## 61st SSC CGL level Question Set, 5th on topic fractions indices and surds

This is the 61st question set of 10 practice problem exercise for SSC CGL exam and 5th on topic fractions indices and surds. Students must complete this 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.**

### 61st question set- 10 problems for SSC CGL exam: 5th on topic Fractions indices and surds - time 12 mins

**Problem 1.**

The total number of prime factors in $4^{10}\times{16^2}\times{7^3}\times{11}\times{10^2}$ is,

- 34
- 37
- 36
- 35

**Problem 2.**

Arrange the following in descending order,

$\sqrt[3]{4}$, $\sqrt{2}$, $\sqrt[6]{3}$, $\sqrt[4]{5}$.

- $\sqrt[6]{3} \gt \sqrt[4]{5} \gt \sqrt[3]{4} \gt \sqrt{2}$
- $\sqrt{2} \gt \sqrt[6]{3} \gt \sqrt[3]{4} \gt \sqrt[4]{5}$
- $\sqrt[3]{4} \gt \sqrt[4]{5} \gt \sqrt{2} \gt \sqrt[6]{3}$
- $\sqrt[4]{5} \gt \sqrt[3]{4} \gt \sqrt[6]{3} \gt \sqrt{2}$

**Problem 3.**

If $\sqrt{15}=3.88$, then the value of $\sqrt{\displaystyle\frac{5}{3}}$ is,

- $1.29$
- $1.295$
- $1.29\overline{3}$
- $1.2934$

**Problem 4.**

The simplified value of $(\sqrt{3}+1)(10+\sqrt{12})(\sqrt{12}-2)(5-\sqrt{3})$ is equal to,

- 132
- 16
- 88
- 176

**Problem 5.**

$\displaystyle\frac{12}{3+\sqrt{5}+2\sqrt{2}}$ is equal to,

- $1-\sqrt{5}-\sqrt{2}+\sqrt{10}$
- $1+\sqrt{5}-\sqrt{2}+\sqrt{10}$
- $1+\sqrt{5}+\sqrt{2}-\sqrt{10}$
- $1-\sqrt{5}+\sqrt{2}+\sqrt{10}$

#### Problem 6.

The value of $\sqrt{\displaystyle\frac{4\displaystyle\frac{1}{7}-2\displaystyle\frac{1}{4}}{3\displaystyle\frac{1}{2}+1\displaystyle\frac{1}{7}}\div{\displaystyle\frac{1}{2+\displaystyle\frac{1}{2+\displaystyle\frac{1}{5-\displaystyle\frac{1}{5}}}}}}$ is,

- 1
- 2
- 3
- 4

**Problem 7.**

Which is the greatest among $(\sqrt{19}-\sqrt{17})$, $(\sqrt{13}-\sqrt{11})$, $(\sqrt{7}-\sqrt{5})$, and $(\sqrt{5}-\sqrt{3})$?

- $(\sqrt{5}-\sqrt{3})$
- $(\sqrt{7}-\sqrt{5})$
- $(\sqrt{19}-\sqrt{17})$
- $(\sqrt{13}-\sqrt{11})$

**Problem 8.**

If $\sqrt{3}=1.732$ what is the value of $\displaystyle\frac{4+3\sqrt{3}}{\sqrt{7+4\sqrt{3}}}$?

- 0.464
- 0.023
- 3.023
- 2.464

**Problem 9.**

The simplified value of $\left[\sqrt[3]{\sqrt[6]{5^9}}\right]^4\left[\sqrt[3]{\sqrt[6]{5^9}}\right]^4$ is,

- $5^4$
- $5^8$
- $5^{12}$
- $5^2$

**Problem 10.**

The smallest of $\sqrt{8}+\sqrt{5}$, $\sqrt{7}+\sqrt{6}$, $\sqrt{10}+\sqrt{3}$, $\sqrt{11}+\sqrt{2}$ is,

- $\sqrt{7}+\sqrt{6}$
- $\sqrt{8}+\sqrt{5}$
- $\sqrt{10}+\sqrt{3}$
- $\sqrt{11}+\sqrt{2}$

For **answers and detailed solutions,** refer to the companion solution set to this question sets at **SSC CGL level Solution Set 61 on fractions indices and surds 5.**