Concept-wise Practice

cube numbers MCQ Questions for Class 11

cube numbers se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

Practice Questions

3 questions tagged with cube numbers.

\(समुच्चय (A={x\in \mathbb{N}:x\) is a perfect cube less than 30}) क्या है?

\(What is (A={x\in \mathbb{N}:x\) is a perfect cube less than 30})?

Explanation opens after your attempt
Correct Answer

A. ({1,8,27})

Step 1

Concept

The natural cubes are \(1^3=1\), \(2^3=8\), and \(3^3=27\).

Step 2

Why this answer is correct

\(4^3=64\), which is greater than (30).

Step 3

Exam Tip

Stop the list when the next term crosses the bound. चरण 1: प्राकृतिक घन \(1^3=1\), \(2^3=8\), \(3^3=27\) हैं। चरण 2: \(4^3=64\), जो (30) से बड़ा है। चरण 3: सीमा से बाहर का अगला पद देखकर सूची रोकें।

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कौन सा समुच्चय ({1,8,27}) के बराबर है?

Which set is equal to ({1,8,27})?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

Cubes of (n=1,2,3) are (1,8,27).

Step 2

Why this answer is correct

The first option gives exactly those three elements.

Step 3

Exam Tip

In power-based questions, substitute values and form the list. चरण 1: (n=1,2,3) के घन (1,8,27) होते हैं। चरण 2: पहला विकल्प वही तीन तत्व देता है। चरण 3: घात वाले प्रश्नों में मान रखकर सूची बनाएं।

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किस विकल्प में \(D=\{1,8,27,64\}\) का सही समुच्चय-निर्माण रूप है?

Which option gives the correct set-builder form of \(D=\{1,8,27,64\}\)?

Explanation opens after your attempt
Correct Answer

A. \(D={n^3:n\in \mathbb{N},1\le n\le 4}\)

Step 1

Concept

(1,8,27,64) are \(1^3,2^3,3^3,4^3\).

Step 2

Why this answer is correct

So the form is \(n^3\), where (n) is a natural number and \(1\le n\le 4\).

Step 3

Exam Tip

It is important to distinguish square and cube patterns. चरण 1: (1,8,27,64) क्रमशः \(1^3,2^3,3^3,4^3\) हैं। चरण 2: इसलिए रूप \(n^3\) होगा जहां (n) प्राकृतिक संख्या है और \(1\le n\le 4\)। चरण 3: वर्ग और घन के पैटर्न को अलग-अलग पहचानना जरूरी है।

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