## 47th SSC CGL level Question Set, 2nd on topic fractions, decimals and surds

This is the 47th question set of 10 practice problem exercise for SSC CGL exam and 2nd on topic Fractions, decimals and surds. Students must complete the question set in prescribed time first and then only refer to the corresponding solution set for extracting maximum benefits from this resource.

In MCQ test, you need to deduce the answer in shortest possible time and select the right choice.

Based on our analysis and experience we have seen that, for accurate and quick answering, the student

- must have complete understanding of the basic concepts in the topic area
- is adequately fast in mental math calculation
- should try to solve each problem using the basic and rich concepts in the specific topic area and
- does most of the deductive reasoning and calculation in his or her head rather than on paper.

Actual problem solving is done in the fourth layer. You need to use **your problem solving abilities** to gain an edge in competition.

Before taking up the test you should refer to our concise tutorial on **Basic and rich concepts on Fractions decimals and surds part 1.**

### 47th question set- 10 problems for SSC CGL exam: 2nd on topic Fractions, decimals and surds - time 18 mins

**Problem 1.**

Simplify $\displaystyle\frac{\displaystyle\frac{1}{3} + \displaystyle\frac{1}{4}\left[\displaystyle\frac{2}{5}-\displaystyle\frac{1}{2}\right]}{1\displaystyle\frac{2}{3}\text{ of } \displaystyle\frac{3}{4} - \displaystyle\frac{3}{4}\text{ of }\displaystyle\frac{4}{5}}$

- $\displaystyle\frac{74}{78}$
- $\displaystyle\frac{37}{13}$
- $\displaystyle\frac{37}{78}$
- $\displaystyle\frac{74}{13}$

**Problem 2.**

The value of $\displaystyle\frac{0.04}{0.03}\text { of }\displaystyle\frac{\left(3\displaystyle\frac{1}{3}-2\displaystyle\frac{1}{2}\right)\div{\displaystyle\frac{1}{2}}\text{ of }1\displaystyle\frac{1}{4}}{\displaystyle\frac{1}{3}+\displaystyle\frac{1}{5}\text{ of }\displaystyle\frac{1}{9}}$ is,

- $\displaystyle\frac{1}{5}$
- $1$
- $5$
- $\displaystyle\frac{1}{2}$

**Problem 3.**

$\sqrt{\displaystyle\frac{(6.1)^2+(61.1)^2+(611.1)^2}{(0.61)^2+(6.11)^2+(61.11)^2}}$ is equal to,

- 0.1
- 100
- 1.1
- 10

**Problem 4.**

$(0.\overline{1})^2\left[1-9(0.1\overline{6})^2\right]$ is equal to,

- $-\displaystyle\frac{1}{162}$
- $\displaystyle\frac{1}{109}$
- $\displaystyle\frac{1}{108}$
- $\displaystyle\frac{7696}{10^6}$

**Problem 5.**

The value of $\displaystyle\frac{2\displaystyle\frac{1}{3}-1\displaystyle\frac{2}{11}}{3+\displaystyle\frac{1}{3+\displaystyle\frac{1}{3+\displaystyle\frac{1}{3}}}}$ is,

- $\displaystyle\frac{38}{109}$
- $\displaystyle\frac{116}{109}$
- $1$
- $\displaystyle\frac{109}{38}$

#### Problem 6.

Find the value of $27\times{1.\overline{2}}\times{5.526\overline{2}}\times{0.\overline{6}}$.

- $121.7\overline{5}$
- $121.\overline{75}$
- $121.\overline{57}$
- $121.576\overline{8}$

** Problem 7.**

If $\displaystyle\frac{(x-\sqrt{24})(\sqrt{75}+\sqrt{50})}{\sqrt{75}-\sqrt{50}}=1$, then $x$ is,

- $5$
- $\sqrt{5}$
- $3\sqrt{5}$
- $2\sqrt{5}$

** Problem 8.**

$\displaystyle\frac{1}{\sqrt{2}+\sqrt{3}-\sqrt{5}}+\displaystyle\frac{1}{\sqrt{2}-\sqrt{3}-\sqrt{5}}$ is equal to,

- $\displaystyle\frac{1}{\sqrt{2}}$
- $0$
- $\sqrt{2}$
- $1$

**Problem 9.**

$\left[8-\left[\displaystyle\frac{4^{\frac{9}{4}}\sqrt{2.2^2}}{2\sqrt{2^{-2}}}\right]^\frac{1}{2}\right]$ is equal to,

- 1
- 32
- 0
- 8

** Problem 10.**

The value of $\sqrt{\displaystyle\frac{(\sqrt{12}-\sqrt{8})(\sqrt{3}+\sqrt{2})}{5+\sqrt{24}}}$ is,

- $\sqrt{6}-\sqrt{2}$
- $\sqrt{6}-2$
- $2-\sqrt{6}$
- $\sqrt{6}+\sqrt{2}$

### Answers to the questions

**Problem 1.** **Answer:** c: $\displaystyle\frac{37}{78}$.

**Problem 2.** **Answer:** Option c : $5$ .

**Problem 3.** **Answer:** Option d: 10.

**Problem 4.** **Answer:** c: $\displaystyle\frac{1}{108}$.

**Problem 5.** **Answer:** Option a: $\displaystyle\frac{38}{109}$.

**Problem 6.** **Answer:** Option d : $121.576\overline{8}$.

**Problem 7.** **Answer:** Option a: $5$.

**Problem 8.** **Answer:** Option a: $\displaystyle\frac{1}{\sqrt{2}}$.

**Problem 9.** **Answer:** Option c: 0.

**Problem 10.** **Answer:** Option b:$\sqrt{6}-2$.

You may refer to the companion solution set to this question sets at **SSC CGL level Solution Set 47 on fractions decimals and surds 2.**