## 81st SSC CGL level Question Set, 17th on Algebra

This is the 81st question set of 10 practice problem exercise for SSC CGL exam and the 17th on topic Algebra. For maximum gains, the test should be taken first and then the corresponding solution set should be referred to.

Answers and solution link are at the end.

Before taking the test you may like to refer to our **concept tutorials** on Algebra and other related topics,

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

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### 81st question set - 10 problems for SSC CGL exam: 17th on topic Algebra - answering time 12 mins

**Q1. **If $x+\displaystyle\frac{1}{x}=3$, then value of $x^8+\displaystyle\frac{1}{x^8}$ is,

- 2213
- 2207
- 2201
- 2203

**Q2.** If $(x-4)(x^2+4x+16)=x^3-p$, then value of $p$ is,

- 27
- 0
- 8
- 64

**Q3. **If $a+b+c=15$ and $\displaystyle\frac{1}{a}+\displaystyle\frac{1}{b}+\displaystyle\frac{1}{c}=\displaystyle\frac{71}{abc}$, then the value of $a^3+b^3+c^3-3abc$ is,

- 180
- 160
- 220
- 200

**Q4. **If $x=12$, and $y=4$, then the value of $(x+y)^{\displaystyle\frac{x}{y}}$ is,

- 570
- 48
- 1792
- 4096

**Q5. **If $xy+yz+zx=1$, then the value of $\displaystyle\frac{1+y^2}{(x+y)(y+z)}$ is,

- 1
- 4
- 2
- 3

**Q6.** If $x+y+z=0$, then the value of $\displaystyle\frac{x^2}{3z}+\displaystyle\frac{y^3}{3xz}+\displaystyle\frac{z^2}{3x}$ is,

- $0$
- $3y$
- $y$
- $xz$

** Q7.** If the expression $(px^3-2x^2-qx+18)$ is completely divisible by $(x^2-9)$, then the ratio of $p$ to $q$ is,

- 9 : 1
- 1 : 9
- 3 : 1
- 1 : 3

**Q8.** If $\displaystyle\frac{x}{3}+\displaystyle\frac{3}{x}=1$, then the value of $x^3$ is,

- $0$
- $27$
- $-27$
- $1$

**Q9.** If $\displaystyle\frac{1}{x}+\displaystyle\frac{1}{y}+\displaystyle\frac{1}{z}=0$ and $x+y+z=9$, then the value of $x^3+y^3+z^3-3xyz$ is,

- 81
- 6561
- 729
- 361

** Q10.** If $a(a+b+c)=45$, $b(a+b+c)=75$ and $c(a+b+c)=105$, then the value of $a^2+b^2+c^2$ is,

- 75
- 83
- 225
- 217

Detailed solution to the questions are available at,

**SSC CGL Level Solution set 81 Algebra 17.**

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

**Part 1: Q1 to Q5**

**Part 2: Q6 to Q10**

### Answers to the questions

**Problem 1.** Answer: Option b: 2207.

**Problem 2.** Answer: Option d : 64.

**Problem 3.** Answer: Option a: 180.

**Problem 4.** Answer: Option d: 4096.

**Problem 5.** Answer: Option a: 1.

**Problem 6.** Answer: Option c : $y$.

**Problem 7.** Answer: Option b: 1 : 9.

**Problem 8.** Answer: Option c: $-27$.

**Problem 9.** Answer: Option c: 729.

**Problem 10.** Answer: Option b: 83.

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