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coprime condition MCQ Questions for Class 10

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2 questions tagged with coprime condition.

Question 1/2 Hard Mathematics Real Numbers Proof of irrationality of √2, √3, √5 Class 10 Level 17

\(\sqrt{5}\) की सिद्धि में (p=5k) और (q=5r) मिलने पर कौन सी आरंभिक शर्त टूटती है?

In the proof of \(\sqrt{5}\), if (p=5k) and (q=5r) are obtained, which initial condition breaks?

Explanation opens after your attempt
Correct Answer

A. (p) और (q) सहअभाज्य हैं(p) and (q) are coprime

Step 1

Concept

(p=5k) and (q=5r) show factor (5) in both (p) and (q).

Step 2

Why this answer is correct

So they cannot be coprime.

Step 3

Exam Tip

This breaks the initial lowest-form condition. चरण 1: (p=5k) और (q=5r) से (p) और (q) दोनों में (5) गुणनखंड है। चरण 2: इसलिए वे सहअभाज्य नहीं हो सकते। चरण 3: यह आरंभिक सरलतम रूप की शर्त को तोड़ता है।

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Question 2/2 Easy Mathematics Real Numbers Proof of irrationality of √2, √3, √5 Class 10 Level 18

कौन सा विकल्प \(\sqrt{2}\) के प्रमाण में सहअभाज्य शर्त टूटने को सही दिखाता है?

Which option correctly shows the breaking of the coprime condition in the proof of \(\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

A. (p=2m) और (q=2n) मिलनाGetting (p=2m) and (q=2n)

Step 1

Concept

(p=2m) and (q=2n) mean both are divisible by (2).

Step 2

Why this answer is correct

Then (2) becomes their common factor.

Step 3

Exam Tip

A lowest-form fraction should not have such a common factor. चरण 1: (p=2m) और (q=2n) का अर्थ है कि दोनों (2) से विभाज्य हैं। चरण 2: तब (2) उनका साझा गुणनखंड बन जाता है। चरण 3: सरलतम भिन्न में ऐसा साझा गुणनखंड नहीं होना चाहिए।

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