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common proof idea MCQ Questions for Class 10

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Practice Questions

2 questions tagged with common proof idea.

Question 1/2 Medium Mathematics Chapter 1: Real Numbers 6: Proof of irrationality of √2, √3, √5 Class 10 Level 18

कौन सा कथन \(\sqrt{2}\), \(\sqrt{3}\), और \(\sqrt{5}\) के प्रमाणों में समान अंतिम विचार है?

Which statement is the common final idea in the proofs of \(\sqrt{2}\), \(\sqrt{3}\), and \(\sqrt{5}\)?

Explanation opens after your attempt
Correct Answer

A. सरलतम भिन्न के अंश और हर में साझा गुणनखंड मिलनाFinding a common factor in numerator and denominator of a lowest-form fraction

Step 1

Concept

In all three, the number is assumed rational and written as a lowest-form fraction.

Step 2

Why this answer is correct

At the end, a common factor is found in numerator and denominator.

Step 3

Exam Tip

This contradicts lowest form. चरण 1: तीनों में संख्या को परिमेय मानकर सरलतम भिन्न लिखते हैं। चरण 2: अंत में अंश और हर में साझा गुणनखंड मिलता है। चरण 3: यही सरलतम रूप से विरोधाभास बनाता है।

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Question 2/2 Medium Mathematics Chapter 1: Real Numbers 6: Proof of irrationality of √2, √3, √5 Class 10 Level 16

कौन सा विकल्प \(\sqrt{2}\), \(\sqrt{3}\), \(\sqrt{5}\) की सिद्धि में सामान्य अंतिम विचार है?

Which option is the common final idea in the proofs of \(\sqrt{2}\), \(\sqrt{3}\), and \(\sqrt{5}\)?

Explanation opens after your attempt
Correct Answer

A. सरलतम भिन्न के अंश और हर में साझा गुणनखंड मिलनाFinding a common factor in numerator and denominator of a lowest-form fraction

Step 1

Concept

In all three, the number is assumed rational and written in lowest form.

Step 2

Why this answer is correct

At the end, numerator and denominator share (2), (3), or (5).

Step 3

Exam Tip

This is the common contradiction. चरण 1: तीनों में संख्या को परिमेय मानकर सरलतम भिन्न लिखते हैं। चरण 2: अंत में अंश और हर में (2), (3), या (5) साझा गुणनखंड मिलता है। चरण 3: यही सामान्य विरोधाभास है।

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