## Eighth SSC CGL level Question Set, topic Algebra

This is the eighth question set of 10 practice problem exercise on topic Algebra for SSC CGL exam. Students must complete this set in prescribed time first and then only refer to the corresponding solution set.

It is emphasized here that answering in MCQ test is not at all the same as answering in a school test where you need to derive the solution in perfectly elaborated steps.

In MCQ test instead, you need basically to deduce the answer in shortest possible time and select the right choice. None will ask you about what steps you followed.

Based on our analysis and experience we have seen that, for accurate and quick answering, the student

- must have complete understanding of the basic concepts of the topics
- is adequately fast in mental math calculation
- should first try to solve each problem using the most basic concepts in the specific topic area and
- does most of the deductive reasoning and calculation in his or her head rather than on paper.

Actual problem solving happens in last step above. How to do that?

You need to use your **your problem solving abilities** only. There is no other recourse.

Before taking the test you may like to refer to our **concept tutorials** on Algebra and related topics,

**Basic and rich Algebraic concepts for elegant solutions of SSC CGL problems,**

**More Basic and rich Algebraic concepts for elegant solutions of SSC CGL problems**

* SSC CGL level difficult Algebra problem solving by Componendo dividendo*.

### Eighth question set on Algebra - 10 problems for SSC CGL exam - time 12 mins

**Q1.** If $a = \sqrt{7 + 2\sqrt{12}}$ and $b = \sqrt{7 - 2\sqrt{12}}$, then $a^3 + b^3$ is,

- 52
- 40
- 44
- 48

**Q2.** If $x + \displaystyle\frac{2}{x} = 1$, then $\displaystyle\frac{x^2 + x + 2}{x^2(1 - x)}$ is,

- 2
- -2
- 1
- -1

**Q3.** If $x^3 + \displaystyle\frac{3}{x} = 4(a^3 + b^3)$ and $3x + \displaystyle\frac{1}{x^3} = 4(a^3 - b^3)$, then $a^2 - b^2$ is,

- 1
- 0
- 4
- 2

**Q4.** If $x^2 -4x + 1 = 0$, then $x^3 + \displaystyle\frac{1}{x^3}$ is,

- 44
- 64
- 48
- 52

**Q5.** If $x^4 + \displaystyle\frac{1}{x^4} = 119$ and $x \gt 1$, then positive value of $x^3 - \displaystyle\frac{1}{x^3}$ is,

- 27
- 36
- 25
- 49

**Q6.** If $x^3 + y^3 = 9$ and $x + y = 3$, then value of $\displaystyle\frac{1}{x} + \displaystyle\frac{1}{y}$ will be,

- $\displaystyle\frac{5}{2}$
- $\displaystyle\frac{3}{2}$
- $-1$
- $\displaystyle\frac{1}{2}$

**Q7.** If $ a : b = 2 : 3$ and $b : c = 4 : 5$, then the value of $a^2 : b^2 : bc$ is,

- 16 : 36 : 20
- 16 : 36 : 45
- 4 : 9 : 45
- 4 : 36 : 40

**Q8.** If $ a : b = 3 : 2$, then the ratio of, $2a^2 + 3b^2 : 3a^2 - 2b^2$ is,

- 6 : 5
- 30 : 19
- 12 : 5
- 5 : 3

**Q9.** The expression $x^4 - 2x^2 + k$ will be a perfect square if value of $k$ is,

- 1
- 2
- -1
- -2

**Q10.** If $a = 11$ and $b = 9$, then the value of, $\displaystyle\frac{a^2 + b^2 + ab}{a^3 - b^3}$ is,

- $20$
- $\displaystyle\frac{1}{2}$
- $\displaystyle\frac{1}{20}$
- $2$

### Solutions to the problems

For detailed conceptual solutions with answers you should refer to the companion **SSC CGL level Solution Set 8 on Algebra.**

#### Video

You may watch the solutions in the two-part video.

**Part I: Q1 to Q5**

**Part II: Q6 to Q10**

### Other resources that you may find valuable

#### Concept tutorials on Algebra and related topics

**Basic and rich algebraic concepts for elegant solutions of SSC CGL problems**

**More rich algebraic concepts and techniques for elegant solutions of SSC CGL problems**

**SSC CGL level difficult Algebra problem solving by Componendo dividendo**

**Proof of least value of sum of reciprocals for any number of positive variables**

**How to factorize 25 selected quadratic equations quickly by factor analysis**

#### General guidelines for successful performance in SSC CGL test

**7 Steps for sure success in SSC CGL tier 1 and tier 2 competitive tests**

#### Difficult algebra problem solving in a few steps

**How to solve difficult algebra problems in a few steps**

#### SSC CGL Tier II level question and solution sets on Algebra

**SSC CGL Tier II level Solution Set 17, Algebra 6**

**SSC CGL Tier II level Question Set 17, Algebra 6**

**SSC CGL Tier II level Question Set 14, Algebra 5**

**SSC CGL Tier II level Solution Set 14, Algebra 5**

**SSC CGL Tier II level Question Set 9, Algebra 4**

**SSC CGL Tier II level Solution Set 9, Algebra 4**

**SSC CGL Tier II level Question Set 3, Algebra 3**

**SSC CGL Tier II level Solution Set 3, Algebra 3**

**SSC CGL Tier II level Question Set 2, Algebra 2**

**SSC CGL Tier II level Solution Set 2, Algebra 2**

**SSC CGL Tier II level Question Set 1 Algebra 1**

**SSC CGL Tier II level Solution Set 1, Algebra 1**

#### SSC CGL level question and solution sets on Algebra

**SSC CGL level Solved Question Set 90, Algebra 18**

**SSC CGL level Question Set 81, Algebra 17**

**SSC CGL level Solution Set 81, Algebra 17**

**SSC CGL level Question Set 74, Algebra 16**

**SSC CGL level Solution Set 74, Algebra 16**

**SSC CGL level Question Set 64, Algebra 15**

**SSC CGL level Solution Set 64, Algebra 15**

**SSC CGL level Question Set 58, Algebra 14**

**SSC CGL level Solution Set 58, Algebra 14**

**SSC CGL level Question Set 57, Algebra 13**

**SSC CGL level Solution Set 57, Algebra 13**

**SSC CGL level Question Set 51, Algebra 12**

**SSC CGL level Solution Set 51, Algebra 12**

**SSC CGL level Question Set 45, Algebra 11**

**SSC CGL level Solution Set 45, Algebra 11**

**SSC CGL level Question Set 35, Algebra 10**

**SSC CGL level Solution Set 35, Algebra 10**

**SSC CGL level Question Set 33, Algebra 9**

**SSC CGL level Solution Set 33, Algebra 9**

**SSC CGL level Question Set 23, Algebra 8**

**SSC CGL level Solution Set 23, Algebra 8**

**SSC CGL level Question Set 22, Algebra 7**

**SSC CGL level Solution Set 22, Algebra 7**

**SSC CGL level Question Set 13, Algebra 6**

**SSC CGL level Solution Set 13, Algebra 6**

**SSC CGL level Question Set 11, Algebra 5**

**SSC CGL level Solution Set 11, Algebra 5**

**SSC CGL level Question Set 10, Algebra 4**

**SSC CGL level Solution Set 10, Algebra 4**

**SSC CGL level Question Set 9, Algebra 3**

**SSC CGL level Solution Set 9, Algebra 3**

**SSC CGL level Question Set 8, Algebra 2**

**SSC CGL level Solution Set 8, Algebra 2**

**SSC CGL level Question Set 1, Algebra 1**

**SSC CGL level Solution Set 1, Algebra 1**

#### SSC CHSL level Solved Question Sets on Algebra

**SSC CHSL level Solved Question set 11 on Algebra 1**

**SSC CHSL level Solved Question set 12 on Algebra 2**

**SSC CHSL level Solved Question set 13 on Algebra 3**

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