SSC CGL Algebra Question Set 1

First SSC CGL Question Set on Algebra

SSC CGL Algebra Question Set 1

This is the first question set of 10 practice problem exercise for SSC CGL exam on Algebra. Students must complete this set in prescribed time first and then only refer to the 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 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 our concept tutorials on Algebra and related topics,

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

SSC CGL level difficult Algebra problem solving by Componendo dividendo.


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

Q1. The value of, $\frac{1}{a^2 +ax + x^2}- \frac{1}{a^2 - ax + x^2} +\frac{2ax}{a^4 + a^2x^2 + x^4}$ 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 $\frac{a^2 + b^2 + c^2}{a^2 - bc}$ 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 $\left(x^3 - \frac{1}{x^3}\right)$,

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

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

You can refer to the corresponding solution set at

SSC CGL level Solution Set 1, Algebra 1.


Other resources that you may find valuable

Concept tutorials on Algebra and other related topics

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

SSC CGL level difficult Algebra problem solving by Componendo dividendo

General guidelines for successful performance in SSC CGL test

7 Steps for sure success in SSC CGL tier 1 and tier 2 competitive tests

Difficult algebra problem solving using high power methods

How to solve difficult algebra problems in a few steps

SSC CGL Tier II level question and solution sets on Algebra

SSC CGL Tier II level Question Set 9, Algebra 4

SSC CGL Tier II level Solution Set 9, Algebra 4

SSC CGL Tier II level Question Set 3, Algebra 3

SSC CGL Tier II level Solution Set 3, Algebra 3

SSC CGL Tier II level Question Set 2, Algebra 2

SSC CGL Tier II level Solution Set 2, Algebra 2

SSC CGL Tier II level Question Set 1 Algebra 1

SSC CGL Tier II level Solution Set 1, Algebra 1

SSC CGL level question and solution sets on Algebra

SSC CGL level Question Set 64, Algebra 15

SSC CGL level Solution Set 64, Algebra 15

SSC CGL level Question Set 58, Algebra 14

SSC CGL level Solution Set 58, Algebra 14

SSC CGL level Question Set 57, Algebra 13

SSC CGL level Solution Set 57, Algebra 13

SSC CGL level Question Set 51, Algebra 12

SSC CGL level Solution Set 51, Algebra 12

SSC CGL level Question Set 45, Algebra 11

SSC CGL level Solution Set 45, Algebra 11

SSC CGL level Question Set 35, Algebra 10

SSC CGL level Solution Set 35, Algebra 10

SSC CGL level Question Set 33, Algebra 9

SSC CGL level Solution Set 33, Algebra 9

SSC CGL level Question Set 23, Algebra 8

SSC CGL level Solution Set 23, Algebra 8

SSC CGL level Question Set 22, Algebra 7

SSC CGL level Solution Set 22, Algebra 7

SSC CGL level Question Set 13, Algebra 6

SSC CGL level Solution Set 13, Algebra 6

SSC CGL level Question Set 11, Algebra 5

SSC CGL level Solution Set 11, Algebra 5

SSC CGL level Question Set 10, Algebra 4

SSC CGL level Solution Set 10, Algebra 4

SSC CGL level Question Set 9, Algebra 3

SSC CGL level Solution Set 9, Algebra 3

SSC CGL level Question Set 8, Algebra 2

SSC CGL level Solution Set 8, Algebra 2

SSC CGL level Question Set 1, Algebra 1

SSC CGL level Solution Set 1, Algebra 1

Getting content links in your mail

You may get link of any content published