## Ninth SSC CGL level Question Set, 3rd on Algebra

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

To solve quickly you have to use suitable concepts and techniques and a number of these 10 are **hard algebra questions**. But don't hesitate. Go ahead and try them.

This forms the 9th question set for SSC CGL and 3rd on Algebra and can be used as a **min mock-test.**

For maximum benefit, you should *take this timed test*, *score your performance* and then *get your doubts clear from the corresponding solution set*.

*The link of the solutions is given at the end.*

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.**

### Ninth question set, 3rd on Algebra - 10 problems for SSC CGL exam - time 12 mins

**Q1.** If $a -2b = 4$, then the value of the expression $a^3 - 8b^3 -24ab -64$ is,

- 0
- 3
- 2
- -1

**Q2.** If $x + \displaystyle\frac{1}{x} = 4$, then $x^4 + \displaystyle\frac{1}{x^4}$ is,

- 124
- 194
- 64
- 81

**Q3.** If $x^2 = y + z$, $y^2= z + x$ and $z^2 = x + y$, then the value of $\displaystyle\frac{1}{x + 1} + \displaystyle\frac{1}{y + 1} + \displaystyle\frac{1}{z + 1} $ is,

- 2
- -1
- 4
- 1

**Q4.** If $x = 7 - 4\sqrt{3}$, then $x^{\frac{1}{2}} + x^{\frac{-1}{2}}$ is,

- $4$
- $3\sqrt{3}$
- $7$
- $2\sqrt{3}$

**Q5.** $(y -z)^3 + (z -x)^3 + (x -y)^3$ is equal to,

- $(x - y)(y + z)(x - z)$
- $(y - z)(z + x)(y - x)$
- $(y - z)(z - x)(x - y)$
- $3(y - z)(z - x)(x - y)$

**Q6.** The sum of $\displaystyle\frac{a}{b}$ and its reciprocal is 1 and $a\neq{0}$, $b\neq{0}$. The value of $a^3 + b^3$ is,

- 2
- 0
- $-1$
- 1

**Q7.** If $ x = b + c - 2a$, $y = c + a - 2b$ and $z = a + b -2c$, then the value of $x^2 + y^2 - z^2 + 2xy$ is,

- $a + b + c$
- $0$
- $a - b + c$
- $a + b - c$

**Q8.** If $x = \displaystyle\frac{4ab}{a + b}$, where $a\neq{b}$, then the value of, $\displaystyle\frac{x + 2a}{x - 2a} + \displaystyle\frac{x + 2b}{x - 2b}$ is,

- a
- 2
- 2ab
- b

**Q9.** If $x = 3 + 2\sqrt{2}$ then the value of $\left(\sqrt{x} - \displaystyle\frac{1}{\sqrt{x}}\right)$ is,

- $2\sqrt{3}$
- $3\sqrt{3}$
- 2
- 1

**Q10.** If $x = 2 - 2^{\frac{1}{3}} + 2^{\frac{2}{3}}$, then the value of $x^3 - 6x^2 + 18x + 18$ is,

- 40
- 33
- 22
- 45

### Answers to the 10 algebra questions

**Q1. Answer:** Option a: 0.

**Q2. Answer:** Option b: 194.

**Q3. Answer:** Option d: 1.

**Q4. Answer:** Option a: $4$.

**Q5. Answer:** Option d: $3(y - z)(z - x)(x - y)$.

**Q6. Answer:** Option b: 0.

**Q7. Answer:** Option b: 0.

**Q8. Answer:** Option b: 2.

**Q9. Answer:** Option c: 2.

**Q10. Answer:** Option a: 40.

### Solutions to the problems

For detailed conceptual solutions with answers you should refer to the companion **SSC CGL level Solution Set 9 on Algebra.**

#### Video

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,*

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