Ravi Kant Kumar

Make 1/3 Terminating Decimal MCQ Question The smallest rational number by which \( \frac{1}{3} \) should be multiplied so that its decimal expansion terminates after one place of decimal is: (a) \( \frac{1}{10} \) (b) \( \frac{3}{10} \) (c) 3 (d) 30 Solution We want: \[ \frac{1}{3} \times x = \text{terminating decimal with one decimal […]

Trailing Zeros in Product MCQ Question The number of consecutive zeroes in \(2^3 \times 3^4 \times 5^4 \times 7\) is: (a) 3 (b) 2 (c) 4 (d) 5 Solution Trailing zeros are formed by factors of \(10 = 2 \times 5\). Count the number of 2s and 5s: \[ 2^3 \Rightarrow 3 \text{ factors of

Irrational Number Between 2 and 2.5 MCQ Question An irrational number between \(2\) and \(2.5\) is: (a) \( \sqrt{11} \) (b) \( \sqrt{5} \) (c) \( \sqrt{22.5} \) (d) \( \sqrt{12.5} \) Solution Square the interval: \[ 2^2 = 4, \quad (2.5)^2 = 6.25 \] So we need a number whose square lies between 4

Sum of 0.23 Bar and 0.22 Bar Question The value of \(0.\overline{23} + 0.\overline{22}\) is: (a) 0.45 (b) 0.43 (c) 0.54 (d) 0.45 Solution Convert recurring decimals into fractions: \[ 0.\overline{23} = \frac{23}{99} \] \[ 0.\overline{22} = \frac{22}{99} \] Add them: \[ \frac{23}{99} + \frac{22}{99} = \frac{45}{99} \] Simplify: \[ \frac{45}{99} = \frac{5}{11} \] Convert

Convert 0.01 Bar into Fraction MCQ Question The number \(0.\overline{01}\) in the form \( \frac{p}{q} \), where \( q \neq 0 \), is: (a) \( \frac{1}{1000} \) (b) \( \frac{1}{100} \) (c) \( \frac{1}{1999} \) (d) \( \frac{1}{99} \) Solution Let \( x = 0.\overline{01} = 0.010101\ldots \) Multiply both sides by 100: \[ 100x

Convert 23.43 Bar into Fraction MCQ Question The number \(23.\overline{43}\) in the form \( \frac{p}{q} \), where \( q \neq 0 \), is: (a) \( \frac{2320}{99} \) (b) \( \frac{2343}{100} \) (c) \( \frac{2343}{999} \) (d) \( \frac{2320}{199} \) Solution Let \( x = 23.\overline{43} = 23.434343\ldots \) Multiply by 100: \[ 100x = 2343.4343\ldots

Convert 0.32 Bar into Fraction MCQ Question The number \(0.3\overline{2}\) in the form \( \frac{p}{q} \), where \( q \neq 0 \), is: (a) \( \frac{8}{25} \) (b) \( \frac{29}{90} \) (c) \( \frac{32}{99} \) (d) \( \frac{32}{199} \) Solution Let \( x = 0.3\overline{2} = 0.32222\ldots \) Multiply by 10: \[ 10x = 3.2222\ldots

Convert 0.3 Bar into Fraction MCQ Question The number \(0.\overline{3}\) in the form \( \frac{p}{q} \), where \( q \neq 0 \), is: (a) \( \frac{33}{100} \) (b) \( \frac{3}{10} \) (c) \( \frac{1}{3} \) (d) \( \frac{3}{100} \) Solution Let \( x = 0.\overline{3} \) \[ x = 0.3333\ldots \] Multiply both sides by

Convert 1.27 Bar into Fraction MCQ Question The number \(1.\overline{27}\) in the form \( \frac{p}{q} \), where \( q \neq 0 \), is: (a) \( \frac{14}{9} \) (b) \( \frac{14}{11} \) (c) \( \frac{14}{13} \) (d) \( \frac{14}{15} \) Solution Let \( x = 1.\overline{27} \) \[ x = 1.272727\ldots \] Multiply both sides by

Irrational Number from Decimal Expansion MCQ Question Which of the following is irrational? (a) 0.15 (b) 0.01516 (c) 0.1516 (d) 0.5015001500015.. Solution Option (a): 0.15 ✘ Rational Terminating decimal → rational number. Option (b): 0.01516 ✘ Rational Terminating decimal → rational number. Option (c): 0.1516 ✘ Rational Terminating decimal → rational number. Option (d): 0.5015001500015..