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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 431/618 Hard Mathematics Sets Sets and their representations Class 11 Level 3

\(यदि (V={x:x\in \mathbb{N},,x\) is a multiple of 4 and \(x<25}), तो सूची रूप क्या है\)?

\(If (V={x:x\in \mathbb{N},,x\) is a multiple of 4 and \(x<25}), what is the roster form\)?

Explanation opens after your attempt

Correct Answer

A. \(V=\{4,8,12,16,20,24\}\)

Step 1

Concept

(25) से छोटी (4) की धनात्मक गुणज संख्याएं लिखें। / Write positive multiples of (4) less than (25).

Step 2

Why this answer is correct

वे (4,8,12,16,20,24) हैं। / They are (4,8,12,16,20,24).

Step 3

Exam Tip

प्राकृतिक संख्या की परिभाषा में (0) शामिल है या नहीं, प्रश्न के पाठ्यक्रम के अनुसार सावधानी रखें; यहां धनात्मक गुणज लिए गए हैं। / Be careful about whether (0) is included in natural numbers; here the intended positive multiples are listed.

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Question 432/618 Hard Mathematics Sets Sets and their representations Class 11 Level 3

कौन-सा समुच्चय अनंत समुच्चय है?

Which of the following is an infinite set?

Explanation opens after your attempt

Correct Answer

C. \(({x:x\in \mathbb{N},,x\) is even})

Step 1

Concept

अनंत समुच्चय में तत्वों की संख्या समाप्त नहीं होती। / An infinite set has no last element.

Step 2

Why this answer is correct

सम प्राकृतिक संख्याएं \(2,4,6,\ldots\) बिना अंत के चलती हैं। / Even natural numbers \(2,4,6,\ldots\) continue without end.

Step 3

Exam Tip

सीमा लगी हो तो अक्सर समुच्चय परिमित होता है। / If a bound is given, the set is often finite.

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Question 433/618 Hard Mathematics Sets Sets and their representations Class 11 Level 3

यदि \(W={x:x\in \mathbb{Z},,x^2=9}\), तो (W) का सूची रूप है?

If \(W={x:x\in \mathbb{Z},,x^2=9}\), what is the roster form of (W)?

Explanation opens after your attempt

Correct Answer

C. \(W=\{-3,3\}\)

Step 1

Concept

\(x^2=9\) से \(x=\pm3\) मिलता है। / From \(x^2=9\), we get \(x=\pm3\).

Step 2

Why this answer is correct

दोनों (-3) और (3) पूर्णांक हैं। / Both (-3) and (3) are integers.

Step 3

Exam Tip

वर्ग समीकरण में धनात्मक और ऋणात्मक दोनों मूल जांचें। / For square equations, check both positive and negative roots.

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Question 434/618 Hard Mathematics Sets Sets and their representations Class 11 Level 3

समुच्चय \(X={x:x=3n-1,,n\in \mathbb{N},,1\leq n\leq5}\) का सूची रूप कौन-सा है?

Which is the roster form of \(X={x:x=3n-1,,n\in \mathbb{N},,1\leq n\leq5}\)?

Explanation opens after your attempt

Correct Answer

A. \(X=\{2,5,8,11,14\}\)

Step 1

Concept

(n=1,2,3,4,5) रखें। / Put (n=1,2,3,4,5).

Step 2

Why this answer is correct

(3n-1) से (2,5,8,11,14) मिलते हैं। / (3n-1) gives (2,5,8,11,14).

Step 3

Exam Tip

सूत्र में (n) की हर कीमत अलग से रखकर सूची बनाएं। / Substitute each allowed value of (n) carefully to form the roster.

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Question 435/618 Hard Mathematics Sets Sets and their representations Class 11 Level 3

\(यदि (Y={x:x\in \mathbb{N},,x\) is prime and x+2 is also prime\(,,x<20}), तो (Y) क्या है\)?

\(If (Y={x:x\in \mathbb{N},,x\) is prime and x+2 is also prime\(,,x<20}), what is (Y)\)?

Explanation opens after your attempt

Correct Answer

A. \(Y=\{3,5,11,17\}\)

Step 1

Concept

(20) से छोटे अभाज्य (2,3,5,7,11,13,17,19) हैं। / Primes less than (20) are (2,3,5,7,11,13,17,19).

Step 2

Why this answer is correct

जिनके साथ (x+2) भी अभाज्य है, वे (3,5,11,17) हैं। / Values for which (x+2) is also prime are (3,5,11,17).

Step 3

Exam Tip

प्रत्येक मान पर दूसरी शर्त अलग से जांचें। / Check the second condition separately for every candidate.

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Question 436/618 Hard Mathematics Sets Sets and their representations Class 11 Level 3

कौन-सा सूची रूप \(Z={x:x\in \mathbb{Z},,-2\leq x<4}\) के लिए सही है?

Which roster form is correct for \(Z={x:x\in \mathbb{Z},,-2\leq x<4}\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

बायीं सीमा \(-2\leq x\) होने से (-2) शामिल है। / Since \(-2\leq x\), (-2) is included.

Step 2

Why this answer is correct

दायीं सीमा (x<4) होने से (4) शामिल नहीं है। / Since (x<4), (4) is not included.

Step 3

Exam Tip

पूर्णांक सूची बनाते समय (0) को न छोड़ें। / While listing integers, do not skip (0).

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Question 437/618 Hard Mathematics Sets Sets and their representations Class 11 Level 3

समुच्चय \(A_1={x:x\in \mathbb{N},,x^2-1=0}\) का सही रूप क्या है?

What is the correct form of \(A_1={x:x\in \mathbb{N},,x^2-1=0}\)?

Explanation opens after your attempt

Correct Answer

B. \(A_1={1}\)

Step 1

Concept

\(x^2-1=0\) से \(x=\pm1\) मिलता है। / From \(x^2-1=0\), we get \(x=\pm1\).

Step 2

Why this answer is correct

प्राकृतिक संख्या में केवल (1) स्वीकार होगा, (-1) नहीं। / In natural numbers, only (1) is accepted, not (-1).

Step 3

Exam Tip

समीकरण के मूलों को दिए गए संख्या-समूह से जरूर मिलाएं। / Always match the roots with the given domain.

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Question 438/618 Hard Mathematics Sets Sets and their representations Class 11 Level 3

\(यदि (B_1={x:x\in \mathbb{N},,x\) is a factor of 72 and x is a multiple of \(6}), तो (B_1) क्या है\)?

\(If (B_1={x:x\in \mathbb{N},,x\) is a factor of 72 and x is a multiple of \(6}), what is (B_1)\)?

Explanation opens after your attempt

Correct Answer

B. \(B_1={6,12,24,36,72}\)

Step 1

Concept

(72) के भाजक (1,2,3,4,6,8,9,12,18,24,36,72) हैं। / Factors of (72) are (1,2,3,4,6,8,9,12,18,24,36,72).

Step 2

Why this answer is correct

इनमें (6) के गुणज (6,12,24,36,72) हैं। / Among them, multiples of (6) are (6,12,24,36,72).

Step 3

Exam Tip

हर गुणज जरूरी नहीं कि भाजक भी हो, इसलिए दोनों शर्तें जांचें। / Every multiple is not necessarily a factor, so verify both conditions.

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Question 439/618 Hard Mathematics Sets Sets and their representations Class 11 Level 3

कौन-सा समुच्चय \(C_1={1,8,27,64}\) को सही दर्शाता है?

Which set correctly represents \(C_1={1,8,27,64}\)?

Explanation opens after your attempt

Correct Answer

B. \(C_1={x:x=n^3,,n\in \mathbb{N},,1\leq n\leq4}\)

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 \(x=n^3\) और \(1\leq n\leq4\) सही है। / Hence \(x=n^3\) with \(1\leq n\leq4\) is correct.

Step 3

Exam Tip

वर्ग और घन में अंतर पहचानना जरूरी है। / Distinguish squares and cubes carefully.

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Question 440/618 Hard Mathematics Sets Sets and their representations Class 11 Level 3

यदि \(D_1={x:x\in \mathbb{Z},,2<x^2\leq16}\), तो \(D_1\) का सूची रूप क्या होगा?

If \(D_1={x:x\in \mathbb{Z},,2<x^2\leq16}\), what is the roster form of \(D_1\)?

Explanation opens after your attempt

Correct Answer

A. \(D_1={-4,-3,-2,2,3,4}\)

Step 1

Concept

\(x^2\leq16\) से \(-4\leq x\leq4\) मिलता है। / \(x^2\leq16\) gives \(-4\leq x\leq4\).

Step 2

Why this answer is correct

\(2<x^2\) होने से \(x^2\) के मान (4,9,16) ही चलेंगे, इसलिए \(x=\pm2,\pm3,\pm4\)। / Since \(2<x^2\), only square values (4,9,16) work, so \(x=\pm2,\pm3,\pm4\).

Step 3

Exam Tip

संयुक्त असमानता में दोनों भागों को साथ लागू करें। / Apply both parts of a compound inequality together.

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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

\(यदि (V={x:x\in \mathbb{N},,x\) is a multiple of 4 and \(x<25}), तो सूची रूप क्या है\)?

Concept

Why this answer is correct

Exam Tip

कौन-सा समुच्चय अनंत समुच्चय है?

Concept

Why this answer is correct

Exam Tip

यदि \(W={x:x\in \mathbb{Z},,x^2=9}\), तो (W) का सूची रूप है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(X={x:x=3n-1,,n\in \mathbb{N},,1\leq n\leq5}\) का सूची रूप कौन-सा है?

Concept

Why this answer is correct

Exam Tip

\(यदि (Y={x:x\in \mathbb{N},,x\) is prime and x+2 is also prime\(,,x<20}), तो (Y) क्या है\)?

Concept

Why this answer is correct

Exam Tip

कौन-सा सूची रूप \(Z={x:x\in \mathbb{Z},,-2\leq x<4}\) के लिए सही है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(A_1={x:x\in \mathbb{N},,x^2-1=0}\) का सही रूप क्या है?

Concept

Why this answer is correct

Exam Tip

\(यदि (B_1={x:x\in \mathbb{N},,x\) is a factor of 72 and x is a multiple of \(6}), तो (B_1) क्या है\)?

Concept

Why this answer is correct

Exam Tip

कौन-सा समुच्चय \(C_1={1,8,27,64}\) को सही दर्शाता है?

Concept

Why this answer is correct

Exam Tip

यदि \(D_1={x:x\in \mathbb{Z},,2<x^2\leq16}\), तो \(D_1\) का सूची रूप क्या होगा?

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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