## 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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#### SSC CGL Tier II level question and solution sets on Algebra

**SSC CGL Tier II level Question Set 14, Algebra 5**

**SSC CGL Tier II level Solution Set 14, Algebra 5**

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**SSC CGL Tier II level Solution Set 9, Algebra 4**

**SSC CGL Tier II level Question Set 3, Algebra 3**

**SSC CGL Tier II level Solution Set 3, Algebra 3**

**SSC CGL Tier II level Question Set 2, Algebra 2**

**SSC CGL Tier II level Solution Set 2, Algebra 2**

**SSC CGL Tier II level Question Set 1 Algebra 1**

**SSC CGL Tier II level Solution Set 1, Algebra 1**

#### SSC CGL level question and solution sets on Algebra

**SSC CGL level Question Set 64, Algebra 15**

**SSC CGL level Solution Set 64, Algebra 15**

**SSC CGL level Question Set 58, Algebra 14**

**SSC CGL level Solution Set 58, Algebra 14**

**SSC CGL level Question Set 57, Algebra 13**

**SSC CGL level Solution Set 57, Algebra 13**

**SSC CGL level Question Set 51, Algebra 12**

**SSC CGL level Solution Set 51, Algebra 12**

**SSC CGL level Question Set 45, Algebra 11**

**SSC CGL level Solution Set 45, Algebra 11**

**SSC CGL level Question Set 35, Algebra 10**

**SSC CGL level Solution Set 35, Algebra 10**

**SSC CGL level Question Set 33, Algebra 9**

**SSC CGL level Solution Set 33, Algebra 9**

**SSC CGL level Question Set 23, Algebra 8**

**SSC CGL level Solution Set 23, Algebra 8**

**SSC CGL level Question Set 22, Algebra 7**

**SSC CGL level Solution Set 22, Algebra 7**

**SSC CGL level Question Set 13, Algebra 6**

**SSC CGL level Solution Set 13, Algebra 6**

**SSC CGL level Question Set 11, Algebra 5**

**SSC CGL level Solution Set 11, Algebra 5**

**SSC CGL level Question Set 10, Algebra 4**

**SSC CGL level Solution Set 10, Algebra 4**

**SSC CGL level Question Set 9, Algebra 3**

**SSC CGL level Solution Set 9, Algebra 3**

**SSC CGL level Question Set 8, Algebra 2**

**SSC CGL level Solution Set 8, Algebra 2**

**SSC CGL level Question Set 1, Algebra 1**

**SSC CGL level Solution Set 1, Algebra 1**

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