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DSSSB TGT — free MCQ practice

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Worked practice questions

Which of the following fractions will have a non-terminating recurring decimal expansion?

  1. $\frac{3}{40}$
  2. $\frac{7}{125}$
  3. $\frac{11}{24}$
  4. $\frac{9}{20}$
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Correct answer: C. $\frac{11}{24}$

A rational number has a recurring decimal if, in lowest terms, the denominator contains a prime factor other than 2 or 5. Since $24=2^3\times 3$ contains 3, $\frac{11}{24}$ is non-terminating recurring. The others have denominators made only of 2s and 5s.

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Which of the following rational numbers has a terminating decimal expansion?

  1. $\frac{7}{12}$
  2. $\frac{13}{25}$
  3. $\frac{11}{18}$
  4. $\frac{5}{21}$
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Correct answer: B. $\frac{13}{25}$

A rational number terminates when, in lowest terms, its denominator has only 2s and/or 5s as prime factors. Here $25=5^2$, so $\frac{13}{25}$ terminates. The other denominators contain 3 or 7, so they are recurring decimals.

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Let $r$ be a non-zero rational number and $x$ be an irrational number. Which of the following must be irrational?

  1. Only $r+x$
  2. Only $rx$
  3. Both $r+x$ and $\frac{x}{r}$
  4. Neither $r+x$ nor $rx$
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Correct answer: C. Both $r+x$ and $\frac{x}{r}$

The notes state that the sum of a rational and an irrational number is irrational. They also state that the product and quotient of a non-zero rational number and an irrational number are irrational. **Hence both $r+x$ and $x/r$ are irrational.**

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