SSC CGL level Question Set 8, Algebra

Eighth SSC CGL level Question Set, 2nd on Algebra

This contains 10 algebra questions and answers for competitive exams, specifically for SSC CGL.

To solve these questions quickly you have to use suitable concepts and techniques.

A number of these 10 are hard algebra questions. But don't hesitate. Go ahead and try them.

This forms the 8th question set for SSC CGL and 2nd on Algebra and can be used as a mini mock test.

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.

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

Q1. If $a = \sqrt{7 + 2\sqrt{12}}$ and $b = \sqrt{7 - 2\sqrt{12}}$, then $a^3 + b^3$ is,

1. 52
2. 40
3. 44
4. 48

Q2. If $x + \displaystyle\frac{2}{x} = 1$, then $\displaystyle\frac{x^2 + x + 2}{x^2(1 - x)}$ is,

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

Q3. If $x^3 + \displaystyle\frac{3}{x} = 4(a^3 + b^3)$ and $3x + \displaystyle\frac{1}{x^3} = 4(a^3 - b^3)$, then $a^2 - b^2$ is,

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

Q4. If $x^2 -4x + 1 = 0$, then $x^3 + \displaystyle\frac{1}{x^3}$ is, 

1. 44
2. 64
3. 48
4. 52

Q5. If $x^4 + \displaystyle\frac{1}{x^4} = 119$ and $x \gt 1$, then positive value of  $x^3 - \displaystyle\frac{1}{x^3}$ is,

1. 27
2. 36
3. 25
4. 49

Q6. If $x^3 + y^3 = 9$ and $x + y = 3$, then value of $\displaystyle\frac{1}{x} + \displaystyle\frac{1}{y}$ will be,

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

Q7. If $ a : b = 2 : 3$ and $b : c = 4 : 5$, then the value of $a^2 : b^2 : bc$ is,

1. 16 : 36 : 20
2. 16 : 36 : 45
3. 4 : 9 : 45
4. 4 : 36 : 40

Q8. If $ a : b = 3 : 2$, then the ratio of, $2a^2 + 3b^2 : 3a^2 - 2b^2$ is,

1. 6 : 5
2. 30 : 19
3. 12 : 5
4. 5 : 3

Q9. The expression $x^4 - 2x^2 + k$ will be a perfect square if value of $k$ is,

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

Q10. If $a = 11$ and $b = 9$, then the value of, $\displaystyle\frac{a^2 + b^2 + ab}{a^3 - b^3}$ is,

1. $20$
2. $\displaystyle\frac{1}{2}$
3. $\displaystyle\frac{1}{20}$
4. $2$

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Answers to the 10 algebra questions

Q1. Answer: Option a: 52.

Q2. Answer: Option c: 1.

Q3. Answer: Option a: 1.

Q4. Answer: Option d: 52.

Q5. Answer: Option b: 36.

Q6. Answer: Option b: $\displaystyle\frac{3}{2}$.

Q7. Answer: Option b: 16 : 36 : 45.

Q8. Answer: Option b: 30 : 19.

Q9. Answer: Option a: 1.

Q10. Answer: Option b: $\displaystyle\frac{1}{2}$.

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Solutions to the problems

For detailed conceptual solutions with answers you should refer to the companion SSC CGL level Solution Set 8 on Algebra.

Video

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

Part I: Q1 to Q5

Part II: Q6 to Q10

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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.

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