## Eleventh SSC CGL level Question Set, topic Algebra

This is the eleventh Question set of 10 practice problems on topic Algebra for SSC CGL exam as well as school students* interested in elegant problem solving*. *Students must complete this question set in prescribed time first and then only refer to the ** corresponding solution set*.

This exercise set containing 10 problems highlights the need of solving the problems using powerful strategies *rather than brute force conventional deduction methods*.

Some of these questions are a bit advanced in nature and require a few new types of algebraic patttern recognition and abilities to be used.

* Recommendation: Before answering the relevant 10 problem question set you may like to go through the Algebra concepts under the subsection of Efficient Math Problem Solving *as well as

*the tutorial on*

**Basic and rich Alegebra concepts**.### Eleventh question set on Algebra - 10 problems for SSC CGL exam - time 12 mins

**Q1.** If $a$, $b$ and $c$ are non-zero and $a + \displaystyle\frac{1}{b} = 1$ and $b + \displaystyle\frac{1}{c} = 1$, the value of $abc$ is,

- 3
- -1
- 1
- -3

**Q2.** If $a + \displaystyle\frac{1}{a - 2} = 4$, then $(a - 2)^2 + \displaystyle\frac{1}{(a - 2)^2}$ is,

- 4
- 0
- -2
- 2

**Q3.** If $a + b + c = 2s$, then $\displaystyle\frac{(s - a)^2 + (s - b)^2 + (s - c)^2}{a^2 + b^2 + c^2}$ is,

- $0$
- $a^2 + b^2 + c^2$
- $1$
- $2$

**Q4.** If $xy(x + y) = 1$, then $\displaystyle\frac{1}{x^3y^3} - x^3 - y^3$ is,

- $1$
- $-1$
- $3$
- $-3$

**Q5.** If $a + b + c = 6$, $a^2 + b^2 + c^2 = 14$ and $a^3 + b^3 + c^3 = 36$, then the value of $abc$ is,

- 3
- 6
- 9
- 12

**Q6.** The minimum value of $(a - 2)(a - 9)$ is,

- $\displaystyle\frac{-11}{4}$
- $0$
- $\displaystyle\frac{-49}{4}$
- $\displaystyle\frac{49}{4}$

**Q7.** The terms $a$, $1$, and $b$ are in AP and the terms $1$, $a$ and $b$ are in GP. Find the values of $a$ and $b$, where $a\neq{b}$.

- 4, 1
- 2, 4
- -2, 1
- -2, 4

**Q8.** If $x\neq{0}$, $y\neq{0}$ and $z\neq{0}$, and $\displaystyle\frac{1}{x^2} + \displaystyle\frac{1}{y^2} + \displaystyle\frac{1}{z^2} = \displaystyle\frac{1}{xy} + \displaystyle\frac{1}{yz} + \displaystyle\frac{1}{zx}$, then the relation between $x$, $y$ and $z$ is,

- $x + y = z$
- $x + y + z = 0$
- $x=y=z$
- $\displaystyle\frac{1}{x} + \displaystyle\frac{1}{y} + \displaystyle\frac{1}{z} = 0$

**Q9.** If $a^2 - 4a - 1 = 0$, then $a^2 + \displaystyle\frac{1}{a^2} + 3a - \displaystyle\frac{3}{a}$ is,

- 25
- 35
- 40
- 30

**Q10.** 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, find the value of $a + b + c$.

- 3
- 0
- 2
- 1

### Solutions to the problems

For detailed conceptual solutions with answers you should refer to the companion * SSC CGL level Solution Set 11 on Algebra* where you will also get link references to all the reading materials on Algebra.