## Tenth SSC CGL level Question Set, topic Algebra

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

* Otherwise,* without attempting the question set with all seriousness in the prescribed time, if the learner goes through the solutions

*he or she won't be able to appreciate and retain the special concepts involved in the solutions.** A golden rule of math problem solving *always will remain true,

Math can't be learned by heart.

This is true for achieving excellence in learning any subject * but is truer especially in Maths.* Here, in Maths you have to

**understand the concepts**and

*within the scope of the topic.*

**acquire the ability to use the concepts with special problem solving strategies to deal with any math problem**Furthermore, **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 elaborate steps.

In MCQ test instead, you need basically to * deduce the answer in shortest possible time and select the right choice*. Solving process will

*rather than on scratch paper.*

**mostly be in your head****Based on our analysis and experience** we have seen that, **for accurate and lightning quick answering**, the student

- must have complete understanding of the
**basic concepts, along with rich concepts**on the topics, - is
**adequately fast in mental math**calculation,*one need not be superfast human calculator*, **should first examine each problem for using the most basic concepts**in the specific topic area and**then use the rich concepts**if required,**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. * This problem solving ability lies at the heart of excellence in performance* in this cutting-edge test.

This problem set containing 10 problems **highlights the need of solving the problems using powerful strategies** *rather than brute force conventional deduction methods*. We have tried to* bring out the underlying strategies, techniques and reasoning that went into solving a problem on an average in about a minute's time*.

If you follow intelligent and dedicated preparation methods using this type of resources, * you should also be able to reach the desired level of competence* for completing such a set of 10 questions comfortably within 12 minutes' share of time.

These questions are a bit advanced in nature and require a few new types of algebraic pattern recognition and use abilities.

Lastly, **these are problems rich with possibilities**. We couldn't cover all aspects of each problem. Later we would deal with a few selected class of such beautiful problems in details. You *may refer to these special problem solving strategy and technique oriented detailed treatments* under the subsection **Efficient Math Problem Solving.**

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.**

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

**Q1.** If $2a + \displaystyle\frac{1}{3a} = 6$, then the value of the expression $3a + \displaystyle\frac{1}{2a}$ is,

- 12
- 9
- 4
- 8

**Q2.** If $x^2 + y^2 - 2x + 6y + 10 = 0$, then $(x^2 + y^2)$ is,

- 6
- 4
- 10
- 8

**Q3.** If $x^2 = 2$, then $x + 1$ is,

- $x - 1$
- $\displaystyle\frac{2}{x - 1}$
- $\displaystyle\frac{x + 1}{3 - 2x}$
- $\displaystyle\frac{x - 1}{3 - 2x}$

**Q4.** If $a^2 + b^2 + \displaystyle\frac{1}{a^2} + \displaystyle\frac{1}{b^2} = 4$ then $a^2 + b^2$ is,

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

**Q5.** If $a + b + c = 6$, $a^2 + b^2 + c^2 = 14$ and $a^3 + b^3 + c^3 = 36$, then the value of $abc$ is,

- 3
- 6
- 9
- 12

**Q6.** If $x + \displaystyle\frac{1}{16x} = 1$, then the value of $64x^3 + \displaystyle\frac{1}{64x^3}$ is,

- 64
- 76
- 52
- 4

**Q7.** If $a^4 + a^2b^2 + b^4 = 8$ and $a^2 + ab + b^2 = 4$, then the value of $ab$ is,

- $0$
- $2$
- $-1$
- $1$

**Q8.** If $x^2 + y^2 + z^2 = xy + yz + zx$, then the value of, $\displaystyle\frac{4x +2y -3z}{2x}$ is,

- 1
- 0
- $\displaystyle\frac{1}{2}$
- $\displaystyle\frac{3}{2}$

**Q9.** If $x\left(3 - \displaystyle\frac{2}{x}\right) = \displaystyle\frac{3}{x}$, and $x\neq{0}$ then $x^2 + \displaystyle\frac{1}{x^2}$ is,

- $2\displaystyle\frac{5}{9}$
- $2\displaystyle\frac{4}{9}$
- $2\displaystyle\frac{1}{3}$
- $2\displaystyle\frac{2}{3}$

**Q10.** If $(x -a)(x - b) = 1$ and $(a - b) + 5 = 0$, then $(x - a)^3 - \displaystyle\frac{1}{(x - a)^3}$ is

- 140
- 125
- -125
- 1

### Solutions to the problems

For detailed conceptual solutions with answers you should refer to the companion * SSC CGL level Solution Set 10 on Algebra* where you will also get link references to all the reading materials on Algebra.