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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।

MathematicsWhat is the decimal expansion of the simplified fraction \(\frac{35}{154}\)?Class 9Number SystemsDecimal representationMedium MathematicsIf \(p/q\) is a rational number, where \(p\) and \(q\) are coprime integers and \(q>0\), which statement about its decimal expansion is correct?Class 9Number SystemsReal NumbersHard MathematicsWhich of the following numbers has a non-terminating, non-recurring decimal expansion?Class 9Number SystemsReal NumbersHard MathematicsA student claims that the sum of any two irrational numbers is always irrational. Which of the following pairs is a counterexample to this claim?Class 9Number SystemsReal NumbersHard MathematicsWhat is the value of \(\left(\sqrt{7}+\sqrt{2}\right)^2-\left(\sqrt{7}-\sqrt{2}\right)^2\)?Class 9Number SystemsReal NumbersHard MathematicsWhat is the value of ((4+√7)/(4−√7)+(4−√7)/(4+√7))?Class 9Number SystemsReal NumbersHard MathematicsA student says that the number \(0.101001000100001\ldots\) is rational because the digit 1 occurs repeatedly. The number of zeros before each successive 1 keeps increasing. Which is the correct evaluation of the student's statement?Class 9Number SystemsReal NumbersHard MathematicsA student says that \(0.101001000100001\ldots\) is a rational number because it contains only the digits 0 and 1. Which is the correct evaluation of the student's statement?Class 9Number SystemsReal NumbersHard MathematicsWhat is the value of 1/(2 + √3) + 1/(2 − √3)?Class 9Number SystemsReal NumbersHard MathematicsA student claims that the sum of two irrational numbers is always irrational. Which of the following examples disproves the claim?Class 9Number SystemsReal NumbersHard MathematicsWhich of the following conditions about the decimal expansion of a real number definitely identifies it as irrational?Class 9Number SystemsReal NumbersHard MathematicsWhat is the value of 1/(√3 − √2) − 1/(√3 + √2)?Class 9Number SystemsReal NumbersHard MathematicsA student says that \(0.1010010001\ldots\) is a rational number because it contains only the digits 0 and 1. Why is the student's statement incorrect?Class 9Number SystemsReal NumbersHard MathematicsIf \(x=-7\), what is the value of \(\sqrt{x^2}-2x\)?Class 9Number SystemsReal NumbersHard MathematicsIf \(x=\sqrt5+2\), what is the value of \(x+\frac1x\)?Class 9Number SystemsReal NumbersMedium MathematicsIf \(x=3-\sqrt5\), what is \(\frac1x\)?Class 9Number SystemsProof of irrationality of square root 2 and square root 3Medium MathematicsWhat is the value of √12 + √75 − √48 − √27?Class 9Number SystemsReal NumbersMedium MathematicsReema claims that the decimal expansion of \(\frac{13}{120}\) will terminate because 120 has both 2 and 5 as factors. Which option correctly identifies the error in Reema’s statement?Class 9Number SystemsReal NumbersHard MathematicsWhat is the value of \(\frac{1}{3-\sqrt7}+\frac{1}{3+\sqrt7}\)?Class 9Number SystemsReal NumbersMedium MathematicsWhat is the simplest form of \(\sqrt{3}+\sqrt{12}+\sqrt{27}+\sqrt{48}\)?Class 9Number SystemsReal NumbersHard