SSC CGL level Question Set 70, Fractions and Surds 6

70th SSC CGL level Question Set, 6th on topic fractions and surds

ssc-cgl-question-set-70-fractions-surds

This is the 70th question set of 10 practice problem exercise for SSC CGL exam and 6th on topic fractions and surds. Students must complete this question set prescribed time first and then only refer to the solution set for extracting maximum benefits from this resource. The link of the solution set along with answers is given at the end.

You may also refer to the related tutorials, question and solution sets listed at the end.

70th question set - 10 problems for SSC CGL exam: 6th on topic Fractions and surds - time 15 mins

Problem 1.

The product of two fractions is $\displaystyle\frac{14}{15}$ and their quotient is $\displaystyle\frac{35}{24}$. The larger of the two fractions is,

  1. $\displaystyle\frac{7}{4}$
  2. $\displaystyle\frac{7}{6}$
  3. $\displaystyle\frac{7}{3}$
  4. $\displaystyle\frac{4}{5}$

Problem 2.

$\displaystyle\frac{4}{5}$, $\displaystyle\frac{7}{8}$, $\displaystyle\frac{6}{7}$, $\displaystyle\frac{5}{6}$ in ascending order is,

  1. $\displaystyle\frac{4}{5}$, $\displaystyle\frac{7}{8}$, $\displaystyle\frac{6}{7}$, $\displaystyle\frac{5}{6}$
  2. $\displaystyle\frac{7}{8}$, $\displaystyle\frac{6}{7}$, $\displaystyle\frac{5}{6}$, $\displaystyle\frac{4}{5}$
  3. $\displaystyle\frac{4}{5}$, $\displaystyle\frac{5}{6}$, $\displaystyle\frac{6}{7}$, $\displaystyle\frac{7}{8}$
  4. $\displaystyle\frac{5}{6}$, $\displaystyle\frac{6}{7}$, $\displaystyle\frac{7}{8}$, $\displaystyle\frac{4}{5}$

Problem 3.

A fraction having denominator 30 and lying between $\displaystyle\frac{5}{8}$ and $\displaystyle\frac{7}{11}$ is,

  1. $\displaystyle\frac{21}{30}$
  2. $\displaystyle\frac{18}{30}$
  3. $\displaystyle\frac{19}{30}$
  4. $\displaystyle\frac{20}{30}$

Problem 4.

If the difference between the reciprocal of a positive proper fraction and the fraction itself be $\displaystyle\frac{9}{20}$, then the fraction is,

  1. $\displaystyle\frac{5}{4}$
  2. $\displaystyle\frac{4}{5}$
  3. $\displaystyle\frac{3}{5}$
  4. $\displaystyle\frac{3}{10}$

Problem 5.

The sum of three fractions is, $2\displaystyle\frac{11}{24}$. On dividing the largest fraction by the smallest result obtained is $\displaystyle\frac{7}{6}$ which is greater than the middle fraction by $\displaystyle\frac{1}{3}$. The smallest fraction then is,

  1. $\displaystyle\frac{5}{8}$
  2. $\displaystyle\frac{3}{7}$
  3. $\displaystyle\frac{3}{4}$
  4. $\displaystyle\frac{5}{6}$

Problem 6.

The value of $\left[\displaystyle\frac{\sqrt{3}+1}{\sqrt{3}-1}+\displaystyle\frac{\sqrt{2}+1}{\sqrt{2}-1}+\displaystyle\frac{\sqrt{3}-1}{\sqrt{3}+1}+\displaystyle\frac{\sqrt{2}-1}{\sqrt{2}+1}\right]$ is,

  1. $10$
  2. $12$
  3. $18$
  4. $14$

Problem 7.

The value of $\displaystyle\frac{1}{\sqrt{12-\sqrt{140}}}-\displaystyle\frac{1}{\sqrt{8-\sqrt{60}}}-\displaystyle\frac{2}{\sqrt{10+\sqrt{84}}}$ is

  1. 3
  2. 0
  3. 1
  4. 2

Problem 8.

If $\displaystyle\frac{4+3\sqrt{3}}{\sqrt{7+4\sqrt{3}}}=A + \sqrt{B}$ then $B-A$ is,

  1. $-13$
  2. $3\sqrt{3}-7$
  3. $13$
  4. $\sqrt{13}$

Problem 9.

The value of $\left(3+\displaystyle\frac{1}{\sqrt{3}}+\displaystyle\frac{1}{3+\sqrt{3}}+\displaystyle\frac{1}{\sqrt{3}-3}\right)$ is,

  1. $1$
  2. $3$
  3. $3-\sqrt{3}$
  4. $3+\sqrt{3}$

Problem 10.

If $\displaystyle\frac{\sqrt{a+2b}+\sqrt{a-2b}}{\sqrt{a+2b}-\sqrt{a-2b}}=\sqrt{3}$ then $a:b$ is,

  1. $4:\sqrt{3}$
  2. $\sqrt{3}:2$
  3. $\sqrt{3}:4$
  4. $2:\sqrt{3}$

The detailed conceptual solution to these question is available in SSC CGL Solution Set 70 on Fractions and Surds.


Answers to the questions

Problem 1. Answer: Option b: $\displaystyle\frac{7}{6}$.

Problem 2. Answer: Option c: $\displaystyle\frac{4}{5}$, $\displaystyle\frac{5}{6}$, $\displaystyle\frac{6}{7}$, $\displaystyle\frac{7}{8}$.

Problem 3. Answer: Option c: $\displaystyle\frac{19}{30}$.

Problem 4. Answer: Option b: $\displaystyle\frac{4}{5}$.

Problem 5. Answer: Option c: $\displaystyle\frac{3}{4}$.

Problem 6. Answer: Option a: $10$.

Problem 7. Answer: Option b: 0.

Problem 8. Answer: Option c: 13.

Problem 9. Answer: Option b: $3$.

Problem 10. Answer: Option a: $4:\sqrt{3}$.


Detailed conceptual solutions to these questions are available here.

Note: If you are an SSC CGL aspirant, you may refer to our useful article 7 steps for sure success in SSC CGL tier 1 and tier 2 tests in which we have included all our student resources on SSC CGL topics as links. Watch out for more student resources on SSC CGL in this article.

You may also like to go through the Fraction and surd related article directly by referring to the following articles.


Concept tutorials on Fractions, Surds, decimals and related topics

Fractions and Surds concepts part 1

How to solve surds part 1, Rationalization

How to solve surds part 2, Double square root surds and surd term factoring

How to solve surds part 3, Surd expression comparison and ranking


Question sets and Solution Sets in Fractions and related topics

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