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If r is a non-zero irrational number and q is a non-zero rational number, which of the following statements is always true?यदि r एक गैर-शून्य अपरिमेय संख्या और q एक गैर-शून्य परिमेय संख्या है, तो निम्नलिखित में से कौन-सा कथन सदैव सत्य है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(qr\) is irrational.\(qr\) अपरिमेय होता है।
Option C is correct. If \(qr\) were rational, then since \(q\ne0\), \(r=\frac{qr}{q}\) would also be rational, a contradiction. Exam tip: test “always” claims using examples such as \(\sqrt2\) and \(-\sqrt2\).विकल्प C सही है। यदि \(qr\) परिमेय होता, तो \(q\ne0\) के कारण \(r=\frac{qr}{q}\) भी परिमेय होता, जो विरोधाभास है। परीक्षा में ‘सदैव’ वाले दावों को \(\sqrt2\) और \(-\sqrt2\) जैसे उदाहरणों से जाँचें।
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