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common misconception MCQ Questions for Class 10

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3 questions tagged with common misconception.

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

कौन सा कथन \(\sqrt{2}\), \(\sqrt{3}\), और \(\sqrt{5}\) की सिद्धियों में सबसे बड़ा सामान्य भ्रम है?

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

Explanation opens after your attempt
Correct Answer

A. वर्गमूल को उसके अंदर की संख्या के बराबर मान लेनाTreating the square root as equal to the number inside it

Step 1

Concept

Writing \(\sqrt{2}=2\), \(\sqrt{3}=3\), or \(\sqrt{5}=5\) is wrong.

Step 2

Why this answer is correct

In the correct proof, rationality is assumed and fraction form is taken.

Step 3

Exam Tip

Do not treat the square root and the number inside as the same. चरण 1: \(\sqrt{2}=2\), \(\sqrt{3}=3\), या \(\sqrt{5}=5\) लिखना गलत है। चरण 2: सही प्रमाण में परिमेय मानकर भिन्न रूप लिया जाता है। चरण 3: वर्गमूल और उसके अंदर की संख्या को एक जैसा न मानें।

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Question 2/3 Hard Mathematics Real Numbers Proof of irrationality of √2, √3, √5 Class 10 Level 16

कौन सा विकल्प \(\sqrt{2}\), \(\sqrt{3}\), और \(\sqrt{5}\) के प्रमाणों में सबसे बड़ा सामान्य भ्रम है?

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

Explanation opens after your attempt
Correct Answer

A. वर्गमूल को उसके अंदर की संख्या के बराबर मान लेनाTreating the square root as equal to the number inside it

Step 1

Concept

Writing \(\sqrt{2}=2\), \(\sqrt{3}=3\), or \(\sqrt{5}=5\) is wrong.

Step 2

Why this answer is correct

In the correct proof, the square root is assumed as a fraction and then squared.

Step 3

Exam Tip

Do not confuse the square root with the number inside it. चरण 1: \(\sqrt{2}=2\), \(\sqrt{3}=3\), या \(\sqrt{5}=5\) लिखना गलत है। चरण 2: सही प्रमाण में वर्गमूल को भिन्न के रूप में मानकर वर्ग किया जाता है। चरण 3: वर्गमूल और अंदर की संख्या को समान न समझें।

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

कौन सा विकल्प तीनों प्रमाणों में गलत सोच को दिखाता है?

Which option shows a wrong idea in all three proofs?

Explanation opens after your attempt
Correct Answer

A. वर्गमूल को उसके अंदर की संख्या के बराबर मान लेनाTreating the square root as equal to the number inside it

Step 1

Concept

Writing \(\sqrt{2}=2\), \(\sqrt{3}=3\), or \(\sqrt{5}=5\) is wrong.

Step 2

Why this answer is correct

The correct method assumes rationality, writes a fraction, and squares.

Step 3

Exam Tip

Do not treat a square root as equal to the number inside. चरण 1: \(\sqrt{2}=2\), \(\sqrt{3}=3\), या \(\sqrt{5}=5\) लिखना गलत है। चरण 2: सही विधि में परिमेय मानकर भिन्न रूप लिया जाता है और वर्ग किया जाता है। चरण 3: वर्गमूल को अंदर की संख्या के बराबर न मानें।

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