Concept-wise Practice

proof completion MCQ Questions for Class 10

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

Practice Questions

2 questions tagged with proof completion.

कौन सा विकल्प \(\sqrt{3}\) के प्रमाण को पूरा करने वाला सही अंतिम वाक्य है?

Which option is the correct final sentence to complete the proof of \(\sqrt{3}\)?

Explanation opens after your attempt
Correct Answer

A. अतः \(\sqrt{3}\) अपरिमेय हैTherefore \(\sqrt{3}\) is irrational

Step 1

Concept

The rational assumption makes both (p) and (q) divisible by (3).

Step 2

Why this answer is correct

This contradicts the coprime condition.

Step 3

Exam Tip

Therefore the final conclusion is that \(\sqrt{3}\) is irrational. चरण 1: परिमेय मान्यता से (p) और (q) दोनों (3) से विभाज्य मिलते हैं। चरण 2: यह सहअभाज्य होने की शर्त से विरोधाभास है। चरण 3: इसलिए अंतिम निष्कर्ष \(\sqrt{3}\) अपरिमेय है।

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कौन सा कथन \(\sqrt{5}\) की अपरिमेयता के प्रमाण को पूरा करता है?

Which statement completes the proof of irrationality of \(\sqrt{5}\)?

Explanation opens after your attempt
Correct Answer

A. अतः \(\sqrt{5}\) अपरिमेय हैTherefore \(\sqrt{5}\) is irrational

Step 1

Concept

The rational assumption makes both (a) and (b) divisible by (5).

Step 2

Why this answer is correct

This contradicts the coprime condition.

Step 3

Exam Tip

Therefore the conclusion is that \(\sqrt{5}\) is irrational. चरण 1: परिमेय मान्यता से (a) और (b) दोनों (5) से विभाज्य मिलते हैं। चरण 2: यह सहअभाज्य होने की शर्त से टकराता है। चरण 3: इसलिए निष्कर्ष है कि \(\sqrt{5}\) अपरिमेय है।

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