answer is correct

इसमें (2) जोड़ने पर \(-1\leq x\leq5\), इसलिए पूर्णांक (-1,0,1,2,3,4,5) हैं। / Adding (2), we get \(-1\leq x\leq5\), so the integers are (-1,0,1,2,3,4,5).

Step 3

Exam Tip

परिमाप वाली असमानता को दो तरफ की असमानता में बदलें। / Convert modulus inequalities into a two-sided inequality.

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Question 419/615 Hard Mathematics Sets Sets and their representations Class 11 Level 3

कौन-सा समुच्चय \(N=\{2,4,8,16,32\}\) को सबसे सही ढंग से दर्शाता है?

Which set best represents \(N=\{2,4,8,16,32\}\)?

Explanation opens after your attempt

Correct Answer

B. \(N={x:x=2^n,,n\in \mathbb{N},,1\leq n\leq5}\)

Step 1

Concept

दिए गए तत्व \(2^1,2^2,2^3,2^4,2^5\) हैं। / The given elements are \(2^1,2^2,2^3,2^4,2^5\).

Step 2

Why this answer is correct

इसलिए \(x=2^n\) और \(1\leq n\leq5\) सही है। / Hence \(x=2^n\) with \(1\leq n\leq5\) is correct.

Step 3

Exam Tip

घात वाले पैटर्न में (n) की शुरुआती कीमत बहुत ध्यान से देखें। / For power patterns, check the starting value of (n) carefully.

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Question 420/615 Hard Mathematics Sets Sets and their representations Class 11 Level 3

\(यदि (P={x:x\in \mathbb{N},,x\) divides 48 and \(x>12}), तो (P) क्या है\)?

\(If (P={x:x\in \mathbb{N},,x\) divides 48 and \(x>12}), what is (P)\)?

Explanation opens after your attempt

Correct Answer

A. \(P=\{16,24,48\}\)

Step 1

Concept

(48) के भाजक (1,2,3,4,6,8,12,16,24,48) हैं। / Factors of (48) are (1,2,3,4,6,8,12,16,24,48).

Step 2

Why this answer is correct

(12) से बड़े भाजक (16,24,48) हैं। / The factors greater than (12) are (16,24,48).

Step 3

Exam Tip

(x>12) में (12) शामिल नहीं होता। / In (x>12), the value (12) itself is not included.

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Mathematics Sets and their representations MCQ Questions for Class 11

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Sets and their representations Practice Questions

समुच्चय \(F={x:x=2n+1,,n\in \mathbb{Z},,-2\leq n\leq2}\) का सूची रूप क्या होगा?

Concept

Why this answer is correct

Exam Tip

कौन-सा विवरण \(G=\{4,9,16,25\}\) को सही समुच्चय-निर्माण रूप में दर्शाता है?

Concept

Why this answer is correct

Exam Tip

\(यदि (H={x:x\in \mathbb{N},,12<x<30,,x\) is divisible by 6}), तो (H) क्या है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(I={x:x\in \mathbb{R},,x^2+1=0}\) के बारे में सही कथन कौन-सा है?

Concept

Why this answer is correct

Exam Tip

\(यदि (J={x:x\) is a letter in the word STATISTICS}), तो सूची रूप में सही समुच्चय कौन-सा है?

Concept

Why this answer is correct

Exam Tip

कौन-सा समुच्चय \(K=\{0,1,4,9,16\}\) के बराबर है?

Concept

Why this answer is correct

Exam Tip

\(यदि (L={x:x\in \mathbb{N},,x\leq20,,x\) is not divisible by 2 but divisible by 3}), तो (L) का सूची रूप है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(M={x:x\in \mathbb{Z},,|x-2|\leq3}\) का सूची रूप क्या होगा?

Concept

Why this answer is correct

Exam Tip

कौन-सा समुच्चय \(N=\{2,4,8,16,32\}\) को सबसे सही ढंग से दर्शाता है?

Concept

Why this answer is correct

Exam Tip

\(यदि (P={x:x\in \mathbb{N},,x\) divides 48 and \(x>12}), तो (P) क्या है\)?

Concept

Why this answer is correct

Exam Tip

Sets and their representations Learning Links

Sets Chapter

Easy Sets and their representations Test

Mathematics Subject

Search Sets and their representations

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