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sqrt2 conclusion MCQ Questions for Class 10

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3 questions tagged with sqrt2 conclusion.

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

यदि \(\sqrt{2}\) परिमेय मानकर विरोधाभास प्राप्त हुआ, तो सही निष्कर्ष क्या होगा?

If assuming \(\sqrt{2}\) rational gives a contradiction, what is the correct conclusion?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{2}\) अपरिमेय है\(\sqrt{2}\) is irrational

Step 1

Concept

In contradiction method, the opposite assumption is taken.

Step 2

Why this answer is correct

If the rational assumption is proved impossible, it is false.

Step 3

Exam Tip

Hence \(\sqrt{2}\) is irrational. चरण 1: विरोधाभास विधि में उलटी मान्यता ली जाती है। चरण 2: यदि परिमेय मान्यता असंभव सिद्ध हो जाए, तो वह गलत है। चरण 3: अतः \(\sqrt{2}\) अपरिमेय है।

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

\(\sqrt{2}\) को परिमेय मानने पर \(\sqrt{2}=\frac{p}{q}\) लिखा। यदि अंत में (p) और (q) दोनों सम हैं, तो सही निष्कर्ष कौन सा है?

After assuming \(\sqrt{2}\) rational, \(\sqrt{2}=\frac{p}{q}\) is written. If finally both (p) and (q) are even, what is the correct conclusion?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{2}\) अपरिमेय है\(\sqrt{2}\) is irrational

Step 1

Concept

(p) and (q) were assumed coprime at the start.

Step 2

Why this answer is correct

Both even shows common factor (2).

Step 3

Exam Tip

This is a contradiction, so \(\sqrt{2}\) is irrational. चरण 1: (p) और (q) को शुरू में सहअभाज्य माना गया था। चरण 2: दोनों सम होना साझा गुणनखंड (2) दिखाता है। चरण 3: यह विरोधाभास है, इसलिए \(\sqrt{2}\) अपरिमेय है।

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

\(\sqrt{2}\) के प्रमाण में अंत में कौन सी बात सिद्ध होती है?

What is proved at the end in the proof of \(\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{2}\) अपरिमेय है\(\sqrt{2}\) is irrational

Step 1

Concept

Assuming rationality makes both (p) and (q) even.

Step 2

Why this answer is correct

This contradicts their being coprime.

Step 3

Exam Tip

Therefore the initial assumption is false and \(\sqrt{2}\) is irrational. चरण 1: परिमेय मानने से (p) और (q) दोनों सम मिलते हैं। चरण 2: यह उनके सहअभाज्य होने के विरुद्ध है। चरण 3: इसलिए आरंभिक मान्यता गलत और \(\sqrt{2}\) अपरिमेय है।

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