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Proof By Contradiction

Class 9 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsIf \(\sqrt{3}=\frac{p}{q}\) is assumed, where \(p\) and \(q\) are coprime, which conclusion produces the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student assumes dfrac{p}{q} is in lowest terms and obtains p^2=3q^2 , where p and q are coprime. Which conclusion proves a contradiction in this assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsWhich statement correctly describes the method used to prove that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsIf \(\sqrt{3}=\frac{m}{n}\) is assumed, where \(m\) and \(n\) are coprime integers, which conclusion produces the contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsIn the proof that \(\sqrt{3}\) is irrational, if \(p^2\) is divisible by 3, which conclusion about \(p\) is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 20Easy MathematicsA student says that if \(\sqrt{3}=\frac{p}{q}\), where \(p\) and \(q\) are coprime integers, then when \(p\) is divisible by 3, \(q\) will also be divisible by 3. What conclusion does this statement lead to?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsA student assumes that ",Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsSuppose a is an integer and 3 divides \(a^2\). Which of the following conclusions is valid in the proof that \(\sqrt{3}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsRima claims that \(2+\sqrt{3}\) is a rational number. Which is the most appropriate argument to prove her claim wrong?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsA student assumes that \(\sqrt{3}\) can be written as \(\frac{a}{b}\) in lowest terms. During the proof, it is found that 3 divides both \(a\) and \(b\). Which conclusion about the student’s assumption is correct?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsA calculator displays \(\sqrt{3}\) as 1.732. Mohan concludes that \(\sqrt{3}\) is rational. What is Mohan’s error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsRiya says that \(\sqrt{2}\) is irrational because its decimal expansion never terminates. What is the flaw in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsA student says that \(5+\sqrt{3}\) may be a rational number. Which argument correctly identifies the error in this statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsA student says, “If \(\sqrt{3}\) is irrational, then \(5\sqrt{3}\) is also irrational.” Which argument correctly proves the statement?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsWhich number-theoretic fact is used decisively while proving the irrationality of \(\sqrt{3}\) by contradiction?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsAmit claims that \(4\sqrt{3}\) is a rational number. Which argument correctly shows the error in his claim?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsSuppose \(\sqrt{2}=\frac{m}{n}\), where \(m\) and \(n\) are integers. Which condition on \(m\) and \(n\) is necessary at the start of a proof by contradiction that \(\sqrt{2}\) is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsIf (a=3k) and (a^2=3b^2), what conclusion follows next?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsIn the proof by contradiction that \(\sqrt{2}\) is irrational, if \(\sqrt{2}=\frac{p}{q}\) is assumed where \(p,q\) are coprime, which conclusion creates a contradiction with the initial assumption?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsWhile proving the irrationality of \(\sqrt{3}\) by contradiction, which property is used to conclude \(3\mid p\) from \(3\mid p^2\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy