## 2nd SSC CGL Tier II level Question Set, 2nd on Algebra

This is the 2nd question set of 10 practice problem exercise for SSC CGL Tier II exam and also the 2nd 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.

### 2nd question set - 10 problems for SSC CGL exam: 2nd on topic Algebra - answering time 12 mins

**Q1. **The number of possible values of $x$ in the equation, $\sqrt{x^2-x+1} +\displaystyle\frac{1}{\sqrt{x^2-x+1}}=2-x^2$ is,

- 1
- 2
- 0
- 4

**Q2.** If $p+\displaystyle\frac{1}{p}=5$, then the value of $\displaystyle\frac{p^4+\displaystyle\frac{1}{p^2}}{p^2-3p+1}$ is,

- 50
- 55
- 70
- 110

**Q3.** If $\sqrt{4x-9} + \sqrt{4x+9}=5 + \sqrt{7}$, find the value of $x$.

- 3
- 4
- 5
- 7

**Q4. **If $\sqrt{2x} - \sqrt{3y}=0$ and $\sqrt{7x} + \sqrt{2y}=0$ then the value of $x+y$ is,

- 1
- 2
- 3
- 0

**Q5. **Find the remainder when $x^5-9x^2+12x-14$ is divided by $(x-3)$.

- 56
- 184
- 0
- 1

**Q6.** If $a + \displaystyle\frac{1}{b}=1$ and $b + \displaystyle\frac{1}{c}=1$, then value of $c + \displaystyle\frac{1}{a}$ is,

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

** Q7.** If $a:b=\displaystyle\frac{2}{9}:\displaystyle\frac{1}{3}$, $b:c=\displaystyle\frac{2}{7}:\displaystyle\frac{5}{14}$ and $d:c=\displaystyle\frac{7}{10}:\displaystyle\frac{3}{5}$ find the value of $a:b:c:d$.

- $8:12:15:7$
- $4:6:7:9$
- $30:35:24:16$
- $16:24:30:35$

** Q8.** If $a$ and $b$ are the roots of the equation $3x^2+2x+1=0$, which of the equations will have the roots, $\displaystyle\frac{1-a}{1+a}$ and $\displaystyle\frac{1-b}{1+b}$?

- $y^2-2y+3=0$
- $y^2+2y-3=0$
- $y^2-2y-3=0$
- $y^2+2y+3=0$

**Q9.** If $2x^2-7xy+3y^2=0$, then the value of $x:y$ is,

- $3:2$
- $5:6$
- $2:3$
- $3:1$ and $1:2$

** Q10.** Find the value of $\alpha$ when the expression $\displaystyle\frac{x^2}{y^2} + {\alpha}x+\displaystyle\frac{y^2}{4}$ is a perfect square.

- $\pm{1}$
- $0$
- $\pm{2}$
- $\pm{7}$

### Answers to the questions

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

**Problem 2:** Answer: Option b : 55.

**Problem 3:** Answer: Option b: 4.

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

**Problem 5:** Answer: Option b: 184.

**Problem 6:** Answer: Option a : 1.

**Problem 7:** Answer: Option d: $16:24:30:35$.

**Problem 8:** Answer: Option a: $y^2-2y+3=0$.

**Problem 9:** Answer: Option d: $3:1$ and $1:2$.

**Problem 10:** Answer: Option a: $\pm {1}$.

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