## 45th SSC CGL level Question Set, 11th on Algebra

This is the 45th question set of 10 practice problem exercise for SSC CGL exam and 11th on topic Algebra.

For maximum gains, the test should be taken first, that is obvious. But more importantly, to absorb the concepts, techniques and deductive reasoning elaborated through the solutions, one must solve many problems in a systematic manner using this conceptual analytical approach.

Learning by doing is the best learning. There is no other alternative towards achieving excellence.

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

**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.**

### 45th question set - 10 problems for SSC CGL exam: 11th on topic Algebra - answering time 15 mins

**Problem 1.**

If $\displaystyle\frac{5x}{2x^2+5x+1}=\frac{1}{3}$, then the value of $\left(x+\displaystyle\frac{1}{2x}\right)$ is,

- 5
- 10
- 15
- 20

**Problem 2.**

If $x^2+1=2x$, then the value of $\displaystyle\frac{x^4+\displaystyle\frac{1}{x^2}}{x^2-3x+1}$ is,

- $1$
- $-2$
- $0$
- $2$

**Problem 3.**

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 equal to,

- $1$
- $0$
- $4$
- $2$

**Problem 4.**

If $ab + bc+ca=0$, then the value of $\displaystyle\frac{1}{a^2-bc} +\displaystyle\frac{1}{b^2-ac}+\displaystyle\frac{1}{c^2-ab}$ is,

- $0$
- $1$
- $-1$
- $2$

**Problem 5.**

If $x$ is a rational number and $\displaystyle\frac{(x+1)^3-(x-1)^3}{(x+1)^2-(x-1)^2}=2$ then the sum of numerator and denominator of $x$ is,

- $7$
- $4$
- $5$
- $3$

**Problem 6.**

If $a+b+c=0$ then the value of $(a+b-c)^2+(b+c-a)^2+(c+a-b)^2$ will be equal to,

- $4(a^2+b^2+c^2)$
- $4(ab+bc+ca)$
- $0$
- $8abc$

**Problem 7.**

If $x^2+y^2=5xy$, ,then the value of $\left(\displaystyle\frac{x^2}{y^2}+\displaystyle\frac{y^2}{x^2}\right)$ is equal to,

- $32$
- $16$
- $-23$
- $23$

**Problem 8.**

If $x+\displaystyle\frac{2}{x}=1$, then tne value of $\displaystyle\frac{x^2+x+2}{x^2(x-1)}$ is,

- $2$
- $1$
- $-1$
- $-2$

**Problem 9.**

If $\displaystyle\frac{1}{\sqrt[3]{4} + \sqrt[3]{2} +1}=a\sqrt[3]{4}+b\sqrt[3]{2}+c$ and $a$, $b$ and $c$ are rational numbers, then $a+b+c$ is equal to,

- 1
- 3
- 0
- 2

**Problem 10.**

If $x=7+4\sqrt{3}$ then the value of $\left(\sqrt{x}+\displaystyle\frac{1}{\sqrt{x}}\right)$ is,

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

### Answers to the questions

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

**Problem 2.** **Answer:** Option b : $-2$.

**Problem 3. Answer:** Option a: $1$.

**Problem 4.** **Answer:** Option a: $0$.

**Problem 5.** **Answer:** Option b: $4$.

**Problem 6.** **Answer:** Option a : $4(a^2+b^2+c^2)$.

**Problem 7.** **Answer:** Option d: $23$.

**Problem 8.** **Answer:** Option c: $-1$.

**Problem 9.** **Answer:** Option c: 0.

**Problem 10.** **Answer: **Option a: $4$.

### Solutions to the problems

For detailed conceptual solutions with answers you should refer to the companion * SSC CGL level Solution Set 45 on Algebra* where you will get detailed explanations on easiest path to the solutions.

### 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,

#### First to read tutorials on Basic and rich Algebra concepts

**More rich algebraic concepts and techniques for elegant solutions of SSC CGL problems**

**Basic and rich algebraic concepts for elegant Solutions of SSC CGL problems**

#### SSC CGL Tier II level Questions and Solutions on Algebra

**SSC CGL Tier II level Question Set 9, Algebra 4**

**SSC CGL Tier II level Solution Set 9, Algebra 4**

**SSC CGL Tier II level Question Set 3, Algebra 3**

**SSC CGL Tier II level Solution Set 3, Algebra 3**

**SSC CGL Tier II level Question Set 2, Algebra 2**

**SSC CGL Tier II level Solution Set 2, Algebra 2**

**SSC CGL Tier II level Question Set 1, Algebra 1**

**SSC CGL Tier II level Solution Set 1, Algebra 1**

#### Efficient solutions for difficult SSC CGL problems on Algebra in a few steps

**How to solve difficult SSC CGL Algebra problems in a few steps 14**

**How to solve difficult SSC CGL Algebra problems in a few steps 13**

**How to solve difficult SSC CGL Algebra problems in a few steps 12**

**How to solve difficult SSC CGL Algebra problems in a few steps 11**

**How to solve difficult SSC CGL Algebra problems in a few assured steps 10**

**How to solve difficult SSC CGL Algebra problems in a few steps 9**

**How to solve difficult SSC CGL Algebra problems in a few steps 8**

**How to solve difficult SSC CGL Algebra problems in a few steps 7**

**How to solve difficult Algebra problems in a few simple steps 6**

**How to solve difficult Algebra problems in a few simple steps 5**

**How to solve difficult surd Algebra problems in a few simple steps 4**

**How to solve difficult Algebra problems in a few simple steps 3**

**How to solve difficult Algebra problems in a few simple steps 2**

**How to solve difficult Algebra problems in a few simple steps 1**

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

**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 levelĀ 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**

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

### Getting content links in your mail

#### You may get link of any content published

- from this site by
or,**site subscription** - on competitive exams by
.**exams subscription**