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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 391/616 Hard Mathematics Sets Sets and their representations Class 11 Level 2

\(समुच्चय (G_1={x:x\in \mathbb{N}\) और x संख्या 18 का गुणज है तथा \(x<100}) का सही सूची रूप कौन सा है\)?

\(Which is the correct roster form of (G_1={x:x\in \mathbb{N}\) and x is a multiple of 18 with \(x<100})\)?

Explanation opens after your attempt

Correct Answer

A. \(G_1={18,36,54,72,90}\)

Step 1

Concept

(18) के धनात्मक गुणज लिखें। / List the positive multiples of (18).

Step 2

Why this answer is correct

(18,36,54,72,90) (100) से कम हैं, जबकि (108) नहीं है। / (18,36,54,72,90) are less than (100), while (108) is not.

Step 3

Exam Tip

गुणजों की सूची बनाते समय अंतिम मान सीमा से बाहर न जाने दें। / When listing multiples, stop before crossing the given bound.

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Question 392/616 Hard Mathematics Sets Sets and their representations Class 11 Level 2

\(यदि (H_1={x:x\in \mathbb{Z}\) और \(x^3=x}), तो (H_1) का सूची रूप क्या है\)?

\(If (H_1={x:x\in \mathbb{Z}\) and \(x^3=x}), what is the roster form of (H_1)\)?

Explanation opens after your attempt

Correct Answer

A. \(H_1={-1,0,1}\)

Step 1

Concept

\(x^3=x\) से \(x^3-x=0\) मिलता है। / From \(x^3=x\), we get \(x^3-x=0\).

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

नियम रूप में समीकरण हो तो गुणनखंड बनाकर सभी हल लिखें। / When a set is defined by an equation, factorize and list all solutions.

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Question 393/616 Hard Mathematics Sets Sets and their representations Class 11 Level 2

\(समुच्चय (I_1={x:x\) संख्या 1 से 50 तक की पूर्ण वर्ग संख्या है}) का सूची रूप चुनिए।

\(Choose the roster form of (I_1={x:x\) is a perfect square number from 1 to 50}).

Explanation opens after your attempt

Correct Answer

A. \(I_1={1,4,9,16,25,36,49}\)

Step 1

Concept

(1) से (50) तक की वर्ग संख्याएँ चाहिए। / We need perfect squares from (1) to (50).

Step 2

Why this answer is correct

\(1^2\) से \(7^2\) तक (1,4,9,16,25,36,49) मिलते हैं और \(8^2=64\) बाहर है। / From \(1^2\) to \(7^2\), we get (1,4,9,16,25,36,49), and \(8^2=64\) is outside.

Step 3

Exam Tip

वर्ग संख्याओं में ऊपरी सीमा से आगे का वर्ग शामिल न करें। / Do not include a square beyond the upper limit.

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Question 394/616 Hard Mathematics Sets Sets and their representations Class 11 Level 2

\(यदि (J_1={x:x\in \mathbb{N}\) और x का केवल एक धनात्मक भाजक है\(}), तो (J_1) क्या है\)?

\(If (J_1={x:x\in \mathbb{N}\) and x has exactly one positive divisor\(}), what is (J_1)\)?

Explanation opens after your attempt

Correct Answer

A. \(J_1={1}\)

Step 1

Concept

किसी प्राकृत संख्या का धनात्मक भाजक गिनना है। / We need to count positive divisors of a natural number.

Step 2

Why this answer is correct

(1) का केवल एक धनात्मक भाजक (1) ही है, जबकि (2) के दो भाजक हैं। / (1) has only one positive divisor, (1), while (2) has two.

Step 3

Exam Tip

भाजकों की संख्या से जुड़े प्रश्नों में (1) को अलग से जाँचें। / In divisor-count questions, check (1) separately.

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Question 395/616 Hard Mathematics Sets Sets and their representations Class 11 Level 2

\(समुच्चय (K_1={x:x\in \mathbb{N}\) और x संख्या 7 से विभाज्य है तथा \(30<x<60}) का सूची रूप क्या है\)?

\(What is the roster form of (K_1={x:x\in \mathbb{N}\) and x is divisible by 7 with \(30<x<60})\)?

Explanation opens after your attempt

Correct Answer

A. \(K_1={35,42,49,56}\)

Step 1

Concept

(30) और (60) के बीच (7) से विभाज्य संख्याएँ खोजें। / Find numbers divisible by (7) between (30) and (60).

Step 2

Why this answer is correct

(35,42,49,56) ही इस खुली सीमा में आते हैं। / The values are (35,42,49,56) within the strict range.

Step 3

Exam Tip

विभाज्यता और सीमा दोनों शर्तें साथ-साथ जाँचें। / Check divisibility and boundary conditions together.

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Question 396/616 Hard Mathematics Sets Sets and their representations Class 11 Level 2

\(यदि (L_1={x:x\in \mathbb{Z}\) और \(-5<x\le 1}), तो (L_1) का सूची रूप कौन सा है\)?

\(If (L_1={x:x\in \mathbb{Z}\) and \(-5<x\le 1}), which is the roster form of (L_1)\)?

Explanation opens after your attempt

Correct Answer

A. \(L_1={-4,-3,-2,-1,0,1}\)

Step 1

Concept

(-5<x) में (-5) शामिल नहीं है।

Step 2

Why this answer is correct

\(x\le 1\) में (1) शामिल है, इसलिए (-4) से (1) तक के पूर्णांक मिलेंगे। / \(x\le 1\) includes (1), so integers from (-4) to (1) are listed.

Step 3

Exam Tip

मिश्रित सीमा में बाएँ और दाएँ छोर अलग-अलग तय करें। / In mixed boundaries, decide each endpoint separately.

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Question 397/616 Hard Mathematics Sets Sets and their representations Class 11 Level 2

\(समुच्चय (M_1={x:x\) संख्या 100 से कम 10 का धनात्मक गुणज है और x संख्या 25 से भी विभाज्य है}) क्या है?

\(What is (M_1={x:x\) is a positive multiple of 10 less than 100 and also divisible by 25})?

Explanation opens after your attempt

Correct Answer

A. \(M_1={50}\)

Step 1

Concept

(100) से कम (10) के गुणज \(10,20,\ldots,90\) हैं। / Positive multiples of (10) less than (100) are \(10,20,\ldots,90\).

Step 2

Why this answer is correct

इनमें (25) से विभाज्य केवल (50) है। / Among them, only (50) is divisible by (25).

Step 3

Exam Tip

और वाली शर्त में सभी शर्तें एक साथ पूरी होनी चाहिए। / An and condition requires every condition to be satisfied together.

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Question 398/616 Hard Mathematics Sets Sets and their representations Class 11 Level 2

\(यदि (N_1={x:x\in \mathbb{N}\) और \(x=\frac{12}{n},\ n\in \mathbb{N}}), तो (N_1) का सूची रूप क्या है\)?

\(If (N_1={x:x\in \mathbb{N}\) and \(x=\frac{12}{n},\ n\in \mathbb{N}}), what is the roster form of (N_1)\)?

Explanation opens after your attempt

Correct Answer

A. \(N_1={1,2,3,4,6,12}\)

Step 1

Concept

\(x=\frac{12}{n}\) प्राकृत होना चाहिए, इसलिए (n) को (12) का भाजक होना चाहिए। / \(x=\frac{12}{n}\) must be natural, so (n) must divide (12).

Step 2

Why this answer is correct

मिलने वाले (x) मान (12,6,4,3,2,1) हैं, जिन्हें समुच्चय में सामान्य क्रम से ({1,2,3,4,6,12}) लिख सकते हैं। / The possible (x)-values are (12,6,4,3,2,1), written as ({1,2,3,4,6,12}).

Step 3

Exam Tip

समुच्चय में क्रम महत्व नहीं रखता। / Order does not matter in a set.

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Question 399/616 Hard Mathematics Sets Sets and their representations Class 11 Level 2

\(समुच्चय (O_1={x:x\) शब्द mathematics में आने वाले अलग-अलग अक्षर हैं}) में कितने सदस्य होंगे?

\(How many elements are in (O_1={x:x\) is a distinct letter occurring in the word mathematics})?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

शब्द के अलग-अलग अक्षर पहचानें। / Identify the distinct letters in the word.

Step 2

Why this answer is correct

(m,a,t,h,e,i,c,s) अलग-अलग अक्षर हैं, इसलिए कुल (8) सदस्य होंगे। / The distinct letters are (m,a,t,h,e,i,c,s), so there are (8) elements.

Step 3

Exam Tip

अक्षर गिनते समय दोहराए हुए अक्षरों को दोबारा न गिनें। / Do not count repeated letters again.

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Question 400/616 Hard Mathematics Sets Sets and their representations Class 11 Level 2

\(यदि (P_1={x:x\in \mathbb{N}\) और \(x^2-10x+21=0}), तो (P_1) कौन सा है\)?

\(If (P_1={x:x\in \mathbb{N}\) and \(x^2-10x+21=0}), which is (P_1)\)?

Explanation opens after your attempt

Correct Answer

A. \(P_1={3,7}\)

Step 1

Concept

समीकरण \(x^2-10x+21=0\) को गुणनखंड करें। / Factorize \(x^2-10x+21=0\).

Step 2

Why this answer is correct

((x-3)(x-7)=0), इसलिए (x=3,7)। / ((x-3)(x-7)=0), so (x=3,7).

Step 3

Exam Tip

हल मिलने के बाद देखें कि वे प्राकृत संख्याएँ हैं या नहीं। / After finding solutions, check that they are natural numbers.

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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

\(समुच्चय (G_1={x:x\in \mathbb{N}\) और x संख्या 18 का गुणज है तथा \(x<100}) का सही सूची रूप कौन सा है\)?

Concept

Why this answer is correct

Exam Tip

\(यदि (H_1={x:x\in \mathbb{Z}\) और \(x^3=x}), तो (H_1) का सूची रूप क्या है\)?

Concept

Why this answer is correct

Exam Tip

\(समुच्चय (I_1={x:x\) संख्या 1 से 50 तक की पूर्ण वर्ग संख्या है}) का सूची रूप चुनिए।

Concept

Why this answer is correct

Exam Tip

\(यदि (J_1={x:x\in \mathbb{N}\) और x का केवल एक धनात्मक भाजक है\(}), तो (J_1) क्या है\)?

Concept

Why this answer is correct

Exam Tip

\(समुच्चय (K_1={x:x\in \mathbb{N}\) और x संख्या 7 से विभाज्य है तथा \(30<x<60}) का सूची रूप क्या है\)?

Concept

Why this answer is correct

Exam Tip

\(यदि (L_1={x:x\in \mathbb{Z}\) और \(-5<x\le 1}), तो (L_1) का सूची रूप कौन सा है\)?

Concept

Why this answer is correct

Exam Tip

\(समुच्चय (M_1={x:x\) संख्या 100 से कम 10 का धनात्मक गुणज है और x संख्या 25 से भी विभाज्य है}) क्या है?

Concept

Why this answer is correct

Exam Tip

\(यदि (N_1={x:x\in \mathbb{N}\) और \(x=\frac{12}{n},\ n\in \mathbb{N}}), तो (N_1) का सूची रूप क्या है\)?

Concept

Why this answer is correct

Exam Tip

\(समुच्चय (O_1={x:x\) शब्द mathematics में आने वाले अलग-अलग अक्षर हैं}) में कितने सदस्य होंगे?

Concept

Why this answer is correct

Exam Tip

\(यदि (P_1={x:x\in \mathbb{N}\) और \(x^2-10x+21=0}), तो (P_1) कौन सा है\)?

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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