SSC CGL level Question Set 73, Surds and Indices 7

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,

1. $11$
2. $-12$
3. $12$
4. $-11$

Problem 2.

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

1. $-2$
2. $-1$
3. $2$
4. $1$

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. $1$
2. $2$
3. $0$
4. $-1$

Problem 4.

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

1. $2$
2. $0$
3. $-1$
4. $1$

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,

1. $0$
2. $-2$
3. $2$
4. $1$

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,

1. $-5$
2. $6$
3. $-6$
4. $5$

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,

1. 807
2. 907
3. 870
4. 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. $-1$
2. $-2$
3. $1$
4. $2$

Problem 9.

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

1. $3^{34}$ > $2^{51}$ > $7^{17}$
2. $2^{51}$ > $3^{34}$ > $7^{17}$
3. $3^{34}$ > $7^{17}$ > $2^{51}$
4. $7^{17}$ > $2^{51}$ > $3^{34}$

Problem 10.

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

1. $3$
2. $11$
3. $13$
4. $17$

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

To get the best results out of the extensive range of articles of tutorials, questions and solutions on fractions, surds and indices in Suresolv, follow the guide,

Suresolv Fractions, Surds and Indices Reading and Practice Guide for SSC CHSL, SSC CGL, SSC CGL Tier II and Other Competitive exams.

The guide list of articles includes ALL articles on Fractions, Surds and Indices​ and relevant topics in Suresolv and is up-to-date.

---