## 9th SSC CGL Tier II level Question Set, 4th on Algebra

This is the 9th question set of 10 practice problem exercise for SSC CGL Tier II exam and the 4th on topic Algebra.

For maximum gains, the test should be taken first, that is obvious. But more importantly, to absorb the concepts, techniques and deductive reasoning elaborated through these solutions, one must solve many problems in a systematic manner using this conceptual analytical approach.

Learning by doing is the best learning. There is no other alternative towards achieving excellence.

### 9th question set - 10 problems for SSC CGL exam: 4th on topic Algebra - answering time 12 mins

**Q1. **If $x+\displaystyle\frac{2}{x}=1$, then the value of $\displaystyle\frac{x^2+x+2}{x^2(1-x)}$ is,

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

**Q2.** If $4x+5y=83$, and $3x : 2y=21 : 22$, then $(y-x)$ equals to,

- 4
- 7
- 3
- 11

**Q3. **If $\displaystyle\frac{3-5x}{2x} + \displaystyle\frac{3-5y}{2y} + \displaystyle\frac{3-5z}{2z}=0$, then the value of $\displaystyle\frac{2}{x}+\displaystyle\frac{2}{y}+\displaystyle\frac{2}{z}$ is,

- 10
- 5
- 20
- 15

**Q4. **If $\displaystyle\frac{2p}{p^2-2p+1}=\frac{1}{4}$ then the value of $\left(p+\displaystyle\frac{1}{p}\right)$ is,

- $1$
- $10$
- $\displaystyle\frac{2}{5}$
- $7$

**Q5. **If $2x=\sqrt{a}+\displaystyle\frac{1}{\sqrt{a}}$, and $a \gt 0$, then the value of $\displaystyle\frac{\sqrt{x^2-1}}{x-\sqrt{x^2-1}}$ is,

- $a+1$
- $a-1$
- $\frac{1}{2}(a-1)$
- $\frac{1}{2}(a+1)$

**Q6.** If $x^2+y^2+z^2=xy+yz+zx$, then the value of $\displaystyle\frac{3x^4+7y^4+5z^4}{5x^2y^2+7y^2z^2+3z^2x^2}$ is,

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

** Q7.** If $\displaystyle\frac{a^2-bc}{a^2+bc}+\displaystyle\frac{b^2-ca}{b^2+ca}+\displaystyle\frac{c^2-ab}{c^2+ab}=1$, then the value of $\displaystyle\frac{a^2}{a^2+bc}+\displaystyle\frac{b^2}{b^2+ca}+\displaystyle\frac{c^2}{c^2+ab}$ is,

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

** Q8.** If $2\left(x^2+\displaystyle\frac{1}{x^2}\right) - \left(x-\displaystyle\frac{1}{x}\right) -7 =0$ then the two valid values of $x$ are,

- $0$, $1$
- $\frac{1}{2}$, $1$
- $1$, $2$
- $2$, $-\frac{1}{2}$

**Q9.** If $x=\sqrt[3]{a+\sqrt{a^2+b^3}}+\sqrt[3]{a-\sqrt{a^2+b^3}}$, then $x^3+3bx$ is equal to,

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

** Q10.** If $bc+ca+ab=abc$, then the value of $\displaystyle\frac{b+c}{bc(a-1)} + \displaystyle\frac{c+a}{ca(b-1)}+\displaystyle\frac{a+b}{ab(c-1)}$ is,

- $0$
- $1$
- $-\frac{1}{2}$
- $-\frac{3}{2}$

For detailed conceptual solutions to the questions refer to * SSC CGL Tier II level Solution set 9 Algebra 4*.

Watch **quick solutions in two-part video.**

**Part I: Q1 to Q5**

**Part II: Q6 to Q10**

### Answers to the questions

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

**Problem 2:** Answer: Option a : 4.

**Problem 3:** Answer: Option a: 10.

**Problem 4:** Answer: Option b: 10.

**Problem 5:** Answer: Option c: $\frac{1}{2}(a-1)$.

**Problem 6:** Answer: Option b : $1$.

**Problem 7:** Answer: Option a: $2$.

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

**Problem 9:** Answer: Option d: $2a$.

**Problem 10:** Answer: Option b: $1$.

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