SSC CGL level Question Set 73, Surds and Indices 7

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

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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.

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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.

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Guided help on Fractions, Surds and Indices in Suresolv

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

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