## 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,

**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.**

### 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* where you will also get link references to all the reading materials on Algebra.