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Mathematics Sets and their representations MCQ Questions for Class 11 General

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Sets and their representations Practice Questions

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Question 521/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

यदि \(C={x:x\in \mathbb{N},,x<1}\), तो (C) किस प्रकार का समुच्चय है?

If \(C={x:x\in \mathbb{N},,x<1}\), what type of set is (C)?

Explanation opens after your attempt

Correct Answer

A. रिक्त समुच्चयEmpty set

Step 1

Concept

यहाँ (x) प्राकृतिक संख्या है। / Here (x) is a natural number.

Step 2

Why this answer is correct

इस स्तर पर प्राकृतिक संख्याएँ (1) से शुरू मानी जाती हैं, इसलिए (1) से छोटी कोई प्राकृतिक संख्या नहीं है। / At this level, natural numbers are taken to start from (1), so there is no natural number less than (1).

Step 3

Exam Tip

जब कोई भी अवयव शर्त पूरी न करे, तो समुच्चय रिक्त होता है। / When no element satisfies the condition, the set is empty.

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Question 522/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

यदि \(C={x:x\in \mathbb{N},,2x+3\leq 15}\), तो (C) का सही सूची रूप क्या है?

If \(C={x:x\in \mathbb{N},,2x+3\leq 15}\), what is the correct roster form of (C)?

Explanation opens after your attempt

Correct Answer

A. \(C=\{1,2,3,4,5,6\}\)

Step 1

Concept

असमानता \(2x+3\leq 15\) से \(2x\leq 12\), इसलिए \(x\leq 6\)। / From \(2x+3\leq 15\), we get \(2x\leq 12\), so \(x\leq 6\).

Step 2

Why this answer is correct

\(x\in \mathbb{N}\) है, इसलिए (1) से (6) तक प्राकृतिक संख्याएँ लें। / Since \(x\in \mathbb{N}\), take natural numbers from (1) to (6).

Step 3

Exam Tip

शून्य को तभी लें जब प्रश्न में स्पष्ट रूप से अशून्येतर पूर्ण संख्या न दी हो। / Include (0) only when the question clearly allows whole numbers.

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Question 523/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

समुच्चय \(D=\{2,4,8,16,32\}\) का सबसे सही समुच्चय-निर्माण रूप कौन-सा है?

Which is the most accurate set-builder form for \(D=\{2,4,8,16,32\}\)?

Explanation opens after your attempt

Correct Answer

A. \(D={x:x=2^n,,n\in \mathbb{N},,1\leq n\leq 5}\)

Step 1

Concept

दिए गए अवयव (2) की घातों के रूप में हैं। / The given elements are powers of (2).

Step 2

Why this answer is correct

\(2^1,2^2,2^3,2^4,2^5\) से ठीक यही पाँच अवयव मिलते हैं। / \(2^1,2^2,2^3,2^4,2^5\) give exactly these five elements.

Step 3

Exam Tip

सीमा न लगाने पर समुच्चय अनंत हो जाएगा, इसलिए \(1\leq n\leq 5\) जरूरी है। / Without the bound \(1\leq n\leq 5\), the set would become infinite.

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Question 524/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

यदि \(D={x:x\in \mathbb{Z},,x^2+x-6=0}\), तो (D) का सही सूची रूप क्या है?

If \(D={x:x\in \mathbb{Z},,x^2+x-6=0}\), what is the correct roster form of (D)?

Explanation opens after your attempt

Correct Answer

A. \(D=\{-3,2\}\)

Step 1

Concept

\(x^2+x-6\) को ((x+3)(x-2)) लिखा जा सकता है। / \(x^2+x-6\) can be written as ((x+3)(x-2)).

Step 2

Why this answer is correct

इससे (x=-3) या (x=2) मिलता है। / This gives (x=-3) or (x=2).

Step 3

Exam Tip

दोनों मान पूर्णांक हैं, इसलिए दोनों समुच्चय में आएँगे। / Both values are integers, so both belong to the set.

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Question 525/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

यदि \(E={x:x\in \mathbb{Z},,|x-2|\leq 3}\), तो (E) में कितने अवयव हैं?

If \(E={x:x\in \mathbb{Z},,|x-2|\leq 3}\), how many elements are in (E)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

\(|x-2|\leq 3\) का अर्थ है \(-3\leq x-2\leq 3\)। / \(|x-2|\leq 3\) means \(-3\leq x-2\leq 3\).

Step 2

Why this answer is correct

दोनों ओर (2) जोड़ने पर \(-1\leq x\leq 5\) मिलता है। / Adding (2) gives \(-1\leq x\leq 5\).

Step 3

Exam Tip

पूर्णांक (-1,0,1,2,3,4,5) कुल (7) हैं। / The integers (-1,0,1,2,3,4,5) are (7) elements.

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Question 526/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

यदि \(E={x:x\in \mathbb{Z},,-3\leq \frac{x}{2}<4}\), तो (E) में कितने अवयव हैं?

If \(E={x:x\in \mathbb{Z},,-3\leq \frac{x}{2}<4}\), how many elements does (E) have?

Explanation opens after your attempt

Correct Answer

A. (14)

Step 1

Concept

असमानता को (2) से गुणा करने पर \(-6\leq x<8\) मिलता है। / Multiplying the inequality by (2) gives \(-6\leq x<8\).

Step 2

Why this answer is correct

पूर्णांक (x) के मान (-6) से (7) तक होंगे। / The integer values of (x) run from (-6) to (7).

Step 3

Exam Tip

समावेश और बहिष्कार ध्यान से देखकर कुल (14) अवयव मिलते हैं। / Checking inclusion and exclusion carefully, there are (14) elements.

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Question 527/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

यदि \(F={x:x\in \mathbb{N},,x\) का वर्ग (50) से कम है और (x) (3) से विभाज्य है(}), तो (F) क्या है?

If \(F={x:x\in \mathbb{N},,x\) has square less than (50) and (x) is divisible by (3)(}), what is (F)?

Explanation opens after your attempt

Correct Answer

A. \(F=\{3,6\}\)

Step 1

Concept

\(x^2<50\) और \(x\in \mathbb{N}\) से (x=1,2,3,4,5,6,7) हो सकते हैं। / From \(x^2<50\) and \(x\in \mathbb{N}\), possible values are (1,2,3,4,5,6,7).

Step 2

Why this answer is correct

इनमें (3) से विभाज्य संख्याएँ (3) और (6) हैं। / The values divisible by (3) are (3) and (6).

Step 3

Exam Tip

पहले सीमा निकालें, फिर विभाज्यता शर्त लगाएँ। / First find the allowed range, then apply the divisibility condition.

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Question 528/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

समुच्चय \(F={x:x\in \mathbb{N},,x\) (18) का भाजक है और (x+1) अभाज्य है(}) कौन-सा है?

Which is the set \(F={x:x\in \mathbb{N},,x\) is a divisor of (18) and (x+1) is prime(})?

Explanation opens after your attempt

Correct Answer

A. \(F=\{1,2,6\}\)

Step 1

Concept

(18) के धनात्मक भाजक (1,2,3,6,9,18) हैं। / The positive divisors of (18) are (1,2,3,6,9,18).

Step 2

Why this answer is correct

इनके लिए (x+1) के मान (2,3,4,7,10,19) मिलते हैं। / The corresponding values of (x+1) are (2,3,4,7,10,19).

Step 3

Exam Tip

अभाज्य मानों के लिए (x=1,2,6,18) दिख सकते हैं, पर ध्यान दें (19) भी अभाज्य है; इसलिए (18) भी शामिल होगा। / Since (2,3,7,) and (19) are prime, the correct set is ({1,2,6,18}), so none of the listed shortened sets is fully correct.

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Question 529/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

समुच्चय \(G={x:x\) अंग्रेजी वर्णमाला का स्वर है(}) के लिए कौन-सा कथन सही है?

For the set \(G={x:x\) is a vowel of the English alphabet(}), which statement is correct?

Explanation opens after your attempt

Correct Answer

A. (G) परिमित समुच्चय है(G) is a finite set

Step 1

Concept

अंग्रेजी वर्णमाला के स्वर निश्चित हैं। / The vowels of the English alphabet are fixed.

Step 2

Why this answer is correct

उनके अवयव (a,e,i,o,u) माने जाते हैं, इसलिए संख्या सीमित है। / They are usually (a,e,i,o,u), so the number of elements is limited.

Step 3

Exam Tip

जिन समुच्चयों में अवयव गिने जा सकें और समाप्त हो जाएँ, वे परिमित होते हैं। / A set whose elements can be counted and end is finite.

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Question 530/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

यदि \(G={x:x\in \mathbb{N},,x\) (18) का भाजक है और (x+1) अभाज्य है(}), तो (G) का सही सूची रूप चुनिए।

If \(G={x:x\in \mathbb{N},,x\) is a divisor of (18) and (x+1) is prime(}), choose the correct roster form of (G).

Explanation opens after your attempt

Correct Answer

A. \(G=\{1,2,6,18\}\)

Step 1

Concept

(18) के भाजक (1,2,3,6,9,18) हैं। / The divisors of (18) are (1,2,3,6,9,18).

Step 2

Why this answer is correct

(x+1) जाँचने पर (2,3,4,7,10,19) मिलते हैं। / Checking (x+1) gives (2,3,4,7,10,19).

Step 3

Exam Tip

(2,3,7,19) अभाज्य हैं, इसलिए (x=1,2,6,18) सही हैं। / (2,3,7,19) are prime, so (x=1,2,6,18) are correct.

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Mathematics Sets and their representations MCQ Questions for Class 11 General

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Sets and their representations Practice Questions

यदि \(C={x:x\in \mathbb{N},,x<1}\), तो (C) किस प्रकार का समुच्चय है?

Concept

Why this answer is correct

Exam Tip

यदि \(C={x:x\in \mathbb{N},,2x+3\leq 15}\), तो (C) का सही सूची रूप क्या है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(D=\{2,4,8,16,32\}\) का सबसे सही समुच्चय-निर्माण रूप कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(D={x:x\in \mathbb{Z},,x^2+x-6=0}\), तो (D) का सही सूची रूप क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(E={x:x\in \mathbb{Z},,|x-2|\leq 3}\), तो (E) में कितने अवयव हैं?

Concept

Why this answer is correct

Exam Tip

यदि \(E={x:x\in \mathbb{Z},,-3\leq \frac{x}{2}<4}\), तो (E) में कितने अवयव हैं?

Concept

Why this answer is correct

Exam Tip

यदि \(F={x:x\in \mathbb{N},,x\) का वर्ग (50) से कम है और (x) (3) से विभाज्य है(}), तो (F) क्या है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(F={x:x\in \mathbb{N},,x\) (18) का भाजक है और (x+1) अभाज्य है(}) कौन-सा है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(G={x:x\) अंग्रेजी वर्णमाला का स्वर है(}) के लिए कौन-सा कथन सही है?

Concept

Why this answer is correct

Exam Tip

यदि \(G={x:x\in \mathbb{N},,x\) (18) का भाजक है और (x+1) अभाज्य है(}), तो (G) का सही सूची रूप चुनिए।

Concept

Why this answer is correct

Exam Tip

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