## 45th SSC CGL level Question Set, 11th on Algebra

This is the 45th question set of 10 practice problem exercise for SSC CGL exam and 11th 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 the 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.

### 45th question set - 10 problems for SSC CGL exam: 11th on topic Algebra - answering time 15 mins

**Problem 1.**

If $\displaystyle\frac{5x}{2x^2+5x+1}=\frac{1}{3}$, then the value of $\left(x+\displaystyle\frac{1}{2x}\right)$ is,

- 5
- 10
- 15
- 20

**Problem 2.**

If $x^2+1=2x$, then the value of $\displaystyle\frac{x^4+\displaystyle\frac{1}{x^2}}{x^2-3x+1}$ is,

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

**Problem 3.**

If $x^3+\displaystyle\frac{3}{x}=4(a^3+b^3)$ and $3x+\displaystyle\frac{1}{x^3}=4(a^3-b^3)$ then $a^2-b^2$ is equal to,

- $1$
- $0$
- $4$
- $2$

**Problem 4.**

If $ab + bc+ca=0$, then the value of $\displaystyle\frac{1}{a^2-bc} +\displaystyle\frac{1}{b^2-ac}+\displaystyle\frac{1}{c^2-ab}$ is,

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

**Problem 5.**

If $x$ is a rational number and $\displaystyle\frac{(x+1)^3-(x-1)^3}{(x+1)^2-(x-1)^2}=2$ then the sum of numerator and denominator of $x$ is,

- $7$
- $4$
- $5$
- $3$

**Problem 6.**

If $a+b+c=0$ then the value of $(a+b-c)^2+(b+c-a)^2+(c+a-b)^2$ will be equal to,

- $4(a^2+b^2+c^2)$
- $4(ab+bc+ca)$
- $0$
- $8abc$

**Problem 7.**

If $x^2+y^2=5xy$, ,then the value of $\left(\displaystyle\frac{x^2}{y^2}+\displaystyle\frac{y^2}{x^2}\right)$ is equal to,

- $32$
- $16$
- $-23$
- $23$

**Problem 8.**

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

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

**Problem 9.**

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 numbers, then $a+b+c$ is equal to,

- 1
- 3
- 0
- 2

**Problem 10.**

If $x=7+4\sqrt{3}$ then the value of $\left(\sqrt{x}+\displaystyle\frac{1}{\sqrt{x}}\right)$ is,

- $2\sqrt{3}$
- $-2\sqrt{3}$
- $4$
- $-4$

### Answers to the questions

**Problem 1.** **Answer:** Option a: 5.

**Problem 2.** **Answer:** Option b : $-2$.

**Problem 3. Answer:** Option a: $1$.

**Problem 4.** **Answer:** Option a: $0$.

**Problem 5.** **Answer:** Option b: $4$.

**Problem 6.** **Answer:** Option a : $4(a^2+b^2+c^2)$.

**Problem 7.** **Answer:** Option d: $23$.

**Problem 8.** **Answer:** Option c: $-1$.

**Problem 9.** **Answer:** Option c: 0.

**Problem 10.** **Answer: **Option a: $4$.

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