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Mathematics Sets and their representations MCQ Questions for Class 11 Science

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Sets and their representations Practice Questions

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Question 511/618 Expert Mathematics Sets Sets and their representations Class 11 Level 1

यदि \(F_2={x \in \mathbb{N}:x^2-1=0}\), तो \(F_2\) कौन सा है?

If \(F_2={x \in \mathbb{N}:x^2-1=0}\), then what is \(F_2\)?

Explanation opens after your attempt

Correct Answer

B. ({1})

Step 1

Concept

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

Step 2

Why this answer is correct

बीजगणितीय हल (-1) और (1) हैं, लेकिन प्राकृतिक संख्या में केवल (1) आता है। / Algebraic solutions are (-1) and (1), but only (1) is a natural number.

Step 3

Exam Tip

हल लिखते समय प्रश्न में दिया गया समुच्चय जरूर देखें। / When writing solutions, always check the given set.

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Question 512/618 Expert Mathematics Sets Sets and their representations Class 11 Level 1

कौन सा विकल्प \(F_3={1,8,27,64}\) का उपयुक्त समुच्चय-निर्माण रूप है?

Which option is a suitable set-builder form for \(F_3={1,8,27,64}\)?

Explanation opens after your attempt

Correct Answer

B. \({x^3:x \in \mathbb{N},1\leq x\leq 4}\)

Step 1

Concept

(1,8,27,64) क्रमशः \(1^3,2^3,3^3,4^3\) हैं। / (1,8,27,64) are \(1^3,2^3,3^3,4^3\).

Step 2

Why this answer is correct

इसलिए \(x^3\) और \(1\leq x\leq 4\) वाली शर्त सही है। / Therefore, the condition using \(x^3\) with \(1\leq x\leq 4\) is correct.

Step 3

Exam Tip

घन और वर्ग के पैटर्न में अंतर स्पष्ट पहचानें। / Clearly distinguish cube patterns from square patterns.

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Question 513/618 Expert Mathematics Sets Sets and their representations Class 11 Level 1

\(समुच्चय (G_1={x \in \mathbb{N}:x\) 24 का गुणनखंड है और \(x>6}) कौन सा है\)?

\(Which is the set (G_1={x \in \mathbb{N}:x\) is a factor of 24 and \(x>6})\)?

Explanation opens after your attempt

Correct Answer

A. ({8,12,24})

Step 1

Concept

(24) के गुणनखंड (1,2,3,4,6,8,12,24) हैं। / The factors of (24) are (1,2,3,4,6,8,12,24).

Step 2

Why this answer is correct

इनमें (6) से बड़े सदस्य (8,12,24) हैं। / The elements greater than (6) are (8,12,24).

Step 3

Exam Tip

(x>6) में (6) शामिल नहीं होता। / In (x>6), (6) is not included.

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Question 514/618 Expert Mathematics Sets Sets and their representations Class 11 Level 1

यदि \(G_2={x \in \mathbb{Z}:x^2\leq 1}\), तो \(G_2\) का सही रोस्टर रूप कौन सा है?

If \(G_2={x \in \mathbb{Z}:x^2\leq 1}\), which is the correct roster form of \(G_2\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

पूर्णांक (x) के लिए \(x^2\leq 1\) देखना है। / For integer (x), check \(x^2\leq 1\).

Step 2

Why this answer is correct

(-1,0,1) के वर्ग क्रमशः (1,0,1) हैं, इसलिए ये शामिल हैं। / The squares of (-1,0,1) are (1,0,1), so these are included.

Step 3

Exam Tip

पूर्णांक वाले वर्ग प्रश्न में (0) को भूलना नहीं चाहिए। / In integer square questions, do not forget (0).

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Question 515/618 Expert Mathematics Sets Sets and their representations Class 11 Level 2

\(यदि (A={x:x\in \mathbb{Z},,x^2<20,,x\) विषम है}), तो (A) की सूची विधि कौन-सी है?

\(If (A={x:x\in \mathbb{Z},,x^2<20,,x\) is odd}), which roster form of (A) is correct?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(x\in \mathbb{Z}\) का अर्थ है कि (x) पूर्णांक होगा। / \(x\in \mathbb{Z}\) means (x) must be an integer.

Step 2

Why this answer is correct

\(x^2<20\) से संभावित पूर्णांक (-4) से (4) तक हैं, पर केवल विषम पूर्णांक रखने हैं।

Step 3

Exam Tip

ऋणात्मक विषम संख्याएँ भी न भूलें, इसलिए (-3,-1,1,3) मिलते हैं। / Do not ignore negative odd integers, so the set is ({-3,-1,1,3}).

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Question 516/618 Expert Mathematics Sets Sets and their representations Class 11 Level 2

यदि \(A={x:x\in \mathbb{Z},,x^2-4x=0}\), तो (A) का सही सूची रूप कौन-सा है?

If \(A={x:x\in \mathbb{Z},,x^2-4x=0}\), which is the correct roster form of (A)?

Explanation opens after your attempt

Correct Answer

A. \(A=\{0,4\}\)

Step 1

Concept

दिए गए नियम में \(x^2-4x=0\) है, जिसे (x(x-4)=0) लिखा जा सकता है। / The given rule is \(x^2-4x=0\), which can be written as (x(x-4)=0).

Step 2

Why this answer is correct

इससे (x=0) या (x=4) मिलता है और दोनों पूर्णांक हैं। / This gives (x=0) or (x=4), and both are integers.

Step 3

Exam Tip

सूची रूप लिखते समय केवल वे मान लिखें जो शर्त को सच बनाते हैं। / In roster form, write only the values that make the condition true.

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Question 517/618 Expert Mathematics Sets Sets and their representations Class 11 Level 2

यदि \(A={x:x\in \mathbb{N}\), \(x\leq 25\), (x) (4) से विभाज्य है पर (8) से विभाज्य नहीं है(}), तो (A) का सही सूची रूप कौन-सा है?

If \(A={x:x\in \mathbb{N}\), \(x\leq 25\), (x) is divisible by (4) but not divisible by (8)(}), which is the correct roster form of (A)?

Explanation opens after your attempt

Correct Answer

A. \(A=\{4,12,20\}\)

Step 1

Concept

(25) तक (4) के गुणज (4,8,12,16,20,24) हैं। / The multiples of (4) up to (25) are (4,8,12,16,20,24).

Step 2

Why this answer is correct

इनमें (8) से विभाज्य (8,16,24) को हटाएँ। / Remove the values divisible by (8): (8,16,24).

Step 3

Exam Tip

बचे हुए (4,12,20) ही समुच्चय के अवयव हैं। / The remaining elements (4,12,20) form the set.

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Question 518/618 Expert Mathematics Sets Sets and their representations Class 11 Level 2

\(यदि (A={x\in \mathbb{Z}: x^2<10\) और \(x>-3}) है, तो रोस्टर रूप में (A) क्या होगा\)?

\(If (A={x\in \mathbb{Z}: x^2<10\) and \(x>-3}), what is (A) in roster form\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

यहां (x) पूर्णांक है, इसलिए केवल पूर्णांक मान ही लिए जाएंगे। / Here (x) is an integer, so only integer values are allowed.

Step 2

Why this answer is correct

शर्त (x>-3) से संभावित मान \(-2,-1,0,1,2,3,\ldots\) मिलते हैं, और \(x^2<10\) से (-3) से (3) के बीच के उपयुक्त मान आते हैं। दोनों शर्तों को साथ रखने पर (-2,-1,0,1,2,3) मिलते हैं। / The condition (x>-3) gives possible values \(-2,-1,0,1,2,3,\ldots\), and \(x^2<10\) keeps the suitable values between (-3) and (3). Combining both conditions gives (-2,-1,0,1,2,3).

Step 3

Exam Tip

परीक्षा में पहले संख्या-समुच्चय पहचानें, फिर सभी शर्तों को एक साथ जांचें। / In exams, first identify the number system, then test all conditions together.

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Question 519/618 Expert Mathematics Sets Sets and their representations Class 11 Level 2

समुच्चय \(B={x:x\) संख्या (36) का धनात्मक भाजक है और (x) अभाज्य नहीं है(}) के अवयव कौन-से हैं?

Which elements belong to \(B={x:x\) is a positive divisor of (36) and (x) is not prime(})?

Explanation opens after your attempt

Correct Answer

A. \(B=\{1,4,6,9,12,18,36\}\)

Step 1

Concept

(36) के धनात्मक भाजक (1,2,3,4,6,9,12,18,36) हैं। / The positive divisors of (36) are (1,2,3,4,6,9,12,18,36).

Step 2

Why this answer is correct

(2) और (3) अभाज्य हैं, इसलिए उन्हें हटाएँ। / Remove (2) and (3) because they are prime.

Step 3

Exam Tip

(1) अभाज्य नहीं होता, इसलिए वह समुच्चय में रहेगा। / (1) is not prime, so it remains in the set.

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Question 520/618 Expert Mathematics Sets Sets and their representations Class 11 Level 2

समुच्चय \(B=\{2,5,10,17,26\}\) को सबसे सही समुच्चय-निर्माण रूप में कैसे लिखा जाएगा?

How can the set \(B=\{2,5,10,17,26\}\) be written most accurately in set-builder form?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

दिए गए अवयव \(1^2+1,2^2+1,3^2+1,4^2+1,5^2+1\) के रूप में मिलते हैं। / The elements are obtained as \(1^2+1,2^2+1,3^2+1,4^2+1,5^2+1\).

Step 2

Why this answer is correct

इसलिए नियम \(x=n^2+1\) होगा। / So the rule is \(x=n^2+1\).

Step 3

Exam Tip

ठीक पाँच अवयव पाने के लिए \(1\leq n\leq 5\) सीमा लिखना जरूरी है। / To get exactly five elements, the bound \(1\leq n\leq 5\) is necessary.

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Mathematics Sets and their representations MCQ Questions for Class 11 Science

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Sets and their representations Practice Questions

यदि \(F_2={x \in \mathbb{N}:x^2-1=0}\), तो \(F_2\) कौन सा है?

Concept

Why this answer is correct

Exam Tip

कौन सा विकल्प \(F_3={1,8,27,64}\) का उपयुक्त समुच्चय-निर्माण रूप है?

Concept

Why this answer is correct

Exam Tip

\(समुच्चय (G_1={x \in \mathbb{N}:x\) 24 का गुणनखंड है और \(x>6}) कौन सा है\)?

Concept

Why this answer is correct

Exam Tip

यदि \(G_2={x \in \mathbb{Z}:x^2\leq 1}\), तो \(G_2\) का सही रोस्टर रूप कौन सा है?

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x:x\in \mathbb{Z},,x^2<20,,x\) विषम है}), तो (A) की सूची विधि कौन-सी है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x:x\in \mathbb{Z},,x^2-4x=0}\), तो (A) का सही सूची रूप कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(A={x:x\in \mathbb{N}\), \(x\leq 25\), (x) (4) से विभाज्य है पर (8) से विभाज्य नहीं है(}), तो (A) का सही सूची रूप कौन-सा है?

Concept

Why this answer is correct

Exam Tip

\(यदि (A={x\in \mathbb{Z}: x^2<10\) और \(x>-3}) है, तो रोस्टर रूप में (A) क्या होगा\)?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(B={x:x\) संख्या (36) का धनात्मक भाजक है और (x) अभाज्य नहीं है(}) के अवयव कौन-से हैं?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(B=\{2,5,10,17,26\}\) को सबसे सही समुच्चय-निर्माण रूप में कैसे लिखा जाएगा?

Concept

Why this answer is correct

Exam Tip

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