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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 481/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

समुच्चय \(P={x \in \mathbb{Z}:x^2=9}\) का रोस्टर रूप कौन सा है?

What is the roster form of the set \(P={x \in \mathbb{Z}:x^2=9}\)?

Explanation opens after your attempt

Correct Answer

C. ({-3,3})

Step 1

Concept

(x) पूर्णांक है, इसलिए धनात्मक और ऋणात्मक दोनों मान जाँचें। / (x) is an integer, so test both positive and negative values.

Step 2

Why this answer is correct

((-3)²=9) और \(3^2=9\), इसलिए दोनों सदस्य हैं। / ((-3)²=9) and \(3^2=9\), so both are elements.

Step 3

Exam Tip

वर्ग वाले प्रश्नों में ऋणात्मक हल अक्सर छूट जाता है। / In square equations, the negative solution is often missed.

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Question 482/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

समुच्चय \(Q={x \in \mathbb{N}:x^2\leq 25}\) का रोस्टर रूप कौन सा है?

Which is the roster form of \(Q={x \in \mathbb{N}:x^2\leq 25}\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

(x) प्राकृतिक संख्या है, इसलिए (1) से शुरू करें। / (x) is a natural number, so start from (1).

Step 2

Why this answer is correct

\(1^2,2^2,3^2,4^2,5^2\) सभी (25) से कम या बराबर हैं। / \(1^2,2^2,3^2,4^2,5^2\) are all less than or equal to (25).

Step 3

Exam Tip

प्राकृतिक संख्या और पूर्णांक के अंतर को ध्यान में रखें। / Keep the difference between natural numbers and integers in mind.

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Question 483/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

समुच्चय \(R={\varnothing}\) में कितने सदस्य हैं?

How many elements are in the set \(R={\varnothing}\)?

Explanation opens after your attempt

Correct Answer

B. (1)

Step 1

Concept

\(\varnothing\) एक समुच्चय है। / \(\varnothing\) is a set.

Step 2

Why this answer is correct

\(R={\varnothing}\) में वही रिक्त समुच्चय एक सदस्य के रूप में रखा गया है। / In \(R={\varnothing}\), the empty set itself is one element.

Step 3

Exam Tip

\(\varnothing\) और \({\varnothing}\) को अलग-अलग समझें। / Understand the difference between \(\varnothing\) and \({\varnothing}\).

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Question 484/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

\(यदि (S={x \in \mathbb{N}:x\) 7 का गुणज है और \(x<30}), तो (S) का सही रूप कौन सा है\)?

\(If (S={x \in \mathbb{N}:x\) is a multiple of 7 and \(x<30}), which is the correct form of (S)\)?

Explanation opens after your attempt

Correct Answer

A. ({7,14,21,28})

Step 1

Concept

(7) के गुणज \(7,14,21,28,35,\ldots\) हैं। / Multiples of (7) are \(7,14,21,28,35,\ldots\).

Step 2

Why this answer is correct

(30) से छोटी संख्याएँ (7,14,21,28) ही हैं। / The ones less than (30) are (7,14,21,28).

Step 3

Exam Tip

अंतिम सीमा से बड़ी संख्या को गलती से न जोड़ें। / Do not accidentally include a number beyond the boundary.

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Question 485/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

\(समुच्चय (T={x \in \mathbb{N}:x\) पूर्ण वर्ग है और \(x<50}) का रोस्टर रूप कौन सा है\)?

\(Which is the roster form of (T={x \in \mathbb{N}:x\) is a perfect square and \(x<50})\)?

Explanation opens after your attempt

Correct Answer

A. ({1,4,9,16,25,36,49})

Step 1

Concept

(50) से छोटे पूर्ण वर्ग पहचानें। / Identify perfect squares less than (50).

Step 2

Why this answer is correct

\(1^2\) से \(7^2\) तक वर्ग (1,4,9,16,25,36,49) मिलते हैं। / Squares from \(1^2\) to \(7^2\) give (1,4,9,16,25,36,49).

Step 3

Exam Tip

\(8^2=64\) सीमा से बाहर है, इसलिए शामिल नहीं होगा। / \(8^2=64\) is outside the limit, so it is excluded.

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Question 486/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

निम्न में से कौन सा समुच्चय \(U=\{3,6,9,12\}\) के बराबर है?

Which of the following is equal to the set \(U=\{3,6,9,12\}\)?

Explanation opens after your attempt

Correct Answer

B. \(({x \in \mathbb{N}:x\) 3 का गुणज है और \(x\leq 12})\)\(({x \in \mathbb{N}:x\) is a multiple of 3 and \(x\leq 12})\)

Step 1

Concept

(U) में (3) के गुणज (12) तक हैं। / (U) contains multiples of (3) up to (12).

Step 2

Why this answer is correct

\(\leq 12\) लिखने पर (3,6,9,12) सभी मिलते हैं। / Using \(\leq 12\) gives (3,6,9,12).

Step 3

Exam Tip

सीमा में (<) और \(\leq\) का फर्क बराबरी बदल सकता है। / The difference between (<) and \(\leq\) can change set equality.

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Question 487/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

यदि \(V={x \in \mathbb{Z}:-2\leq x<3}\), तो (n(V)) क्या है?

If \(V={x \in \mathbb{Z}:-2\leq x<3}\), what is (n(V))?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

दिए गए पूर्णांक (-2,-1,0,1,2) हैं। / The integers are (-2,-1,0,1,2).

Step 2

Why this answer is correct

कुल (5) सदस्य हैं, इसलिए (n(V)=5)। / There are (5) elements, so (n(V)=5).

Step 3

Exam Tip

बाएँ सिरे पर \(\leq\) होने से (-2) शामिल होगा और दाएँ सिरे पर (<) होने से (3) शामिल नहीं होगा। / Because the left endpoint has \(\leq\), (-2) is included; because the right endpoint has (<), (3) is excluded.

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Question 488/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

\(समुच्चय (W={x \in \mathbb{N}:x\) 18 का गुणनखंड है और x सम है}) का रोस्टर रूप कौन सा है?

\(Which is the roster form of (W={x \in \mathbb{N}:x\) is a factor of 18 and x is even})?

Explanation opens after your attempt

Correct Answer

B. ({2,6,18})

Step 1

Concept

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

Step 2

Why this answer is correct

इनमें सम सदस्य (2,6,18) हैं। / The even elements among them are (2,6,18).

Step 3

Exam Tip

संयुक्त शर्त में पहले सभी संभावित सदस्य लिखकर फिर छँटाई करें। / For combined conditions, list possible elements first and then filter them.

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Question 489/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

\(समुच्चय (X={x \in \mathbb{N}:x\) 4 और 6 दोनों का गुणज है और \(x<30}) कौन सा है\)?

\(Which is the set (X={x \in \mathbb{N}:x\) is a multiple of both 4 and 6 and \(x<30})\)?

Explanation opens after your attempt

Correct Answer

B. ({12,24})

Step 1

Concept

(4) और (6) दोनों का गुणज उनके लघुत्तम समापवर्त्य (12) का गुणज होगा। / A number that is a multiple of both (4) and (6) must be a multiple of their LCM (12).

Step 2

Why this answer is correct

(30) से छोटे (12) के गुणज (12) और (24) हैं। / Multiples of (12) less than (30) are (12) and (24).

Step 3

Exam Tip

दोनों का गुणज का अर्थ अलग-अलग गुणजों की सूची जोड़ना नहीं है। / Multiple of both does not mean combining separate lists of multiples.

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Question 490/615 Expert Mathematics Sets Sets and their representations Class 11 Level 1

कौन सा विकल्प \(Y=\{0\}\) के बारे में सही है?

Which option is correct about \(Y=\{0\}\)?

Explanation opens after your attempt

Correct Answer

B. यह एकल समुच्चय हैIt is a singleton set

Step 1

Concept

(Y) में (0) एक सदस्य के रूप में उपस्थित है। / (0) is present as an element in (Y).

Step 2

Why this answer is correct

इसलिए यह रिक्त नहीं, बल्कि एक सदस्य वाला एकल समुच्चय है। / So it is not empty; it is a singleton set with one element.

Step 3

Exam Tip

({0}) और \(\varnothing\) को कभी समान न मानें। / Never treat ({0}) and \(\varnothing\) as the same.

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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 \(P={x \in \mathbb{Z}:x^2=9}\) का रोस्टर रूप कौन सा है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(Q={x \in \mathbb{N}:x^2\leq 25}\) का रोस्टर रूप कौन सा है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(R={\varnothing}\) में कितने सदस्य हैं?

Concept

Why this answer is correct

Exam Tip

\(यदि (S={x \in \mathbb{N}:x\) 7 का गुणज है और \(x<30}), तो (S) का सही रूप कौन सा है\)?

Concept

Why this answer is correct

Exam Tip

\(समुच्चय (T={x \in \mathbb{N}:x\) पूर्ण वर्ग है और \(x<50}) का रोस्टर रूप कौन सा है\)?

Concept

Why this answer is correct

Exam Tip

निम्न में से कौन सा समुच्चय \(U=\{3,6,9,12\}\) के बराबर है?

Concept

Why this answer is correct

Exam Tip

यदि \(V={x \in \mathbb{Z}:-2\leq x<3}\), तो (n(V)) क्या है?

Concept

Why this answer is correct

Exam Tip

\(समुच्चय (W={x \in \mathbb{N}:x\) 18 का गुणनखंड है और x सम है}) का रोस्टर रूप कौन सा है?

Concept

Why this answer is correct

Exam Tip

\(समुच्चय (X={x \in \mathbb{N}:x\) 4 और 6 दोनों का गुणज है और \(x<30}) कौन सा है\)?

Concept

Why this answer is correct

Exam Tip

कौन सा विकल्प \(Y=\{0\}\) के बारे में सही 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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