May 2026

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): \( \frac{\sqrt{1250}}{\sqrt{8}} \) \[ = \sqrt{\frac{1250}{8}} = \sqrt{156.25} = 12.5 \]

π vs 22/7 Rational or Irrational MCQ Question Which of the following statements is true? (a) \( \pi \) and \( \frac{22}{7} \) are both rationals (b) \( \pi \) and \( \frac{22}{7} \) are both irrationals (c) \( \pi \) is rational and \( \frac{22}{7} \) is irrational (d) \( \pi \) is irrational

Decimal Expansion Not Possible for Rational Number Question The decimal expansion that a rational number cannot have is: (a) 0.25 (b) \(0.25\overline{28}\) (c) \(0.\overline{2528}\) (d) 0.5030030003… Solution A rational number has decimal expansion that is either: Terminating Non-terminating but repeating Option (a): 0.25 ✔ Possible Terminating decimal → Rational Option (b): \(0.25\overline{28}\) ✔ Possible Repeating

Repeating Block Length of 17/7 Question How many digits are there in the repeating block of digits in the decimal expansion of \( \frac{17}{7} \)? (a) 16 (b) 6 (c) 26 (d) 7 Solution First, convert \( \frac{17}{7} \) into decimal form: \[ \frac{17}{7} = 2.428571428571\ldots \] The repeating block is: \[ 428571 \] This

Rational Number Identification MCQ Question Which of the following is a rational number? (a) \( \pi \) (b) \( \sqrt{5} \) (c) 0.101001000100001 … (d) 0.835835835 … Solution Option (a): \( \pi \) ✘ Irrational \( \pi \) is non-terminating and non-repeating. Option (b): \( \sqrt{5} \) ✘ Irrational \( \sqrt{5} \) cannot be expressed

Convert 1.6 Bar into Fraction MCQ Question The simplest form of \(1.\overline{6}\) is: (a) \( \frac{8}{5} \) (b) \( \frac{5}{3} \) (c) \( \frac{833}{500} \) (d) \( \frac{7}{6} \) Solution Let \( x = 1.\overline{6} \) \[ x = 1.6666\ldots \] Multiply both sides by 10: \[ 10x = 16.6666\ldots \] Subtract the first equation