Concept-wise Practice

rational-root MCQ Questions for Class 10

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Practice Questions

6 questions tagged with rational-root.

Question 1/6 Hard Mathematics Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26

यदि \(\sqrt{m}\) परिमेय है और (m) धनात्मक पूर्णांक है, तो (m) के बारे में सही कथन क्या है?

If \(\sqrt{m}\) is rational and (m) is a positive integer, what is true about (m)?

Explanation opens after your attempt
Correct Answer

B. (m) पूर्ण वर्ग है(m) is a perfect square

Step 1

Concept

For a positive integer (m), \(\sqrt{m}\) is rational only when (m) is a perfect square. Identifying perfect squares is important in exams.

Step 2

Why this answer is correct

The correct answer is B. (m) पूर्ण वर्ग है / (m) is a perfect square. For a positive integer (m), \(\sqrt{m}\) is rational only when (m) is a perfect square. Identifying perfect squares is important in exams.

Step 3

Exam Tip

धनात्मक पूर्णांक (m) के लिए \(\sqrt{m}\) परिमेय तभी होगा जब (m) पूर्ण वर्ग हो। परीक्षा में पूर्ण वर्ग पहचानना जरूरी है।

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Question 2/6 Hard Mathematics Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि \(\sqrt{m}=a\) जहाँ (a) परिमेय है और (m) धनात्मक पूर्णांक है, तो (m) के लिए क्या आवश्यक है?

If \(\sqrt{m}=a\), where (a) is rational and (m) is a positive integer, what is necessary for (m)?

Explanation opens after your attempt
Correct Answer

A. (m) पूर्ण वर्ग होना चाहिए(m) must be a perfect square

Step 1

Concept

The square root of a positive integer is rational only when it is a perfect square. This is the key rule for roots.

Step 2

Why this answer is correct

The correct answer is A. (m) पूर्ण वर्ग होना चाहिए / (m) must be a perfect square. The square root of a positive integer is rational only when it is a perfect square. This is the key rule for roots.

Step 3

Exam Tip

धनात्मक पूर्णांक की वर्गमूल परिमेय तभी होती है जब वह पूर्ण वर्ग हो। यह जड़ों की प्रकृति का मुख्य नियम है।

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Question 3/6 Medium Mathematics Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27

यदि \(\sqrt{m}\) परिमेय है और (m) धनात्मक पूर्णांक है तो कौन सा (m) हो सकता है?

If \(\sqrt{m}\) is rational and (m) is a positive integer, which (m) can be correct?

Explanation opens after your attempt
Correct Answer

A. (m=400)

Step 1

Concept

\(400=20^2\) is a perfect square so \(\sqrt{400}\) is rational. The other options are not perfect squares.

Step 2

Why this answer is correct

The correct answer is A. (m=400). \(400=20^2\) is a perfect square so \(\sqrt{400}\) is rational. The other options are not perfect squares.

Step 3

Exam Tip

\(400=20^2\) पूर्ण वर्ग है इसलिए \(\sqrt{400}\) परिमेय है। बाकी विकल्प पूर्ण वर्ग नहीं हैं।

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Question 4/6 Medium Mathematics Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26

यदि (m) धनात्मक पूर्णांक है और \(\sqrt{m}\) परिमेय है तो (m) क्या होना चाहिए?

If (m) is a positive integer and \(\sqrt{m}\) is rational, what must (m) be?

Explanation opens after your attempt
Correct Answer

A. पूर्ण वर्गPerfect square

Step 1

Concept

The square root of a positive integer is rational only when it is a perfect square. Apply this rule directly.

Step 2

Why this answer is correct

The correct answer is A. पूर्ण वर्ग / Perfect square. The square root of a positive integer is rational only when it is a perfect square. Apply this rule directly.

Step 3

Exam Tip

धनात्मक पूर्णांक की वर्गमूल परिमेय तभी होती है जब वह पूर्ण वर्ग हो। इस नियम को सीधे लागू करें।

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Question 5/6 Medium Mathematics Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि \(\sqrt{n}\) परिमेय है और (n) धनात्मक पूर्णांक है तो (n) के बारे में सही कथन क्या है?

If \(\sqrt{n}\) is rational and (n) is a positive integer, what is correct about (n)?

Explanation opens after your attempt
Correct Answer

A. (n) पूर्ण वर्ग है(n) is a perfect square

Step 1

Concept

The square root of a positive integer is rational only when the number is a perfect square. This is a direct exam rule.

Step 2

Why this answer is correct

The correct answer is A. (n) पूर्ण वर्ग है / (n) is a perfect square. The square root of a positive integer is rational only when the number is a perfect square. This is a direct exam rule.

Step 3

Exam Tip

धनात्मक पूर्णांक की वर्गमूल परिमेय तभी होती है जब संख्या पूर्ण वर्ग हो। यह सीधा परीक्षा नियम है।

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Question 6/6 Easy Mathematics Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26

किसी धनात्मक पूर्णांक (n) के लिए यदि \(\sqrt{n}\) परिमेय है तो (n) के बारे में क्या कहा जा सकता है?

For a positive integer (n), if \(\sqrt{n}\) is rational then what can be said about (n)?

Explanation opens after your attempt
Correct Answer

A. (n) पूर्ण वर्ग है(n) is a perfect square

Step 1

Concept

The square root of a positive integer is rational only when the number is a perfect square. This is a direct MCQ rule.

Step 2

Why this answer is correct

The correct answer is A. (n) पूर्ण वर्ग है / (n) is a perfect square. The square root of a positive integer is rational only when the number is a perfect square. This is a direct MCQ rule.

Step 3

Exam Tip

धनात्मक पूर्णांक की वर्गमूल परिमेय तभी होती है जब संख्या पूर्ण वर्ग हो। यह MCQ में सीधा नियम है।

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