SSC CGL level Question Set 73, Surds and Indices 7

73rd SSC CGL level Question Set, 7th on topic Surds and Indices

ssc cgl question set 73 surds indices

This is the 73rd question set of 10 practice problem exercise for SSC CGL exam and 7th on topic Surds and Indices. 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. The link of the solution set is given at the end.

You may refer to the related tutorials, question and solution sets listed at the end.

73rd question set—10 problems for SSC CGL exam: 7th on topic Surds and Indices - 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.


Detailed conceptual solutions to these questions are available here.

Note: If you are an SSC CGL aspirant, you may refer to our useful article 7 steps for sure success in SSC CGL tier 1 and tier 2 tests in which we have included all our student resources on SSC CGL topics as links. Watch out for more student resources on SSC CGL in this article.

You may also like to go through the Fraction and surd related article directly by referring to the following articles.


Concept tutorials on Fractions, Surds, decimals and related topics

Fractions and Surds concepts part 1

How to solve surds part 1, Rationalization

How to solve surds part 2, Double square root surds and surd term factoring

How to solve surds part 3, Surd expression comparison and ranking


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