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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 531/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

यदि \(H={x:x\in \mathbb{N},,x+5=x}\), तो (H) किस प्रकार का समुच्चय है?

If \(H={x:x\in \mathbb{N},,x+5=x}\), what type of set is (H)?

Explanation opens after your attempt

Correct Answer

A. रिक्त समुच्चयEmpty set

Step 1

Concept

समीकरण (x+5=x) से (5=0) जैसा असंभव परिणाम मिलता है। / The equation (x+5=x) gives the impossible statement (5=0).

Step 2

Why this answer is correct

कोई प्राकृतिक संख्या इस शर्त को पूरा नहीं करती। / No natural number satisfies this condition.

Step 3

Exam Tip

जिस समुच्चय में कोई अवयव न हो, उसे रिक्त समुच्चय कहते हैं। / A set with no element is called an empty set.

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Question 532/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

समुच्चय \(H={x:x\in \mathbb{Z},,x^2\leq 9}\) के लिए सही कथन कौन-सा है?

Which statement is correct for the set \(H={x:x\in \mathbb{Z},,x^2\leq 9}\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

\(x^2\leq 9\) से \(-3\leq x\leq 3\) मिलता है। / From \(x^2\leq 9\), we get \(-3\leq x\leq 3\).

Step 2

Why this answer is correct

(x) पूर्णांक है, इसलिए इस सीमा के सभी पूर्णांक लिखे जाएँगे। / Since (x) is an integer, all integers in this range are included.

Step 3

Exam Tip

वर्ग वाली असमानता में बीच के सभी मान भी शामिल होते हैं। / In a square inequality like this, all middle values also matter.

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Question 533/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

समुच्चय \(I={x:x\in \mathbb{Z},,x^2=16}\) के लिए सही कथन चुनिए।

Choose the correct statement for \(I={x:x\in \mathbb{Z},,x^2=16}\).

Explanation opens after your attempt

Correct Answer

A. \(I=\{-4,4\}\)

Step 1

Concept

\(x^2=16\) के दो पूर्णांक हल (x=4) और (x=-4) हैं। / The equation \(x^2=16\) has two integer solutions, (x=4) and (x=-4).

Step 2

Why this answer is correct

वर्ग लेने पर दोनों का मान (16) आता है। / Squaring both values gives (16).

Step 3

Exam Tip

वर्ग वाले प्रश्नों में धनात्मक और ऋणात्मक दोनों मान जाँचें। / In square equations, check both positive and negative values.

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Question 534/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

यदि \(I={x:x\) दो अंकों की प्राकृतिक संख्या है और उसके दोनों अंक बराबर हैं(}), तो (I) क्या है?

If \(I={x:x\) is a two-digit natural number and both its digits are equal(}), what is (I)?

Explanation opens after your attempt

Correct Answer

A. \(I=\{11,22,33,44,55,66,77,88,99\}\)

Step 1

Concept

दो अंकों की संख्या (10) से (99) तक होती है। / A two-digit number lies from (10) to (99).

Step 2

Why this answer is correct

दोनों अंक बराबर होने पर (11,22,33,44,55,66,77,88,99) मिलते हैं। / When both digits are equal, we get (11,22,33,44,55,66,77,88,99).

Step 3

Exam Tip

(00) दो अंकों की प्राकृतिक संख्या नहीं है। / (00) is not a two-digit natural number.

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Question 535/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

यदि \(J={x:x\in \mathbb{N},,10<x<20,,x\) और (2x+1) दोनों अभाज्य हैं(}), तो (J) है:

If \(J={x:x\in \mathbb{N},,10<x<20,,x\) and (2x+1) are both prime(}), then (J) is:

Explanation opens after your attempt

Correct Answer

A. \(J=\{11\}\)

Step 1

Concept

(10<x<20) में अभाज्य (x) हैं (11,13,17,19)। / The prime values of (x) between (10) and (20) are (11,13,17,19).

Step 2

Why this answer is correct

(2x+1) के मान (23,27,35,39) मिलते हैं। / The values of (2x+1) are (23,27,35,39).

Step 3

Exam Tip

इनमें केवल (23) अभाज्य है, इसलिए (x=11) ही रहेगा। / Only (23) is prime, so only (x=11) remains.

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Question 536/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

कौन-सा विकल्प \(J={x:x\in \mathbb{N},,x=3n-1,,1\leq n\leq 5}\) का सही सूची रूप है?

Which option is the correct roster form of \(J={x:x\in \mathbb{N},,x=3n-1,,1\leq n\leq 5}\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

(n) के मान (1,2,3,4,5) रखे जाएँगे। / Substitute (n=1,2,3,4,5).

Step 2

Why this answer is correct

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

Step 3

Exam Tip

सीमा में दिया आखिरी मान भी शामिल करें, क्योंकि \(n\leq 5\) लिखा है। / Include the last value because the condition says \(n\leq 5\).

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Question 537/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

समुच्चय \(K={x:x\in \mathbb{Z},,-2<x\leq 3}\) को सूची विधि में लिखने पर कौन-सा रूप सही है?

Which roster form is correct for \(K={x:x\in \mathbb{Z},,-2<x\leq 3}\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

(-2<x) होने से (-2) शामिल नहीं होगा। / Since (-2<x), (-2) is not included.

Step 2

Why this answer is correct

\(x\leq 3\) होने से (3) शामिल होगा। / Since \(x\leq 3\), (3) is included.

Step 3

Exam Tip

खुले और बंद असमानता चिह्नों को ध्यान से पढ़ना परीक्षा में बहुत जरूरी है। / Reading strict and non-strict inequalities carefully is very important in exams.

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Question 538/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

यदि \(K={x:x\in \mathbb{N},,x\) (40) से कम है और (x) का ठीक तीन धनात्मक भाजक हैं(}), तो (K) क्या है?

If \(K={x:x\in \mathbb{N},,x\) is less than (40) and has exactly three positive divisors(}), what is (K)?

Explanation opens after your attempt

Correct Answer

A. \(K=\{4,9,25\}\)

Step 1

Concept

ठीक तीन भाजक वाली संख्या किसी अभाज्य संख्या के वर्ग के रूप में होती है। / A number with exactly three positive divisors is the square of a prime number.

Step 2

Why this answer is correct

(40) से कम ऐसे वर्ग \(2^2,3^2,5^2\) हैं, अर्थात (4,9,25)। / Below (40), such squares are \(2^2,3^2,5^2\), giving (4,9,25).

Step 3

Exam Tip

\(7^2=49\) सीमा से बाहर है, इसलिए शामिल नहीं होगा। / \(7^2=49\) is outside the limit, so it is not included.

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Question 539/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

कौन-सा विकल्प \(L=\{1,8,27,64,125\}\) को सही ढंग से दर्शाता है?

Which option correctly represents \(L=\{1,8,27,64,125\}\)?

Explanation opens after your attempt

Correct Answer

A. \(L={x:x=n^3,,n\in \mathbb{N},,1\leq n\leq 5}\)

Step 1

Concept

(1,8,27,64,125) क्रमशः \(1^3,2^3,3^3,4^3,5^3\) हैं। / (1,8,27,64,125) are \(1^3,2^3,3^3,4^3,5^3\).

Step 2

Why this answer is correct

इसलिए नियम \(x=n^3\) होगा। / Therefore the rule is \(x=n^3\).

Step 3

Exam Tip

ठीक पाँच अवयव पाने के लिए \(1\leq n\leq 5\) सीमा लगानी होगी। / To get exactly five elements, the bound \(1\leq n\leq 5\) is needed.

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Question 540/616 Expert Mathematics Sets Sets and their representations Class 11 Level 2

समुच्चय \(L={x:x\in \mathbb{Z},,|x+1|<3}\) का सही सूची रूप कौन-सा है?

Which is the correct roster form of \(L={x:x\in \mathbb{Z},,|x+1|<3}\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

(|x+1|<3) का अर्थ है (-3<x+1<3)।

Step 2

Why this answer is correct

(1) घटाने पर (-4<x<2) मिलता है। / Subtracting (1) gives (-4<x<2).

Step 3

Exam Tip

पूर्णांक मान (-3,-2,-1,0,1) होंगे; सीमा के मान शामिल नहीं होंगे। / The integer values are (-3,-2,-1,0,1); endpoints are not included.

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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

यदि \(H={x:x\in \mathbb{N},,x+5=x}\), तो (H) किस प्रकार का समुच्चय है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(H={x:x\in \mathbb{Z},,x^2\leq 9}\) के लिए सही कथन कौन-सा है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(I={x:x\in \mathbb{Z},,x^2=16}\) के लिए सही कथन चुनिए।

Concept

Why this answer is correct

Exam Tip

यदि \(I={x:x\) दो अंकों की प्राकृतिक संख्या है और उसके दोनों अंक बराबर हैं(}), तो (I) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(J={x:x\in \mathbb{N},,10<x<20,,x\) और (2x+1) दोनों अभाज्य हैं(}), तो (J) है:

Concept

Why this answer is correct

Exam Tip

कौन-सा विकल्प \(J={x:x\in \mathbb{N},,x=3n-1,,1\leq n\leq 5}\) का सही सूची रूप है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(K={x:x\in \mathbb{Z},,-2<x\leq 3}\) को सूची विधि में लिखने पर कौन-सा रूप सही है?

Concept

Why this answer is correct

Exam Tip

यदि \(K={x:x\in \mathbb{N},,x\) (40) से कम है और (x) का ठीक तीन धनात्मक भाजक हैं(}), तो (K) क्या है?

Concept

Why this answer is correct

Exam Tip

कौन-सा विकल्प \(L=\{1,8,27,64,125\}\) को सही ढंग से दर्शाता है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(L={x:x\in \mathbb{Z},,|x+1|<3}\) का सही सूची रूप कौन-सा है?

Concept

Why this answer is correct

Exam Tip

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