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Number Systems

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

MathematicsIf a number is even then what type will its square be?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsWhy are a and b assumed to be coprime in √3 = a/b?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 MathematicsWhat kind of beginning is used in the proofs of both √2 and √3?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 MathematicsFrom (b^2=3k^2), what conclusion follows about (b)?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 MathematicsRima says that \(\sqrt{2}\) is rational because its decimal form begins with 1.414.... What is the correct error in her reasoning?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsIf (a^2) is divisible by (3), what is the correct conclusion about (a)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsFrom (a^2=3b^2), which conclusion is obtained about (a^2)?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 MathematicsWhich method is used in the proof of the irrationality of √2?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsWhat is the final contradiction in the proof that √2 is irrational?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsFrom (q^2=2r^2) what conclusion follows about (q)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsIf (p=2r) and (p^2=2q^2), which conclusion follows next?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsA student sees \(\sqrt{3}\) displayed as 1.732 on a calculator and claims that \(\sqrt{3}\) is rational because the decimal ends. Which statement correctly identifies the error?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsIf (p^2) is even then what is the correct conclusion about (p)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsFrom (p^2=2q^2) what conclusion is obtained about (p^2)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy MathematicsWhich of the following numbers is irrational and can be proved irrational using a contradiction based on divisibility by 3?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Level 19Easy