SSC CGL level Question Set 70, Fractions and Surds 6 | SureSolv

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SSC CGL level Question Set 70, Fractions and Surds 6

70th SSC CGL level Question Set, 6th on topic fractions and 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 in 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: $4:\sqrt{3}$.

Guided help on Fractions, Surds and Indices in Suresolv

To get the best results out of the extensive range of articles of tutorials, questions and solutions on fractions, surds and indices in Suresolv, follow the guide,

Suresolv Fractions, Surds and Indices Reading and Practice Guide for SSC CHSL, SSC CGL, SSC CGL Tier II and Other Competitive exams.

The guide list of articles includes ALL articles on Fractions, Surds and Indices​ and relevant topics in Suresolv and is up-to-date.