## 7th Question Set on Surds and Indices, 73rd for SSC CGL

10 surds and indices questions form 7th practice set on surds and indices and 73rd for SSC CGL. Useful for competitive exams with surds and indices.

Master **most used surds techniques** from * How to solve surds 2* and answer confidently the 8 hard surds questions out of total 10 in this set.

Refer to **answers and link to the detailed solutions** at the end.

Best way to use this surds and indices question set is to *first practice on a few earlier question sets on the topic* and **then take this test with timer on.**

For *gaining complete grip on surds indices problems*, refer and use **Surds and indices guide** that lists all tutorials, questions sets and solution sets on surds and indices.

### 7th Question set on Surds and Indices - 73rd for SSC CGL: answering time 15 mins

#### Problem 1.

The value of $\displaystyle\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}+\displaystyle\frac{\sqrt{12}}{\sqrt{3}-\sqrt{2}}$ is,

- $11$
- $-12$
- $12$
- $-11$

#### Problem 2.

Value of $\displaystyle\frac{\sqrt{5}+\sqrt{3}}{\sqrt{80}+\sqrt{48}-\sqrt{45}-\sqrt{27}}$ is,

- $-2$
- $-1$
- $2$
- $1$

#### Problem 3.

Simplify $\displaystyle\frac{6}{2\sqrt{3}-\sqrt{6}}+\displaystyle\frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}-\displaystyle\frac{4\sqrt{3}}{\sqrt{6}-\sqrt{2}}$ is,

- $1$
- $2$
- $0$
- $-1$

#### Problem** 4.**

Simplify $\displaystyle\frac{4\sqrt{18}}{\sqrt{12}}-\displaystyle\frac{8\sqrt{75}}{\sqrt{32}}+\displaystyle\frac{9\sqrt{2}}{\sqrt{3}}$.

- $2$
- $0$
- $-1$
- $1$

#### Problem** 5.**

Value of

$\displaystyle\frac{1}{1+\sqrt{2}}+\displaystyle\frac{1}{\sqrt{2}+\sqrt{3}}+\displaystyle\frac{1}{\sqrt{3}+\sqrt{4}}$

$+\displaystyle\frac{1}{\sqrt{4}+\sqrt{5}}+\displaystyle\frac{1}{\sqrt{5}+\sqrt{6}}+\displaystyle\frac{1}{\sqrt{6}+\sqrt{7}}$

$+\displaystyle\frac{1}{\sqrt{7}+\sqrt{8}}+\displaystyle\frac{1}{\sqrt{8}+\sqrt{9}}$ is,

- $0$
- $-2$
- $2$
- $1$

#### Problem 6.

If $a=\displaystyle\frac{1}{3+2\sqrt{2}}$ and $b=\displaystyle\frac{1}{3-2\sqrt{2}}$, the value of $a^2b +ab^2$ is,

- $-5$
- $6$
- $-6$
- $5$

#### Problem** 7.**

If $x=\displaystyle\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ and $y=\displaystyle\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$, the value of $x^3+y^3$ is,

- 807
- 907
- 870
- 970

#### Problem** 8.**

If $x=\sqrt{\displaystyle\frac{5+2\sqrt{6}}{5-2\sqrt{6}}}$ find the value of $x^2(x-10)^2$,

- $-1$
- $-2$
- $1$
- $2$

#### Problem** 9.**

Arrange $3^{34}$, $2^{51}$, and $7^{17}$ in ascending order,

- $3^{34}$ > $2^{51}$ > $7^{17}$
- $2^{51}$ > $3^{34}$ > $7^{17}$
- $3^{34}$ > $7^{17}$ > $2^{51}$
- $7^{17}$ > $2^{51}$ > $3^{34}$

#### Problem** 10.**

$4^{61}+4^{62}+4^{63}+4^{64}$ is divisible by,

- $3$
- $11$
- $13$
- $17$

For detailed solutions to the questions refer to, **SSC CGL level Solution Set 73 on Surds and Indices 7.**

### Answers to the questions

**Problem 1.** Answer: Option a: $11$.

**Problem 2.** Answer. Option d: $1$.

**Problem 3.** Answer: Option c: $0$.

**Problem 4.** Answer: Option b: $0$.

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

**Problem 6.** Answer: Option b: $6$.

**Problem 7.** Answer: Option d: 970.

**Problem 8.** Answer: Option c: 1.

**Problem 9.** Answer. Option a: $3^{34}$ > $2^{51}$ > $7^{17}$.

**Problem 10.** Answer: Option d: 17.

### Guided help on Fractions, Surds and Indices in Suresolv

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