## 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.

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### 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,

- $\displaystyle\frac{7}{4}$
- $\displaystyle\frac{7}{6}$
- $\displaystyle\frac{7}{3}$
- $\displaystyle\frac{4}{5}$

#### Problem 2.

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

- $\displaystyle\frac{4}{5}$, $\displaystyle\frac{7}{8}$, $\displaystyle\frac{6}{7}$, $\displaystyle\frac{5}{6}$
- $\displaystyle\frac{7}{8}$, $\displaystyle\frac{6}{7}$, $\displaystyle\frac{5}{6}$, $\displaystyle\frac{4}{5}$
- $\displaystyle\frac{4}{5}$, $\displaystyle\frac{5}{6}$, $\displaystyle\frac{6}{7}$, $\displaystyle\frac{7}{8}$
- $\displaystyle\frac{5}{6}$, $\displaystyle\frac{6}{7}$, $\displaystyle\frac{7}{8}$, $\displaystyle\frac{4}{5}$

#### Problem 3.

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

- $\displaystyle\frac{21}{30}$
- $\displaystyle\frac{18}{30}$
- $\displaystyle\frac{19}{30}$
- $\displaystyle\frac{20}{30}$

#### 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,

- $\displaystyle\frac{5}{4}$
- $\displaystyle\frac{4}{5}$
- $\displaystyle\frac{3}{5}$
- $\displaystyle\frac{3}{10}$

#### 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,

- $\displaystyle\frac{5}{8}$
- $\displaystyle\frac{3}{7}$
- $\displaystyle\frac{3}{4}$
- $\displaystyle\frac{5}{6}$

#### 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,

- $10$
- $12$
- $18$
- $14$

#### 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

- 3
- 0
- 1
- 2

#### Problem** 8.**

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

- $-13$
- $3\sqrt{3}-7$
- $13$
- $\sqrt{13}$

#### 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,

- $1$
- $3$
- $3-\sqrt{3}$
- $3+\sqrt{3}$

#### Problem** 10.**

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

- $4:\sqrt{3}$
- $\sqrt{3}:2$
- $\sqrt{3}:4$
- $2:\sqrt{3}$

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

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