You are here

SSC CGL level Question Set 22, Algebra

Hard algebra questions with answers for competitive exams SSC CGL Math 22

Hard algebra questions answers test set SSC CGL math 22

The 10 hard algebra questions with answers for SSC CGL math test will greatly benefit your practice and proficiency in solving difficult algebra questions.

The questions we have selected are from actual previous SSC CGL exams, ensuring maximum impact in a short time.

The practice will also prepare you for SSC CHSL, SSC CPO, and other competitive exams, while establishing a strong foundation for the SSC CGL Tier II exam.

Check your performance with the answers at the end.

Set the timer ON and take the test now in all seriousness. And after the test, make sure you don’t miss our valuable TIPs on quick answering objective hard algebra questions quickly and confidently.

Hard algebra questions for competitive exams - SSC CGL math mock-test set 22 - time to answer 12 mins

Q1. The value of $a = \displaystyle\frac{b^2}{b-a}$, then the value of $a^3 + b^3$ is,

  1. 1
  2. 6ab
  3. 2
  4. 0

Q2. If $x = \sqrt[3]{5} + 2$, then the value of $x^3 - 6x^2 + 12x -13$, is,

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

Q3. If $p=124$, then the value of $\sqrt[3]{p(p^2 + 3p + 3) + 1}$, is,

  1. 123
  2. 5
  3. 7
  4. 125

Q4. The factors of $(a^2 + 4b^2 + 4b - 4ab - 2a - 8)$ are,

  1. $(a + 2b - 4)(a + 2b + 2)$
  2. $(a - 2b - 4)(a - 2b + 2)$
  3. $(a + 2b - 1)(a - 2b + 1)$
  4. $(a - b + 2)(a - 4b - 4)$

Q5. When the expression $12x^3 - 13x^2 -5x + 7$ is divided by $3x + 2$ the remainder is,

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

Q6. If $x(x-3)=-1$ then the value of $x^3(x^3 - 18)$ will be,

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

Q7. If $x = \sqrt{5} + 2$, then the value of $\displaystyle\frac{2x^2 - 3x - 2}{3x^2 - 4x - 3}$ is,

  1. 0.525
  2. 0.625
  3. 0.785
  4. 0.185

Q8. If $\displaystyle\frac{p}{a} + \displaystyle\frac{q}{b} + \displaystyle\frac{r}{c} = 1$, and $\displaystyle\frac{a}{p} + \displaystyle\frac{b}{q} + \displaystyle\frac{c}{r} = 0$, where $p$, $q$, $r$, $a$, $b$ and $c$ are non-zero, the value of $\displaystyle\frac{p^2}{a^2} + \displaystyle\frac{q^2}{b^2} + \displaystyle\frac{r^2}{c^2}$ is,

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

Q9. If equation $2x^2 -7x + 12 = 0$ has two roots $\alpha$ and $\beta$, then the value of $\displaystyle\frac{\alpha}{\beta} + \displaystyle\frac{\beta}{\alpha}$ is,

  1. $\displaystyle\frac{1}{24}$
  2. $\displaystyle\frac{7}{24}$
  3. $\displaystyle\frac{7}{2}$
  4. $\displaystyle\frac{97}{24}$

Q10. If $a - b= 3$, and $a^3 - b^3 = 117$, then absolute value of $a + b$ is,

  1. 5
  2. 7
  3. 3
  4. 9

Answers to the Hard algebra questions - SSC CGL math mini-mock test set 22

Q1. Answer: Option d. $0$.

Q2. Answer: Option a. $0$.

Q3. Answer: Option d. $125$.

Q4. Answer: Option b. $(a - 2b - 4)(a - 2b + 2)$.

Q5. Answer: Option c. $1$.

Q6. Answer: Option d. $-1$.

Q7. Answer: Option b. $0.625$.

Q8. Answer: Option d. $1$.

Q9. Answer: Option a. $\displaystyle\frac{1}{24}$.

Q10. Answer: Option b. $7$.

It’s okay if you don’t finish answering all 10 hard SSC CGL Algebra questions correctly in time. Repeated practice and pattern-based techniques will help you achieve the perfect score in 12 minutes or less.

Read on to learn how you can do it.

How to solve the questions quick and correct

To know how it is possible, learn the conceptual techniques for quickly and correctly solving this SSC CGL Algebra question set in the solutions,

SSC CGL level Solution Set 22, Algebra 7.

And go through the extensive Quick Algebra selected question solutions to build a strong foundation on how to use ALL pattern-based special algebra problem solving techniques.

Use these tips to further improve your skills.

TIPS for QUICK ANSWERING Objective Hard Algebra Questions

From years of experience in solving SSC CGL algebra questions quickly, the short list of tips for accurate and quick answering of difficult algebra questions are compiled.


1. Must have a good understanding of the BASIC CONCEPTS of the topic.

2. Are ADEQUATELY fast in mental math calculation: For SSC CGL math, lightning fast mental calculation NOT NEEDED at all.

3. Should FORGET USING TRICKS. Instead, first use basic concepts and then advanced concepts created from basic concepts. Identifying key patterns in a problem is vital for quick solution.

4. DO NOT MEMORIZE formulas. Practice solving many SELECTED problems, if needed REPEATEDLY, to know by heart how to identify the key patterns in the problem and take the action for solving the problem quick and correct.

5. WRITE DOWN the most used concepts and formulas for solving algebra MCQs in two sheets of paper (try to be short because it is for yourself). This writing down will help in recall when you need. You will get PRACTICALLY ALL FORMULAS AND TECHNIQUES NEEDED FOR SOLVING ALGEBRA MCQS IN SSC CGL in Suresolv. Go through the articles at your pace using the links in Guided help on Algebra in Suresolv.

6. DO MOST of the REASONING IN YOUR HEAD without touching pen on paper. Make it a habit during practice sessions. If needed repeat a test of 10 algebra mcqs.

7. Go through the most used algebra problem solving FORMULAS AND TECHNIQUES in Basic and rich Algebraic concepts for elegant solutions of SSC CGL problems.

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.