## 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,

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

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