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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 491/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

समुच्चय \(Z={x \in \mathbb{Z}:|x|<3}\) का रोस्टर रूप कौन सा है?

Which is the roster form of \(Z={x \in \mathbb{Z}:|x|<3}\)?

Explanation opens after your attempt

Correct Answer

B. ({-2,-1,0,1,2})

Step 1

Concept

(|x|<3) का अर्थ है (x) की दूरी (0) से (3) से कम हो।

Step 2

Why this answer is correct

पूर्णांक मान (-2,-1,0,1,2) हैं। / The integer values are (-2,-1,0,1,2).

Step 3

Exam Tip

(|x|<3) में (-3) और (3) शामिल नहीं होते। / In (|x|<3), (-3) and (3) are not included.

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Question 492/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

यदि \(A_1={x \in \mathbb{N}:1\leq x\leq 5}\), तो \(A_1\) का सही रोस्टर रूप कौन सा है?

If \(A_1={x \in \mathbb{N}:1\leq x\leq 5}\), which is the correct roster form of \(A_1\)?

Explanation opens after your attempt

Correct Answer

C. ({1,2,3,4,5})

Step 1

Concept

(x) प्राकृतिक संख्या है और (1) से (5) तक जा सकता है। / (x) is a natural number from (1) to (5).

Step 2

Why this answer is correct

दोनों सिरों पर \(\leq\) है, इसलिए (1) और (5) दोनों शामिल होंगे। / Both endpoints have \(\leq\), so (1) and (5) are included.

Step 3

Exam Tip

बंद सीमा वाले प्रश्नों में दोनों अंतिम मान जरूर जाँचें। / In closed-boundary questions, check both endpoint values.

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Question 493/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

समुच्चय \(A_2={x \in \mathbb{Z}:0<x<1}\) के लिए सही विकल्प कौन सा है?

Which option is correct for the set \(A_2={x \in \mathbb{Z}:0<x<1}\)?

Explanation opens after your attempt

Correct Answer

D. \(\varnothing\)

Step 1

Concept

(x) पूर्णांक होना चाहिए। / (x) must be an integer.

Step 2

Why this answer is correct

(0) और (1) के बीच कोई पूर्णांक नहीं है। / There is no integer between (0) and (1).

Step 3

Exam Tip

वास्तविक संख्याओं और पूर्णांकों के अंतर को पहचानना जरूरी है। / It is important to distinguish between real numbers and integers.

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Question 494/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

कौन सा विकल्प \(B_1={x \in \mathbb{R}:1<x<4}\) का रोस्टर रूप नहीं बन सकता?

Which option cannot be the roster form of \(B_1={x \in \mathbb{R}:1<x<4}\)?

Explanation opens after your attempt

Correct Answer

B. ({2,3})

Step 1

Concept

(1) और (4) के बीच असंख्य वास्तविक संख्याएँ होती हैं। / There are infinitely many real numbers between (1) and (4).

Step 2

Why this answer is correct

केवल ({2,3}) लिखना सभी वास्तविक संख्याओं को नहीं दिखाता। / Writing only ({2,3}) does not show all real numbers.

Step 3

Exam Tip

वास्तविक संख्याओं के खुले अंतराल को सामान्यतः रोस्टर रूप में पूरा नहीं लिखा जाता। / An open interval of real numbers is usually not fully written in roster form.

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Question 495/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

\(समुच्चय (B_2={x \in \mathbb{Z}:x\) 15 का धनात्मक गुणनखंड है}) में कितने सदस्य हैं?

\(How many elements are in (B_2={x \in \mathbb{Z}:x\) is a positive factor of 15})?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

(15) के धनात्मक गुणनखंड (1,3,5,15) हैं। / The positive factors of (15) are (1,3,5,15).

Step 2

Why this answer is correct

कुल (4) सदस्य हैं। / There are (4) elements in total.

Step 3

Exam Tip

धनात्मक शब्द हो तो ऋणात्मक गुणनखंड शामिल न करें। / When the word positive is used, do not include negative factors.

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Question 496/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

समुच्चय \(B_3={x \in \mathbb{Z}:x^2-5x+6=0}\) का रोस्टर रूप कौन सा है?

Which is the roster form of \(B_3={x \in \mathbb{Z}:x^2-5x+6=0}\)?

Explanation opens after your attempt

Correct Answer

B. ({2,3})

Step 1

Concept

बहुपद को ((x-2)(x-3)=0) के रूप में लिख सकते हैं। / The polynomial can be written as ((x-2)(x-3)=0).

Step 2

Why this answer is correct

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

Step 3

Exam Tip

समुच्चय में हलों को अलग-अलग सदस्य के रूप में लिखें। / Write the solutions as separate elements of the set.

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Question 497/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

कौन सा विकल्प \(C_1={2,3,5,7,11}\) को सबसे सटीक समुच्चय-निर्माण रूप में दर्शाता है?

Which option represents \(C_1={2,3,5,7,11}\) most accurately in set-builder form?

Explanation opens after your attempt

Correct Answer

A. \(({x \in \mathbb{N}:x\) अभाज्य है और \(x<12})\)\(({x \in \mathbb{N}:x\) is prime and \(x<12})\)

Step 1

Concept

दिए गए सदस्य (12) से छोटी अभाज्य संख्याएँ हैं। / The given elements are prime numbers less than (12).

Step 2

Why this answer is correct

विकल्प में (x<12) और अभाज्य दोनों शर्तें ठीक बैठती हैं। / The condition prime and (x<12) matches exactly.

Step 3

Exam Tip

समुच्चय-निर्माण रूप में अनावश्यक या गलत शर्त न जोड़ें। / Do not add unnecessary or wrong conditions in set-builder form.

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Question 498/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

\(यदि (C_2={x \in \mathbb{N}:x\) 2 और 3 दोनों से विभाज्य है तथा \(x\leq 18}), तो (C_2) कौन सा है\)?

\(If (C_2={x \in \mathbb{N}:x\) is divisible by both 2 and 3 and \(x\leq 18}), then what is (C_2)\)?

Explanation opens after your attempt

Correct Answer

B. ({6,12,18})

Step 1

Concept

(2) और (3) दोनों से विभाज्य संख्या (6) की गुणज होती है। / A number divisible by both (2) and (3) is a multiple of (6).

Step 2

Why this answer is correct

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

Step 3

Exam Tip

दोनों से विभाज्य का अर्थ (2) या (3) से विभाज्य नहीं, बल्कि दोनों शर्तें एक साथ हैं। / Divisible by both means both conditions together, not either one.

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Question 499/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

\(समुच्चय (C_3={x \in \mathbb{N}:x\) 9 का गुणनखंड है और x अभाज्य है}) कौन सा है?

\(Which is the set (C_3={x \in \mathbb{N}:x\) is a factor of 9 and x is prime})?

Explanation opens after your attempt

Correct Answer

B. ({3})

Step 1

Concept

(9) के गुणनखंड (1,3,9) हैं। / The factors of (9) are (1,3,9).

Step 2

Why this answer is correct

इनमें केवल (3) अभाज्य है। / Among these, only (3) is prime.

Step 3

Exam Tip

(1) को अभाज्य मानने की गलती परीक्षा में बहुत सामान्य है। / Treating (1) as prime is a very common exam mistake.

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Question 500/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

\(कौन सा विकल्प (D_1={x \in \mathbb{N}:x\) 5 का गुणज है}) को सही तरह समझाता है?

\(Which option correctly describes (D_1={x \in \mathbb{N}:x\) is a multiple of 5})?

Explanation opens after your attempt

Correct Answer

C. यह अनंत समुच्चय हैIt is an infinite set

Step 1

Concept

(5) के गुणज \(5,10,15,20,\ldots\) चलते रहते हैं। / Multiples of (5) are \(5,10,15,20,\ldots\) and continue.

Step 2

Why this answer is correct

कोई अंतिम गुणज नहीं है, इसलिए समुच्चय अनंत है। / There is no last multiple, so the set is infinite.

Step 3

Exam Tip

यदि कोई ऊपरी सीमा नहीं दी है तो गुणजों का समुच्चय अक्सर अनंत होगा। / If no upper limit is given, a set of multiples is usually infinite.

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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 \(Z={x \in \mathbb{Z}:|x|<3}\) का रोस्टर रूप कौन सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(A_1={x \in \mathbb{N}:1\leq x\leq 5}\), तो \(A_1\) का सही रोस्टर रूप कौन सा है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(A_2={x \in \mathbb{Z}:0<x<1}\) के लिए सही विकल्प कौन सा है?

Concept

Why this answer is correct

Exam Tip

कौन सा विकल्प \(B_1={x \in \mathbb{R}:1<x<4}\) का रोस्टर रूप नहीं बन सकता?

Concept

Why this answer is correct

Exam Tip

\(समुच्चय (B_2={x \in \mathbb{Z}:x\) 15 का धनात्मक गुणनखंड है}) में कितने सदस्य हैं?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(B_3={x \in \mathbb{Z}:x^2-5x+6=0}\) का रोस्टर रूप कौन सा है?

Concept

Why this answer is correct

Exam Tip

कौन सा विकल्प \(C_1={2,3,5,7,11}\) को सबसे सटीक समुच्चय-निर्माण रूप में दर्शाता है?

Concept

Why this answer is correct

Exam Tip

\(यदि (C_2={x \in \mathbb{N}:x\) 2 और 3 दोनों से विभाज्य है तथा \(x\leq 18}), तो (C_2) कौन सा है\)?

Concept

Why this answer is correct

Exam Tip

\(समुच्चय (C_3={x \in \mathbb{N}:x\) 9 का गुणनखंड है और x अभाज्य है}) कौन सा है?

Concept

Why this answer is correct

Exam Tip

\(कौन सा विकल्प (D_1={x \in \mathbb{N}:x\) 5 का गुणज है}) को सही तरह समझाता है?

Concept

Why this answer is correct

Exam Tip

Sets and their representations Learning Links

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Easy Sets and their representations Test

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