## 70th set of Surds and fraction questions for SSC CGL

Carefully chosen surds and fraction questions for SSC CGL are to be solved 10 in 12 minutes. Verify from answers and learn to solve from solution.

For best results try to solve all the 10 questions within 12 minutes' time. At the end of this period, score your efforts with 1 mark for every correct answer and minus 0.25 for every wrong one.

You will **find the answers at the end** of the questions.

After taking the test go through the solutions carefully to learn how to solve the questions quickly and correctly from the paired solution set. If needed repeat the test again after some time to check how much you have retained.

**Link to the solution set is also at the end.**

Now set your timer on and start.

### 10 Surds and Fraction Questions for SSC CGL Set 70 - time to solve 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 10 Surds and Fraction Questions for SSC CGL Set 70

**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: $4:\sqrt{3}$.

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