## 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,**

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

* SSC CGL level difficult Algebra problem solving by Componendo dividendo*.

### 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.**

### 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.

### Additional help on SSC CGL Algebra

Apart from a **large number of question and solution sets** and a valuable article on "* 7 Steps for sure success on Tier 1 and Tier 2 of SSC CGL*" rich with concepts and links, you may refer to our other articles specifically on Algebra listed on latest shown first basis,

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#### SSC CGL level Question and Solution Sets on Algebra

**SSC CGL level Question Set 81, Algebra 17**

**SSC CGL level Solution Set 81, Algebra 17**

**SSC CGL level Question Set 74, Algebra 16**

**SSC CGL level Solution Set 74, Algebra 16**

**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 Solution Set 35 on Algebra 10**

**SSC CGL level Question Set 35 on Algebra 10**

**SSC CGL level Solution Set 33 on Algebra 9**

**SSC CGL level Question Set 33 on Algebra 9**

**SSC CGL level Solution Set 23 on Algebra 8**

**SSC CGL level Question Set 23 on Algebra 8**

**SSC CGL level Solution Set 22 on Algebra 7**

**SSC CGL level Question Set 22 on Algebra 7**

**SSC CGL level Solution Set 13 on Algebra 6**

**SSC CGL level Question Set 13 on Algebra 6**

**SSC CGL level Question Set 11 on Algebra 5**

**SSC CGL level Solution Set 11 on Algebra 5**

**SSC CGL level Question Set 10 on Algebra 4**

**SSC CGL level Solution Set 10 on Algebra 4**

**SSC CGL level Question Set 9 on Algebra 3**

**SSC CGL level Solution Set 9 on Algebra 3**

**SSC CGL level Question Set 8 on Algebra 2**

**SSC CGL level Solution Set 8 on Algebra 2**

**SSC CGL level Question Set 1 on Algebra 1**

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