## 51st SSC CGL level question Set, 12th on Algebra

This is the 51st question set of 10 practice problem exercise for SSC CGL exam and 12th 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 these 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 go through 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 problem solving by Componendo dividendo.**

### 51st question set - 10 problems for SSC CGL exam: 12th on topic Algebra - answering time 15 mins

**Problem 1.**

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

- $1$
- $4$
- $-1$
- $-4$

**Problem 2.**

If $a^2+b^2+c^2+3=2(a+b+c)$ then the value of $(a+b+c)$ is,

- 2
- 3
- 5
- 4

**Problem 3.**

If $a^2-4a-1=0$, then the value of $a^2+\displaystyle\frac{1}{a^2}+3a-\displaystyle\frac{3}{a}$ is,

- 40
- 35
- 30
- 25

**Problem 4.**

If $x+\displaystyle\frac{1}{x}=99$, find the value of $\displaystyle\frac{100x}{2x^2+102x+2}$.

- $\displaystyle\frac{1}{6}$
- $\displaystyle\frac{1}{3}$
- $\displaystyle\frac{1}{2}$
- $\displaystyle\frac{1}{4}$

**Problem 5.**

If $\sqrt{1+\displaystyle\frac{x}{961}}=\displaystyle\frac{32}{31}$, then the value of $x$ is,

- 63
- 64
- 61
- 65

**Problem 6.**

If $1.5a=0.04b$ then the value of $\displaystyle\frac{b-a}{b+a}$ will be equal to,

- $\displaystyle\frac{73}{77}$
- $\displaystyle\frac{75}{2}$
- $\displaystyle\frac{2}{75}$
- $\displaystyle\frac{77}{33}$

**Problem 7.**

The value of the expression, $\displaystyle\frac{(a-b)^2}{(b-c)(c-a)}+\displaystyle\frac{(b-c)^2}{(a-b)(c-a)}+\displaystyle\frac{(c-a)^2}{(a-b)(b-c)}$ is,

- $2$
- $3$
- $0$
- $\displaystyle\frac{1}{3}$

**Problem 8.**

If $9\sqrt{x}=\sqrt{12}+\sqrt{147}$, then $x$ is,

- 5
- 2
- 3
- 4

**Problem 9.**

If $p:q=r:s=t:u=2:3$ then $(mp+nr+ot):(mq+ns+ou)$ is equal to,

- 2 : 3
- 3 : 2
- 2 : 1
- 1 : 2

**Problem 10.**

If $\displaystyle\frac{1}{a+1}+\displaystyle\frac{1}{b+1}+\displaystyle\frac{1}{c+1}=2$ then $a^2+b^2+c^2$ is,

- $\displaystyle\frac{3}{4}$
- $\displaystyle\frac{1}{3}$
- $\displaystyle\frac{27}{16}$
- $\displaystyle\frac{4}{3}$

### Answers to the questions

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

Problem 2. **Answer:** Option b : 3.

Problem 3. **Answer:** Option c: 30.

Problem 4. **Answer:** Option b: $\displaystyle\frac{1}{3}$.

Problem 5. **Answer:** Option a: 63.

Problem 6. **Answer:** Option a : $\displaystyle\frac{73}{77}$.

Problem 7. **Answer:** Option b: $3$.

Problem 8. **Answer:** Option c: 3.

Problem 9. **Answer:** Option a: 2 : 3.

problem 10. **Answer: **Option a: $\displaystyle\frac{3}{4}$.

### Solutions to the problems

For detailed conceptual solutions with answers you should refer to the companion **S*** SC CGL level Solution Set 51 on Algebra 12* where you will get detailed explanations on easiest path to the solutions.

Watch **quick solutions on two-part video**.

**Part I: Q1 to Q5**

**Part II: Q6 to Q10**

### Guided help on Suresolv Algebra

All Suresolv Algebra articles are listed with links at the end, but it is unguided list.

To use this *extensive range of articles on quick algebra* problem solving **effectively**, *follow the guide,*

**5 step Suresolv Algebra Reading and Practice Guide for SSC CGL Tier II and Other competitive exams.**

*Basically, it is how to read and practice Suresolv Algebra guide.*

**This contains even list of puzzles or even high school math articles on Algebra. **

Wish you all the sure success.

### Resources on Suresolv 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 and other related topics

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

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

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

**Proof of least value of sum of reciprocals for any number of positive variables**

**How to factorize 25 selected quadratic equations quickly by factor analysis**

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

**SSC CGL Tier II level Solved Question Set 30, Algebra 7**

**SSC CGL Tier II level Solution Set 17, Algebra 6**

**SSC CGL Tier II level Question Set 17, Algebra 6**

**SSC CGL Tier II level Question Set 14, Algebra 5**

**SSC CGL Tier II level Solution Set 14, Algebra 5**

**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 a difficult surd algebra question by repeated componendo dividendo in a few steps 17**

**How to solve difficult SSC CGL level problem mentally using patterns and methods 16**

**How to solve a difficult SSC CGL Algebra problem mentally in quick time 15**

**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 Solved Question Set 90, Algebra 18**

**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 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**

#### SSC CPO CAPF CISF level Solved Question sets on Algebra

**SSC CPO level Solved Question Set 1 Algebra 1**

**SSC CPO level Solved Question Set 2 Algebra 2**

#### SSC CHSL level Solved Question Sets on Algebra

**SSC CHSL level Solved Question set 11 on Algebra 1**

**SSC CHSL level Solved Question set 12 on Algebra 2**

**SSC CHSL level Solved Question set 13 on Algebra 3**

**SSC CHSL level Solved Question set 14 on Algebra 4**

### 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**