May 2026

Repeating Decimal Rational Number MCQ Question The number \(0.318564318564318564\ldots\) is: (a) a natural number (b) an integer (c) a rational number (d) an irrational number Solution The decimal \(0.318564318564318564\ldots\) has a repeating block: \[ 318564 \] Since the decimal expansion is non-terminating but repeating, it represents a rational number. Also, it is not a natural […]

Rational Number Identification MCQ Question Which of the following is rational? (a) \( \sqrt{3} \) (b) \( \pi \) (c) \( \frac{4}{0} \) (d) \( \frac{0}{4} \) Solution Option (a): \( \sqrt{3} \) ✘ Irrational Square root of a non-perfect square is irrational. Option (b): \( \pi \) ✘ Irrational \( \pi \) is non-terminating

Irrational Number from Decimal Expansion MCQ Question Which of the following is irrational? (a) 0.14 (b) 0.1416 (c) 0.1416 (d) 0.1014001400014.. Solution Option (a): 0.14 ✘ Rational Terminating decimal → rational number. Option (b): 0.1416 ✘ Rational Terminating decimal → rational number. Option (c): 0.1416 ✘ Rational Same as above → rational number. Option (d):

Irrational Number Identification MCQ Question Which of the following is irrational? (a) \( \sqrt{\frac{4}{9}} \) (b) \( \frac{4}{5} \) (c) \( \sqrt{7} \) (d) \( \sqrt{81} \) Solution Option (a): \( \sqrt{\frac{4}{9}} \) \[ \sqrt{\frac{4}{9}} = \frac{2}{3} \] ✔ Rational Option (b): \( \frac{4}{5} \) ✔ Rational It is already in fraction form. Option (c):

Rational and Irrational Number Properties MCQ Question Which of the following statements is true? (a) Product of two irrational numbers is always irrational (b) Product of a non-zero rational and an irrational number is always irrational (c) Sum of two irrational numbers can never be irrational (d) Sum of an integer and a rational number

Rational and Irrational Numbers Properties MCQ Question Which of the following is a correct statement? (a) Sum of two irrational numbers is always irrational (b) Sum of a rational and irrational number is always an irrational number (c) Square of an irrational number is always a rational number (d) Sum of two rational numbers can

Sum of Two Irrational Numbers MCQ Question Which one of the following statements is true? (a) The sum of two irrational numbers is always an irrational number (b) The sum of two irrational numbers is always a rational number (c) The sum of two irrational numbers may be a rational number or an irrational number

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