Ravi Kant Kumar

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

Convert 0.4 Bar into Fraction MCQ Question The value of \(0.\overline{4}\) in the form \( \frac{p}{q} \), where \(q \neq 0\), is: (a) \( \frac{4}{9} \) (b) \( \frac{2}{5} \) (c) \( \frac{1}{5} \) (d) \( \frac{4}{5} \) Solution Let \( x = 0.\overline{4} \) Then, \[ x = 0.4444\ldots \] Multiply both sides by

Irrational Number from Decimal Expansion MCQ Question Which of the following is an irrational number? (a) 0.13 (b) 0.1315 (c) 0.1315 (d) 0.301323100523 … Solution Option (a): 0.13 ✘ Rational This is a terminating decimal, so it is rational. Option (b): 0.1315 ✘ Rational This is also a terminating decimal, hence rational. Option (c): 0.1315

Decimal Representation of Irrational Numbers MCQ Question A number is irrational if and only if its decimal representation is: (a) non-terminating (b) non-terminating and repeating (c) non-terminating and non-repeating (d) terminating Solution An irrational number cannot be expressed in the form \( \frac{p}{q} \). Its decimal expansion has two important properties: It is non-terminating (never

Decimal Expansion of Rational Numbers MCQ Question The decimal expansion of a rational number is: (a) terminating or non-terminating non-repeating (b) terminating or non-terminating repeating (c) terminating and repeating (d) none of these Solution A rational number can be written in the form \( \frac{p}{q} \), where \( q \neq 0 \). Its decimal expansion

Which Statements are Correct in Number System? Question Which of the following statements is/are correct? (i) Every integer is a rational number (ii) Every rational number is an integer (iii) A real number is either rational or irrational number (iv) Every whole number is a natural number Options: (a) (ii) (b) (iii) (c) (i) and