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.
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