## 74th SSC CGL level Question Set, 16th on Algebra

This is the 74th question set of 10 practice problem exercise for SSC CGL exam and the 16th on topic Algebra. For maximum gains, this test should be taken first and then its corresponding solution set should be referred to.

Before taking the test you may like to refer to 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 Algebra problem solving by Componendo dividendo*.

### 74th question set - 10 problems for SSC CGL exam: 16th on topic Algebra - answering time 12 mins

**Q1. **If $a:b=2:3$ and $b:c=4:5$, find $a^2:b^2:bc$.

- $16:36:20$
- $4:9:45$
- $4:36:40$
- $16:36:45$

**Q2.** If $a+b+c=4\sqrt{3}$ and $a^2+b^2+c^2=16$, then the ratio of $a:b:c$ is,

- $1:\sqrt{2}:\sqrt{3}$
- $1:2:3$
- $1:1:1$
- None of these

**Q3. **If $x^2+y^2+z^2=2(x+z-1)$, then the value of $x^3+y^3+z^3$ is,

- $0$
- $1$
- $2$
- $-1$

**Q4. **If $a+b+c=0$, then the value of $2b^2c^2+2c^2a^2+2a^2b^2 - a^4-b^4-c^4$ is,

- 7
- 0
- 28
- 14

**Q5. **If $\displaystyle\frac{a}{b}=\frac{2}{3}$ and $\displaystyle\frac{b}{c}=\frac{4}{5}$ then the value of the ratio $\displaystyle\frac{a+b}{b+c}$ is,

- $\displaystyle\frac{20}{27}$
- $\displaystyle\frac{8}{6}$
- $\displaystyle\frac{6}{8}$
- $\displaystyle\frac{27}{20}$

**Q6.** If $U_n=\displaystyle\frac{1}{n}-\displaystyle\frac{1}{n+1}$, then the value of $U_1+U_2+U_3+U_4+U_5$ is,

- $\displaystyle\frac{1}{2}$
- $\displaystyle\frac{1}{3}$
- $\displaystyle\frac{5}{6}$
- $\displaystyle\frac{2}{5}$

** Q7.** If $a*b=2a+3b-ab$, then the value of $(3*5+5*3)$ is,

- 2
- 4
- 6
- 10

** Q8.** If $\displaystyle\frac{x}{2x^2+5x+2}=\frac{1}{6}$, then the value of $x+\displaystyle\frac{1}{x}$ is,

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

**Q9.** If $x=\displaystyle\frac{\sqrt{3}+1}{\sqrt{3}-1}$, and $y=\displaystyle\frac{\sqrt{3}-1}{\sqrt{3}+1}$, then the value of $x^2+y^2$ is,

- $13$
- $0$
- $14$
- $15$

** Q10.** If $\displaystyle\frac{2x-y}{x+2y}=\displaystyle\frac{1}{2}$, then the value of $\displaystyle\frac{3x-y}{3x+y}$ is,

- $1$
- $\displaystyle\frac{3}{5}$
- $\displaystyle\frac{1}{5}$
- $\displaystyle\frac{4}{5}$

The conceptual solutions in a few steps to these questions are available in the corresponding solution set, * SSC CGL level Solution Set 74, Algebra 16*.

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

**Part 1: Q1 to Q5**

**Part 2: Q6 to Q10**

### Answers to questions

**Problem 1.** Answer: Option d: $16:36:45$.

**Problem 2.** Answer: Option c : $1:1:1$.

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

**Problem 4.** Answer: Option b: 0.

**Problem 5.** Answer: Option a: $\displaystyle\frac{20}{27}$.

**Problem 6.** Answer: Option c : $\displaystyle\frac{5}{6}$.

**Problem 7.** Answer: Option d: 10.

**Problem 8.** Answer: Option d: $\displaystyle\frac{1}{2}$.

**Problem 9.** Answer: Option c: $14$.

**Problem 10.** Answer: Option b: $\displaystyle\frac{3}{5}$.

### Additional help on SSC CGL Algebra

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