SSC CGL level Question Set 10, Algebra

Tenth SSC CGL level Question Set, topic Algebra

SSC CGL level Question set10 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 acquire the ability to use the concepts with special problem solving strategies to deal with any math problem within the scope of the topic.

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 mostly be in your head rather than on scratch paper.

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,

  1. 12
  2. 9
  3. 4
  4. 8

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

  1. 6
  2. 4
  3. 10
  4. 8

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

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

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

  1. $1$
  2. $2\displaystyle\frac{1}{2}$
  3. $1\displaystyle\frac{1}{2}$
  4. $2$

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,

  1. 3
  2. 6
  3. 9
  4. 12

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

  1. 64
  2. 76
  3. 52
  4. 4

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

  1. $0$
  2. $2$
  3. $-1$
  4. $1$

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

  1. 1
  2. 0
  3. $\displaystyle\frac{1}{2}$
  4. $\displaystyle\frac{3}{2}$

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,

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

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

  1. 140
  2. 125
  3. -125
  4. 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.