## Thirteenth SSC CGL level Question Set, Algebra

This is the thirteenth question set of 10 practice problem exercise for SSC CGL exam on topic Algebra. Students must complete this question set in prescribed time first and then only refer to the **corresponding solution set.**

It is emphasized here that answering in MCQ test is not the same as answering in a school test where you have to write the solution in detailed steps.

In MCQ test instead, you need to deduce the answer in shortest possible time and select the right choice. None will ask you about what steps you followed.

Based on our analysis and experience we have seen that, for accurate and quick answering, the student

- must have complete understanding of the basic and rich concepts on the topics,
- is adequately fast in mental math calculations,
- should try to solve each problem using the most basic concepts in the specific topic area, failing which will use the rich concept set and
- does most of the deductive reasoning and calculation in his or her head rather than on paper.

Actual problem solving happens in the last step. But how to do that?

You need to use **your problem solving abilities** only. There is no other recourse.

**Recommendation:**

*It is recommended that before you attempt the questions, you go through the basic and rich concepts on number system and concepts on algebra in addition to our algebra solution set 1, solution set 8, solution set 9, solution set 10 and solution set 11.*

*For general guidance in SSC CGL you may find 7 steps to success in SSC CGL Tier 1 and Tier 2 competitive tests useful.*

### Thirteenth question set- 10 problems for SSC CGL exam: topic Algebra - time 12 mins

**Q1. **The value of $\sqrt{(x - 2)^2} + \sqrt{(x - 4)^2}$, where $2\lt{x}\lt{3}$, is,

- $2x - 6$
- 3
- 2
- 4

**Q2.** If $x = 10^{0.48}$, $y = 10^{0.70}$ and $x^z = y^2$, then approximate value of $z$ is

- 1.88
- 2.9
- 3.7
- 1.45

**Q3.** If $\displaystyle\frac{a}{1 - a} + \displaystyle\frac{b}{1 - b} + \displaystyle\frac{c}{1 - c} = 1$, thenĀ the value of $\displaystyle\frac{1}{1 - a} + \displaystyle\frac{1}{1 - b} + \displaystyle\frac{1}{1 - c}$,

- 4
- 2
- 1
- 3

**Q4. **If $x$ is real then the minimum value of $4x^2 - x - 1$ is,

- $\displaystyle\frac{5}{8}$
- $-\displaystyle\frac{15}{16}$
- $\displaystyle\frac{15}{16}$
- $-\displaystyle\frac{17}{16}$

**Q5. **If $9\sqrt{x} = \sqrt{12} + \sqrt{147}$ then the value of $x$ is,

- 3
- 4
- 5
- 2

**Q6.** If $a$ and $b$ are positive integers such that $a^2 - b^2 = 19$ then $a$ is,

- 8
- 0
- 9
- 10

** Q7.** If $ax^2 + bx + c = a(x - p)^2$, then the relation between $a$, $b$ and $c$ can be expressed as,

- $b^2 = ac$
- $abc = 1$
- $2b = a + c$
- $b^2 = 4ac$

** Q8.** If $x = 5 - \sqrt{21}$, then value of $\displaystyle\frac{\sqrt{x}}{\sqrt{32 - 2x} - \sqrt{21}}$ is,

- $\displaystyle\frac{1}{\sqrt{2}}(\sqrt{3} - \sqrt{7})$
- $\displaystyle\frac{1}{\sqrt{2}}(\sqrt{7} - \sqrt{3})$
- $\displaystyle\frac{1}{\sqrt{2}}(\sqrt{7} + \sqrt{3})$
- $\displaystyle\frac{1}{\sqrt{2}}(3 + \sqrt{7})$

**Q9.** If $a^{\frac{1}{3}} = 11$ then $a^2 - 331a$ is

- 1331331
- 1334331
- 1331000
- 1330030

** Q10.** If $a = \displaystyle\frac{xy}{x + y}$, $b = \displaystyle\frac{xz}{x + z}$ and $c = \displaystyle\frac{yz}{y + z}$, where $a$, $b$ and $c$ are all non-zero numbers, then the value of $x$ is,

- $\displaystyle\frac{2abc}{ab + ac - bc}$
- $\displaystyle\frac{2abc}{ab + bc - ac}$
- $\displaystyle\frac{2abc}{ab + bc + ac}$
- $\displaystyle\frac{2abc}{ac + bc - ab}$

### Solutions to the questions

You may refer to the corresponding **solution set here.**

#### Video

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

**Part I:Q1 to Q5**

**Part II: Q6 to Q10**

### Other resources that you may find valuable

#### Concept tutorials on Algebra 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 Algebra problem solving by Componendo dividendo**

#### General guidelines for successful performance in SSC CGL test

**7 Steps for sure success in SSC CGL tier 1 and tier 2 competitive tests**

#### Difficult algebra problem solving using high power methods

**How to solve difficult algebra problems in a few steps**

#### SSC CGL Tier II level question and solution sets on Algebra

**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**

#### 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 level Solution Set 45, Algebra 11**

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

**SSC CGL level Solution Set 35, Algebra 10**

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

#### 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**

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