Ravi Kant Kumar

Decimal Expansion of Rational and Irrational Numbers MCQ Question Which one of the following is a correct statement? (a) Decimal expansion of a rational number is terminating (b) Decimal expansion of a rational number is non-terminating (c) Decimal expansion of an irrational number is terminating (d) Decimal expansion of an irrational number is non-terminating and […]

x² Irrational but x⁴ Rational MCQ Question There is a number \( x \) such that \( x^2 \) is irrational but \( x^4 \) is rational. Then \( x \) can be: (a) \( \sqrt{5} \) (b) \( \sqrt{2} \) (c) \( 3\sqrt{2} \) (d) \( 4\sqrt{5} \) Solution We need a number \(

Product of 0.2 Bar and 0.5 Bar Question The value of \(0.\overline{2} \times 0.\overline{5}\) is: (a) 1 (b) \( \frac{10}{9} \) (c) \( \frac{10}{81} \) (d) \( \frac{10}{99} \) Solution Convert recurring decimals into fractions: \[ 0.\overline{2} = \frac{2}{9} \] \[ 0.\overline{5} = \frac{5}{9} \] Multiply them: \[ \frac{2}{9} \times \frac{5}{9} = \frac{10}{81} \] Final

Sum of 0.2 Bar and 0.5 Bar Question The sum of \(0.\overline{2}\) and \(0.\overline{5}\) is: (a) \( \frac{7}{10} \) (b) \( \frac{7}{9} \) (c) \( \frac{7}{99} \) (d) \( \frac{3}{10} \) Solution Convert recurring decimals into fractions: \[ 0.\overline{2} = \frac{2}{9} \] \[ 0.\overline{5} = \frac{5}{9} \] Add them: \[ \frac{2}{9} + \frac{5}{9} = \frac{7}{9}

Sum of 0.2 Bar and 0.5 Bar Question The sum of \(0.\overline{2}\) and \(0.\overline{5}\) is: (a) \( \frac{7}{10} \) (b) \( \frac{7}{9} \) (c) \( \frac{7}{99} \) (d) \( \frac{3}{10} \) Solution Convert recurring decimals into fractions: \[ 0.\overline{2} = \frac{2}{9} \] \[ 0.\overline{5} = \frac{5}{9} \] Add them: \[ \frac{2}{9} + \frac{5}{9} = \frac{7}{9}

Product of Rational and Irrational Number MCQ Question The product of a non-zero rational number with an irrational number is: (a) irrational number (b) rational number (c) whole number (d) natural number Solution Let a non-zero rational number be \( r \) and an irrational number be \( x \). If their product \( r

Irrational Number from Decimal Expansion MCQ Question Which of the following is an irrational number? (a) 3.14 (b) 3.141414 … (c) 3.1444444… (d) 3.14114111411114 … Solution Option (a): 3.14 ✘ Rational Terminating decimal → rational number. Option (b): 3.141414 … ✘ Rational Repeating decimal → rational number. Option (c): 3.1444444… ✘ Rational Non-terminating but repeating

Rational Number Between -3 and 3 MCQ Question A rational number between \( -3 \) and \( 3 \) is: (a) \( 0 \) (b) \( -4.3 \) (c) \( -3.4 \) (d) 1.101100110001 … Solution Option (a): \( 0 \) ✔ Rational and lies between -3 and 3 \( 0 \) is a rational

Rational Number Identification MCQ Question Which of the following is a rational number? (a) \( \sqrt{3} + 1 \) (b) \( \pi \) (c) \( 2\sqrt{3} \) (d) \( 0 \) Solution Option (a): \( \sqrt{3} + 1 \) ✘ Irrational \( \sqrt{3} \) is irrational, so adding 1 keeps it irrational. Option (b): \(

Irrational Numbers with Surds MCQ Question Which of the following numbers is irrational? (a) \( \sqrt{\frac{4}{9}} \) (b) \( \frac{\sqrt{1250}}{\sqrt{8}} \) (c) \( \sqrt{8} \) (d) \( \frac{\sqrt{24}}{\sqrt{6}} \) Solution Option (a): \( \sqrt{\frac{4}{9}} \) \[ \sqrt{\frac{4}{9}} = \frac{2}{3} \] ✔ Rational Option (b): \( \frac{\sqrt{1250}}{\sqrt{8}} \) \[ = \sqrt{\frac{1250}{8}} = \sqrt{156.25} = 12.5 \]