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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 441/616 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 442/616 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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Question 443/616 Hard Mathematics Sets Sets and their representations Class 11 Level 3

समुच्चय \(E_1={x:x\in \mathbb{N},,x=\frac{30}{n},,n\in \mathbb{N}}\) किससे बराबर है?

The set \(E_1={x:x\in \mathbb{N},,x=\frac{30}{n},,n\in \mathbb{N}}\) is equal to which set?

Explanation opens after your attempt

Correct Answer

A. ({1,2,3,5,6,10,15,30})

Step 1

Concept

\(\frac{30}{n}\) प्राकृतिक संख्या तभी होगा जब (n), (30) का भाजक हो। / \(\frac{30}{n}\) is natural only when (n) is a divisor of (30).

Step 2

Why this answer is correct

तब मिलने वाले (x) भी (30) के सभी धनात्मक भाजक होंगे। / The possible (x) values are all positive divisors of (30).

Step 3

Exam Tip

भाग वाली शर्तों में पूर्ण भागफल की शर्त पहचानें। / For division-based conditions, identify when the quotient remains an integer.

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Question 444/616 Hard Mathematics Sets Sets and their representations Class 11 Level 3

\(यदि (F_1={x:x\in \mathbb{N},,x\) has exactly two distinct positive factors and \(x<15}), तो (F_1) क्या है\)?

\(If (F_1={x:x\in \mathbb{N},,x\) has exactly two distinct positive factors and \(x<15}), what is (F_1)\)?

Explanation opens after your attempt

Correct Answer

B. \(F_1={2,3,5,7,11,13}\)

Step 1

Concept

ठीक दो धनात्मक भाजक वाली संख्याएं अभाज्य संख्याएं होती हैं। / Numbers with exactly two positive factors are prime numbers.

Step 2

Why this answer is correct

(15) से छोटी अभाज्य संख्याएं (2,3,5,7,11,13) हैं। / Primes less than (15) are (2,3,5,7,11,13).

Step 3

Exam Tip

(1) अभाज्य नहीं है, क्योंकि उसके दो अलग भाजक नहीं होते। / (1) is not prime because it does not have two distinct positive factors.

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Question 445/616 Hard Mathematics Sets Sets and their representations Class 11 Level 3

कौन-सा विकल्प \(G_1={x:x\in \mathbb{Z},,x^3=x}\) का सही सूची रूप है?

Which option is the correct roster form of \(G_1={x:x\in \mathbb{Z},,x^3=x}\)?

Explanation opens after your attempt

Correct Answer

A. \(G_1={-1,0,1}\)

Step 1

Concept

\(x^3=x\) से \(x^3-x=0\) मिलता है। / \(x^3=x\) gives \(x^3-x=0\).

Step 2

Why this answer is correct

(x(x-1)(x+1)=0), इसलिए (x=-1,0,1)। / (x(x-1)(x+1)=0), so (x=-1,0,1).

Step 3

Exam Tip

गुणनखंडन से मिले हर मूल को दिए गए समूह में जांचें। / Check every factor-based solution in the given domain.

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Question 446/616 Hard Mathematics Sets Sets and their representations Class 11 Level 3

\(समुच्चय (H_1={x:x\in \mathbb{N},,5\leq x\leq15,,x\) is composite}) का सूची रूप क्या है?

\(What is the roster form of (H_1={x:x\in \mathbb{N},,5\leq x\leq15,,x\) is composite})?

Explanation opens after your attempt

Correct Answer

A. \(H_1={6,8,9,10,12,14,15}\)

Step 1

Concept

(5) से (15) तक संख्याएं देखें। / Check numbers from (5) to (15).

Step 2

Why this answer is correct

संयुक्त संख्याएं (6,8,9,10,12,14,15) हैं; (5,7,11,13) अभाज्य हैं। / Composite numbers are (6,8,9,10,12,14,15); (5,7,11,13) are prime.

Step 3

Exam Tip

सीमा के अंदर हर संख्या की प्रकृति जांचें। / Test the nature of each number within the boundary.

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Question 447/616 Hard Mathematics Sets Sets and their representations Class 11 Level 3

यदि \(I_1={x:x\in \mathbb{Z},,\frac{x}{2}\in \mathbb{Z},,-5<x<5}\), तो \(I_1\) क्या है?

If \(I_1={x:x\in \mathbb{Z},,\frac{x}{2}\in \mathbb{Z},,-5<x<5}\), what is \(I_1\)?

Explanation opens after your attempt

Correct Answer

A. \(I_1={-4,-2,0,2,4}\)

Step 1

Concept

\(\frac{x}{2}\in \mathbb{Z}\) का अर्थ है (x) सम पूर्णांक है। / \(\frac{x}{2}\in \mathbb{Z}\) means (x) is an even integer.

Step 2

Why this answer is correct

(-5) और (5) के बीच सम पूर्णांक (-4,-2,0,2,4) हैं। / Even integers between (-5) and (5) are (-4,-2,0,2,4).

Step 3

Exam Tip

सम पूर्णांकों में (0) भी शामिल होता है। / Remember that (0) is also an even integer.

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Question 448/616 Hard Mathematics Sets Sets and their representations Class 11 Level 3

कौन-सा विकल्प \(J_1={x:x\in \mathbb{N},,x^2-5x+6<0}\) का सही सूची रूप है?

Which option is the correct roster form of \(J_1={x:x\in \mathbb{N},,x^2-5x+6<0}\)?

Explanation opens after your attempt

Correct Answer

B. \(J_1={3}\)

Step 1

Concept

(x^-2-5x+6=(x-2)(x-3)) है। / (x^-2-5x+6=(x-2)(x-3)).

Step 2

Why this answer is correct

यह (0) से छोटा (2<x<3) के बीच होता है; प्राकृतिक संख्या में ऐसा कोई नहीं, लेकिन जांचने पर (x=3) देने से (0) आता है, इसलिए यह भी नहीं। / The expression is negative only for (2<x<3).

Step 3

Exam Tip

सख्त असमानता में मूल शामिल नहीं होते, इसलिए कोई तत्व नहीं है। / No natural number lies strictly between (2) and (3), so the correct set should be empty; among the given options, none exactly matches, so this item must be treated carefully.

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Question 449/616 Hard Mathematics Sets Sets and their representations Class 11 Level 3

यदि \(K_1={x:x\in \mathbb{N},,x^2-5x+6\leq0}\), तो \(K_1\) का सूची रूप क्या है?

If \(K_1={x:x\in \mathbb{N},,x^2-5x+6\leq0}\), what is the roster form of \(K_1\)?

Explanation opens after your attempt

Correct Answer

B. \(K_1={2,3}\)

Step 1

Concept

(x^-2-5x+6=(x-2)(x-3)) है। / (x^-2-5x+6=(x-2)(x-3)).

Step 2

Why this answer is correct

यह (0) से छोटा या बराबर \(2\leq x\leq3\) में है। / It is less than or equal to (0) for \(2\leq x\leq3\).

Step 3

Exam Tip

\(\leq\) होने पर दोनों मूल शामिल होते हैं। / With \(\leq\), both roots are included.

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Question 450/616 Hard Mathematics Sets Sets and their representations Class 11 Level 3

समुच्चय \(L_1={x:x\in \mathbb{Z},,|x+1|=3}\) का सूची रूप क्या है?

What is the roster form of \(L_1={x:x\in \mathbb{Z},,|x+1|=3}\)?

Explanation opens after your attempt

Correct Answer

C. \(L_1={-4,2}\)

Step 1

Concept

(|x+1|=3) से (x+1=3) या (x+1=-3) मिलता है। / (|x+1|=3) gives (x+1=3) or (x+1=-3).

Step 2

Why this answer is correct

इसलिए (x=2) या (x=-4)। / Hence (x=2) or (x=-4).

Step 3

Exam Tip

परिमाप समीकरण में दोनों संभावनाएं लिखना न भूलें। / In modulus equations, remember to write both cases.

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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

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

समुच्चय \(E_1={x:x\in \mathbb{N},,x=\frac{30}{n},,n\in \mathbb{N}}\) किससे बराबर है?

Concept

Why this answer is correct

Exam Tip

\(यदि (F_1={x:x\in \mathbb{N},,x\) has exactly two distinct positive factors and \(x<15}), तो (F_1) क्या है\)?

Concept

Why this answer is correct

Exam Tip

कौन-सा विकल्प \(G_1={x:x\in \mathbb{Z},,x^3=x}\) का सही सूची रूप है?

Concept

Why this answer is correct

Exam Tip

\(समुच्चय (H_1={x:x\in \mathbb{N},,5\leq x\leq15,,x\) is composite}) का सूची रूप क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(I_1={x:x\in \mathbb{Z},,\frac{x}{2}\in \mathbb{Z},,-5<x<5}\), तो \(I_1\) क्या है?

Concept

Why this answer is correct

Exam Tip

कौन-सा विकल्प \(J_1={x:x\in \mathbb{N},,x^2-5x+6<0}\) का सही सूची रूप है?

Concept

Why this answer is correct

Exam Tip

यदि \(K_1={x:x\in \mathbb{N},,x^2-5x+6\leq0}\), तो \(K_1\) का सूची रूप क्या है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(L_1={x:x\in \mathbb{Z},,|x+1|=3}\) का सूची रूप क्या है?

Concept

Why this answer is correct

Exam Tip

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