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SSC CGL level Question Set 61, Fractions indices and surds 5

Comparison of surds, surds and indices question set SSC CGL 61

Comparison of surds, surds and indices questions SSC CGL Set 61

10 questions on comparison of surds and surds and indices in SSC CGL set 61 to be solved in 12 minutes. Verify correctness from answers.

Contents are,

  1. Comparison of surds questions.
  2. Surds simplification questions.
  3. Indices questions.
  4. Answers to the 10 questions.

Link to the solutions is at the end.


Comparison of surds and surds and indices questions SSC CGL set 61 - time to solve 12 mins

Problem 1.

The total number of prime factors in $4^{10}\times{16^2}\times{7^3}\times{11}\times{10^2}$ is,

  1. 34
  2. 37
  3. 36
  4. 35

Problem 2.

Arrange the following in descending order,

$\sqrt[3]{4}$, $\sqrt{2}$, $\sqrt[6]{3}$, $\sqrt[4]{5}$.

  1. $\sqrt[6]{3} \gt \sqrt[4]{5} \gt \sqrt[3]{4} \gt \sqrt{2}$
  2. $\sqrt{2} \gt \sqrt[6]{3} \gt \sqrt[3]{4} \gt \sqrt[4]{5}$
  3. $\sqrt[3]{4} \gt \sqrt[4]{5} \gt \sqrt{2} \gt \sqrt[6]{3}$
  4. $\sqrt[4]{5} \gt \sqrt[3]{4} \gt \sqrt[6]{3} \gt \sqrt{2}$

Problem 3.

If $\sqrt{15}=3.88$, then the value of $\sqrt{\displaystyle\frac{5}{3}}$ is,

  1. $1.29$
  2. $1.295$
  3. $1.29\overline{3}$
  4. $1.2934$

Problem 4.

The simplified value of $(\sqrt{3}+1)(10+\sqrt{12})(\sqrt{12}-2)(5-\sqrt{3})$ is equal to,

  1. 132
  2. 16
  3. 88
  4. 176

Problem 5.

$\displaystyle\frac{12}{3+\sqrt{5}+2\sqrt{2}}$ is equal to,

  1. $1-\sqrt{5}-\sqrt{2}+\sqrt{10}$
  2. $1+\sqrt{5}-\sqrt{2}+\sqrt{10}$
  3. $1+\sqrt{5}+\sqrt{2}-\sqrt{10}$
  4. $1-\sqrt{5}+\sqrt{2}+\sqrt{10}$

Problem 6.

The value of $\sqrt{\displaystyle\frac{4\displaystyle\frac{1}{7}-2\displaystyle\frac{1}{4}}{3\displaystyle\frac{1}{2}+1\displaystyle\frac{1}{7}}\div{\displaystyle\frac{1}{2+\displaystyle\frac{1}{2+\displaystyle\frac{1}{5-\displaystyle\frac{1}{5}}}}}}$ is,

  1. 1
  2. 2
  3. 3
  4. 4

Problem 7.

Which is the greatest among $(\sqrt{19}-\sqrt{17})$, $(\sqrt{13}-\sqrt{11})$, $(\sqrt{7}-\sqrt{5})$, and $(\sqrt{5}-\sqrt{3})$?

  1. $(\sqrt{5}-\sqrt{3})$
  2. $(\sqrt{7}-\sqrt{5})$
  3. $(\sqrt{19}-\sqrt{17})$
  4. $(\sqrt{13}-\sqrt{11})$

Problem 8.

If $\sqrt{3}=1.732$ what is the value of $\displaystyle\frac{4+3\sqrt{3}}{\sqrt{7+4\sqrt{3}}}$?

  1. 0.464
  2. 0.023
  3. 3.023
  4. 2.464

Problem 9.

The simplified value of $\left[\sqrt[3]{\sqrt[6]{5^9}}\right]^4\left[\sqrt[3]{\sqrt[6]{5^9}}\right]^4$ is,

  1. $5^4$
  2. $5^8$
  3. $5^{12}$
  4. $5^2$

Problem 10.

The smallest of $\sqrt{8}+\sqrt{5}$, $\sqrt{7}+\sqrt{6}$, $\sqrt{10}+\sqrt{3}$, $\sqrt{11}+\sqrt{2}$ is,

  1. $\sqrt{7}+\sqrt{6}$
  2. $\sqrt{8}+\sqrt{5}$
  3. $\sqrt{10}+\sqrt{3}$
  4. $\sqrt{11}+\sqrt{2}$

For detailed solutions, refer to the companion solution set to this question sets at SSC CGL level Solution Set 61 on fractions indices and surds 5.

Answers to the comparison of surds, surds and indices questions SSC CGL set 61

Problem 1. Answer: Option c: 36.

Problem 2. Answer: Option c: $\sqrt[3]{4}$, $\sqrt[4]{5}$, $\sqrt{2}$, $\sqrt[6]{3}$.

Problem 3. Answer: Option c: $1.29\overline{3}$.

Problem 4. Answer: Option d: 176.

Problem 5. Answer: Option c: $1+\sqrt{5}+\sqrt{2}-\sqrt{10}$.

Problem 6. Answer: Option a: 1.

Problem 7. Answer: Option a: $(\sqrt{5}-\sqrt{3})$.

Problem 8. Answer: Option d: 2.464.

Problem 9. Answer: Option a: $5^4$.

Problem 10. Answer: Option d: $\sqrt{11}+\sqrt{2}$.


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