## First SSC CGL Question Set on Algebra

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

It is emphasized here that answering in MCQ test is not at all the same as answering in a school test where you need to derive the solution in perfectly elaborated steps.

In MCQ test instead, you need basically 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 concepts of the topics
- is adequately fast in mental math calculation
- should try to solve each problem using the most basic concepts in the specific topic area and
- does most of the deductive reasoning and calculation in his head rather than on paper.

Actual problem solving happens in item 3 and 4 above. How to do that?

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

### First question set- 10 problems for SSC CGL exam - time 18 mins

**Q1.** The value of, $\frac{1}{a^2 +ax + x^2}- \frac{1}{a^2 - ax + x^2} +\frac{2ax}{a^4 + a^2x^2 + x^4}$ is,

- 2
- 1
- -1
- 0

**Q2.** If $x^3 + y^3 = 9$ and $x + y = 3$ then the value of $x^4 + y^4$ is,

- 81
- 32
- 27
- 17

**Q3.** For any real number $x$ the maximum value of $4 - 6x - x^2$ is,

- 4
- 7
- 9
- 13

**Q4.** If $5^{\sqrt{x}} + 12^{\sqrt{x}} = 13^{\sqrt{x}}$ then value of $x$ is,

- $\frac{25}{4}$
- 4
- 6
- 9

**Q5.** If $a + b + c = 0$ then the value of $\frac{a^2 + b^2 + c^2}{a^2 - bc}$ is,

- 0
- 1
- 2
- 3

**Q6.** If $x^2 + 2 = 2x$ then the value of $x^4 - x^3 + x^2 + 2$ will be,

- 0
- 1
- -1
- $\sqrt{2}$

**Q7.** If $x = (\sqrt{2} + 1)^{-\frac{1}{3}}$, then the value of $\left(x^3 - \frac{1}{x^3}\right)$,

- $0$
- $-2$
- $-\sqrt{2}$
- $\sqrt{2}$

**Q8.** If $4b^2 + \frac{1}{b^2}=2$, then value of $8b^3 + \frac{1}{b^3}$ is,

- 0
- 2
- 1
- 5

**Q9.** If $x^\frac{1}{3} + y^\frac{1}{3} - z^\frac{1}{3} = 0$ then value of $(x + y - z)^3 + 27xyz$ is,

- $-1$
- 1
- 0
- 27

**Q10.** If $x^{x\sqrt{x}} = (x\sqrt{x})^x$ then $x$ is equal to,

- $\frac{4}{9}$
- $\frac{2}{3}$
- $\frac{9}{4}$
- $\frac{3}{2}$

You can refer to the corresponding solution set at