## 23rd SSC CGL level Question Set, Algebra

This is the 23rd question set of 10 practice problem exercise for SSC CGL exam and 8th on topic Algebra.

For maximum gains, the test should be taken first, that is obvious. But more importantly, to absorb the concepts, techniques and deductive reasoning elaborated through the solutions, one must solve many problems in a systematic manner using the conceptual analytical approach.

Learning by doing is the best learning. There is no alternative towards achieving excellence.

### Method of taking the test for getting the best results from the test:

**Before start,**go through any short but good material to refresh your concepts if you so require.**Answer the questions**in an undisturbed environment with no interruption, full concentration and alarm set at 15 minutes.**When the time limit of 15 minutes is over,**mark up to which you have answered,**but go on to complete the set.****At the end,**refer to the answers given at the end to mark your score at 15 minutes. For every correct answer add 1 and for every incorrect answer deduct 0.25 (or whatever is the scoring pattern in the coming test). Write your score on top of the answer sheet with date and time.**Identify and analyze**the problems that**you couldn't do**to learn how to solve those problems.**Identify and analyze**the problems that**you solved incorrectly**. Identify the reasons behind the errors. If it is because of**your shortcoming in topic knowledge**improve it by referring to**only that part of concept**from the best source you can get hold of. You might google it. If it is because of**your method of answering,**analyze and improve those aspects specifically.**Identify and analyze**the**problems that posed difficulties for you and delayed you**. Analyze and learn how to solve the problems using basic concepts and relevant problem solving strategies and techniques.**Give a gap**before you take a 10 problem practice test again.

Important:bothandpractice testsmust be timed, analyzed, improving actions taken and then repeated. With intelligent method, it is possible to reach highest excellence level in performance.mock tests

### Recommended reading before the test

#### Concept tutorials on Algebra

**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.**

### 23rd question set - 10 problems for SSC CGL exam: 8th on topic Algebra - answering time 15 mins

**Q1. **If $x = \sqrt[3]{a + \sqrt{a^2 + b^3}} + \sqrt[3]{a - \sqrt{a^2 + b^3}}$, then the value of $x^3 + 3bx$ is,

- 1
- 0
- a
- 2a

**Q2.** If $x = 2015$, $y = 2014$ and $z = 2013$ then the value of $x^2 + y^2 + z^2 - xy - yz -zx$ is,

- 4
- 3
- 2
- 6

**Q3.** The area in square unit of triangle formed by the graphs of $x=4$, $y=3$ and $3x + 4y= 12$ is,

- 12
- 8
- 10
- 6

**Q4. **If $2\left(x^2 + \displaystyle\frac{1}{x^2}\right) - \left(x - \displaystyle\frac{1}{x}\right) - 7 = 0$, then the two values of $x$ are,

- $2$, $-\frac{1}{2}$
- $1$, $2$
- $0$, $1$
- $\frac{1}{2}$, $1$

**Q5. **If $\left(x + \displaystyle\frac{1}{x}\right)^2 = 3$ then the value of,

$x^{206} + x^{200} + x^{90} + x^{84} + x^{18} $

$\hspace{24mm} + x^{12} + x^6 + 1$ is,

- 0
- 1
- 206
- 84

**Q6.** If $1.5x=0.04y$ then the value of $\displaystyle\frac{y^2 - x^2}{y^2 + 2xy + x^2}$ will be,

- $\frac{73}{77}$
- $\frac{74}{77}$
- $\frac{73}{770}$
- $\frac{730}{77}$

** Q7.** If $x + \displaystyle\frac{1}{x} = 3$ then the value of $x^5 + \displaystyle\frac{1}{x^5}$ is,

- 322
- 113
- 123
- 126

** Q8.** If $\|a\|$ is the greatest integer equal to or less than $a$, then the value of $\|-\frac{1}{4}\| + \|4\frac{1}{4}\| + \|3\|$ is,

- 4
- 5
- 7
- 6

**Q9.** One of the factors of $(a^2 - b^2)^3 + (b^2 - c^2)^3 + (c^2 - a^2)^3$ is,

- $(b - c)(b - c)$
- $(a + b)(a - b)$
- $(a + b)(a + b)$
- $(a - b)(a - b)$

** Q10.** If $x^2 + y^2 + z^2 = xy + yz + zx$, then the value of $\displaystyle\frac{z + x}{y}$ is,

- 2
- 0
- 1
- -1

### Solutions to the problems

For detailed conceptual solutions with answers you should refer to the companion * SSC CGL level Solution Set 23 on Algebra* where you will also get link references to all the reading materials on Algebra.

### Additional help on SSC CGL Algebra

Apart from a **large number of question and solution sets** and a valuable article on "* 7 Steps for sure success on Tier 1 and Tier 2 of SSC CGL*" rich with concepts and links, you may refer to our other articles specifically on Algebra listed on latest shown first basis,

#### First to read tutorials on Basic and rich Algebra concepts

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

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

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