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SSC CGL Algebra Question Set 1

10 algebra questions with answers set 1

First SSC CGL Question Set, 1st on Algebra

This contains 10 algebra questions with answers for competitive exams, specifically for SSC CGL. A number of these 10 are hard algebra questions that you need to solve by suitable concepts and techniques. This forms the 1st question set for SSC CGL and 1st on Algebra.

The question set can very well be used as a unit of mock test or mini mock test.

For maximum benefit, you should take this timed test, score your performance from the answers and then get your doubts clear from the corresponding solution set. The link of the solutions is given at the end.

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 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 head rather than on paper.

Actual problem solving happens in item 3 and 4 above. How to do that?

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

Before taking the test you may like to refer to the following concept tutorial on Algebra that has a good collection of basic to powerful algebra problem solving techniques,

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

First question set- 10 problems for SSC CGL exam - time 18 mins

Q1. The value of, $\displaystyle\frac{1}{a^2 +ax + x^2}- \displaystyle\frac{1}{a^2 - ax + x^2} +\displaystyle\frac{2ax}{a^4 + a^2x^2 + x^4}$ is,

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

Q2. If $x^3 + y^3 = 9$ and $x + y = 3$ then the value of $x^4 + y^4$ is,

  1. 81
  2. 32
  3. 27
  4. 17

Q3. For any real number $x$ the maximum value of $4 - 6x - x^2$ is,

  1. 4
  2. 7
  3. 9
  4. 13

Q4. If $5^{\sqrt{x}} + 12^{\sqrt{x}} = 13^{\sqrt{x}}$ then value of $x$ is,

  1. $\frac{25}{4}$
  2. 4
  3. 6
  4. 9

Q5. If $a + b + c = 0$ then the value of $\displaystyle\frac{a^2 + b^2 + c^2}{a^2 - bc}$ is,

  1. 0
  2. 1
  3. 2
  4. 3

Q6. If $x^2 + 2 = 2x$ then the value of $x^4 - x^3 + x^2 + 2$ will be,

  1. 0
  2. 1
  3. -1
  4. $\sqrt{2}$

Q7. If $x = (\sqrt{2} + 1)^{-\frac{1}{3}}$, then the value of $\left(x^3 - \displaystyle\frac{1}{x^3}\right)$,

  1. $0$
  2. $-2$
  3. $-\sqrt{2}$
  4. $\sqrt{2}$

Q8. If $4b^2 + \displaystyle\frac{1}{b^2}=2$, then value of $8b^3 + \displaystyle\frac{1}{b^3}$ is,

  1. 0
  2. 2
  3. 1
  4. 5

Q9. If $x^\frac{1}{3} + y^\frac{1}{3} - z^\frac{1}{3} = 0$ then value of $(x + y - z)^3 + 27xyz$ is,

  1. $-1$
  2. 1
  3. 0
  4. 27

Q10. If $x^{x\sqrt{x}} = (x\sqrt{x})^x$ then $x$ is equal to,

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

Answers to the 10 algebra questions

Q1. Answer: Option 4: 0.

Q2. Answer: Option 4: 17.

Q3. Answer: Option 4: 13.

Q4. Answer: Option 2: 4.

Q5. Answer: Option 3: 2.

Q6. Answer: Option 1: 0.

Q7. Answer: Option 2: $-2$.

Q8. Answer: Option 1: 0.

Q9. Answer: Option 3: 0.

Q10. Answer: Option 3: $\frac{9}{4}$.

Solutions to the questions

You can refer to the corresponding solution set at

SSC CGL level Solution Set 1, Algebra 1.


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

Part I: Q1 to Q5

Part II: Q6 to Q10

Guided help on Algebra in Suresolv

To get the best results out of the extensive range of articles of tutorials, questions and solutions on Algebra in Suresolv, follow the guide,

Suresolv Algebra Reading and Practice Guide for SSC CHSL, SSC CGL, SSC CGL Tier II and Other Competitive exams.

The guide list of articles includes ALL articles on Algebra in Suresolv and is up-to-date.