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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 351/616 Hard Mathematics Sets Sets and their representations Class 11 Level 1

समुच्चय \(Q={x:x\in N,\ x\) (20) से छोटा है और (x) न तो (2) से न (3) से विभाज्य है(}) कौन सा है?

Which is the set \(Q={x:x\in N,\ x\) is less than (20) and (x) is divisible by neither (2) nor (3})?

Explanation opens after your attempt

Correct Answer

A. \(Q=\{1,5,7,11,13,17,19\}\)

Step 1

Concept

(20) से छोटी प्राकृतिक संख्याओं में वे चुनें जो (2) और (3) दोनों से विभाज्य न हों। / From natural numbers less than (20), choose those not divisible by both (2) and (3).

Step 2

Why this answer is correct

ऐसे अवयव (1,5,7,11,13,17,19) हैं। / The elements are (1,5,7,11,13,17,19).

Step 3

Exam Tip

“न तो” वाली शर्त में दोनों विभाज्यताओं को हटाएँ। / For “neither” conditions, remove numbers satisfying each excluded divisibility.

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Question 352/616 Hard Mathematics Sets Sets and their representations Class 11 Level 1

यदि \(R={x:x\in N,\ x+4=4}\), तो (R) क्या है?

If \(R={x:x\in N,\ x+4=4}\), what is (R)?

Explanation opens after your attempt

Correct Answer

C. \(R=\phi\)

Step 1

Concept

(x+4=4) से (x=0) मिलता है। / From (x+4=4), we get (x=0).

Step 2

Why this answer is correct

लेकिन \(x\in N\) है और यहाँ प्राकृतिक संख्याएँ (1) से शुरू मानी जाती हैं, इसलिए कोई अवयव नहीं है। / But \(x\in N\), and here natural numbers start from (1), so there is no element.

Step 3

Exam Tip

हल मिलने के बाद यह देखना जरूरी है कि वह दिए गए समुच्चय में आता है या नहीं। / After solving, always check whether the solution belongs to the given domain.

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Question 353/616 Hard Mathematics Sets Sets and their representations Class 11 Level 1

कौन सा विकल्प \(\phi\) और \({\phi}\) के बारे में सही है?

Which option about \(\phi\) and \({\phi}\) is correct?

Explanation opens after your attempt

Correct Answer

C. \({\phi}\) में एक अवयव है\({\phi}\) has one element

Step 1

Concept

\(\phi\) रिक्त समुच्चय है, इसमें कोई अवयव नहीं होता। / \(\phi\) is the empty set and has no element.

Step 2

Why this answer is correct

\({\phi}\) में \(\phi\) स्वयं एक अवयव है, इसलिए इसमें एक अवयव है। / \({\phi}\) contains \(\phi\) itself as one element.

Step 3

Exam Tip

किसी समुच्चय को अवयव के रूप में रखने से नया समुच्चय रिक्त नहीं रहता। / Putting a set as an element makes a new set that is not empty.

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Question 354/616 Hard Mathematics Sets Sets and their representations Class 11 Level 1

यदि \(S={x:x\in N,\ x\) (8) का गुणज है और (x<50}), तो (S) का रोस्टर रूप क्या है?

If \(S={x:x\in N,\ x\) is a multiple of (8) and (x<50}), what is the roster form of (S)?

Explanation opens after your attempt

Correct Answer

A. \(S=\{8,16,24,32,40,48\}\)

Step 1

Concept

(8) के धन गुणज \(8,16,24,32,40,48,\ldots\) हैं। / The positive multiples of (8) are \(8,16,24,32,40,48,\ldots\).

Step 2

Why this answer is correct

(50) से छोटे गुणज (8,16,24,32,40,48) तक ही हैं। / The multiples less than (50) stop at (48).

Step 3

Exam Tip

धन प्राकृतिक गुणज में (0) शामिल नहीं किया जाता। / (0) is not included among positive natural multiples.

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Question 355/616 Hard Mathematics Sets Sets and their representations Class 11 Level 1

समुच्चय \(T={x:x\in Z,\ x^2\le 4}\) में कितने अवयव हैं?

How many elements are there in \(T={x:x\in Z,\ x^2\le 4}\)?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

\(x^2\le 4\) के पूर्णांक मान (-2,-1,0,1,2) हैं। / The integer values satisfying \(x^2\le 4\) are (-2,-1,0,1,2).

Step 2

Why this answer is correct

ये कुल (5) अवयव बनाते हैं। / These form (5) elements.

Step 3

Exam Tip

वर्ग वाली असमानता में शून्य और दोनों ओर के मान शामिल करें। / For square inequalities, include zero and values on both sides.

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Question 356/616 Hard Mathematics Sets Sets and their representations Class 11 Level 1

यदि \(U={x:x\in N,\ 2x+1<12}\), तो (U) कौन सा है?

If \(U={x:x\in N,\ 2x+1<12}\), which set is (U)?

Explanation opens after your attempt

Correct Answer

A. \(U=\{1,2,3,4,5\}\)

Step 1

Concept

(2x+1<12) से (2x<11), इसलिए \(x<\frac{11}{2}\)। / From (2x+1<12), we get (2x<11), so \(x<\frac{11}{2}\).

Step 2

Why this answer is correct

प्राकृतिक मान (1,2,3,4,5) होंगे। / The natural values are (1,2,3,4,5).

Step 3

Exam Tip

असमानता में भिन्न सीमा आने पर पूर्णांक मान अलग से चुनें। / When an inequality gives a fractional boundary, choose integer values carefully.

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Question 357/616 Hard Mathematics Sets Sets and their representations Class 11 Level 1

कौन सा विकल्प समुच्चय ({0,1,8,27,64}) को सही निर्माण रूप देता है?

Which option gives the correct set-builder form for ({0,1,8,27,64})?

Explanation opens after your attempt

Correct Answer

A. \({x:x=n^3,\ n\in W,\ 0\le n\le 4}\)

Step 1

Concept

(0,1,8,27,64) क्रमशः \(0^3,1^3,2^3,3^3,4^3\) हैं। / (0,1,8,27,64) are \(0^3,1^3,2^3,3^3,4^3\).

Step 2

Why this answer is correct

इसलिए \(x=n^3,\ n\in W,\ 0\le n\le 4\) सही है। / Thus \(x=n^3,\ n\in W,\ 0\le n\le 4\) is correct.

Step 3

Exam Tip

घन और वर्ग के पैटर्न को अलग-अलग पहचानें। / Distinguish cube patterns from square patterns.

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Question 358/616 Hard Mathematics Sets Sets and their representations Class 11 Level 1

यदि \(V={x:x\in N,\ x\) (9) और (12) का सामान्य गुणज है तथा \(x\le 100}\), तो (V) क्या है?

If \(V={x:x\in N,\ x\) is a common multiple of (9) and (12), and \(x\le 100}\), what is (V)?

Explanation opens after your attempt

Correct Answer

A. \(V=\{36,72\}\)

Step 1

Concept

(9) और (12) का लघुत्तम सामान्य गुणज (36) है। / The least common multiple of (9) and (12) is (36).

Step 2

Why this answer is correct

(100) तक (36) के धन गुणज (36,72) हैं। / The positive multiples of (36) up to (100) are (36,72).

Step 3

Exam Tip

सामान्य गुणज में पहले लघुत्तम सामान्य गुणज निकालना तेज तरीका है। / For common multiples, first find the least common multiple.

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Question 359/616 Hard Mathematics Sets Sets and their representations Class 11 Level 1

समुच्चय \(W={x:x\in Z,\ -4<x<4,\ x\) सम है(}) का रोस्टर रूप कौन सा है?

Which is the roster form of \(W={x:x\in Z,\ -4<x<4,\ x\) is even(})?

Explanation opens after your attempt

Correct Answer

B. \(W=\{-2,0,2\}\)

Step 1

Concept

(-4) और (4) के बीच पूर्णांक (-3,-2,-1,0,1,2,3) हैं। / The integers between (-4) and (4) are (-3,-2,-1,0,1,2,3).

Step 2

Why this answer is correct

इनमें सम पूर्णांक (-2,0,2) हैं। / The even integers among them are (-2,0,2).

Step 3

Exam Tip

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

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Question 360/616 Hard Mathematics Sets Sets and their representations Class 11 Level 1

यदि \(X={x:x\in N,\ x^2\) विषम है और (x<8}), तो (X) क्या है?

If \(X={x:x\in N,\ x^2\) is odd and (x<8}), what is (X)?

Explanation opens after your attempt

Correct Answer

A. \(X=\{1,3,5,7\}\)

Step 1

Concept

किसी प्राकृतिक संख्या का वर्ग विषम तभी होता है जब संख्या स्वयं विषम हो। / The square of a natural number is odd exactly when the number itself is odd.

Step 2

Why this answer is correct

(8) से छोटी विषम प्राकृतिक संख्याएँ (1,3,5,7) हैं। / The odd natural numbers less than (8) are (1,3,5,7).

Step 3

Exam Tip

वर्ग की सम-विषम प्रकृति मूल संख्या जैसी रहती है। / The parity of a square matches the parity of the original integer.

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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 \(Q={x:x\in N,\ x\) (20) से छोटा है और (x) न तो (2) से न (3) से विभाज्य है(}) कौन सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(R={x:x\in N,\ x+4=4}\), तो (R) क्या है?

Concept

Why this answer is correct

Exam Tip

कौन सा विकल्प \(\phi\) और \({\phi}\) के बारे में सही है?

Concept

Why this answer is correct

Exam Tip

यदि \(S={x:x\in N,\ x\) (8) का गुणज है और (x<50}), तो (S) का रोस्टर रूप क्या है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(T={x:x\in Z,\ x^2\le 4}\) में कितने अवयव हैं?

Concept

Why this answer is correct

Exam Tip

यदि \(U={x:x\in N,\ 2x+1<12}\), तो (U) कौन सा है?

Concept

Why this answer is correct

Exam Tip

कौन सा विकल्प समुच्चय ({0,1,8,27,64}) को सही निर्माण रूप देता है?

Concept

Why this answer is correct

Exam Tip

यदि \(V={x:x\in N,\ x\) (9) और (12) का सामान्य गुणज है तथा \(x\le 100}\), तो (V) क्या है?

Concept

Why this answer is correct

Exam Tip

समुच्चय \(W={x:x\in Z,\ -4<x<4,\ x\) सम है(}) का रोस्टर रूप कौन सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(X={x:x\in N,\ x^2\) विषम है और (x<8}), तो (X) क्या है?

Concept

Why this answer is correct

Exam Tip

Sets and their representations Learning Links

Sets Chapter

Easy Sets and their representations Test

Mathematics Subject

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