## 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.

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

Detailed conceptual solutions are available in * SSC CGL Tier II level Solution Set 2 Algebra 2*.

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 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: $\pm {1}$.

### Additional help on Suresolv Algebra

To use the *extensive range of articles on quick algebra* problem solving, *follow the guide,*

**5 step Suresolv Algebra Reading and Practice Guide for SSC CGL Tier II.**

You will get ** step by step recommended actions** for success in SSC CGL Tier II and other relevant competitive exams along with the

**full list of articles on Algebra with links.**

**The list includes:** *ALL Concept articles* on Algebra, *ALL articles on How to solve difficult Algebra problems* in a few steps, *ALL Question and Solution Sets for SSC CGL* and *ALL Question and Solution sets for SSC CGL Tier II*.

#### Important points to remember

- SSC CGL problem solving builds the foundation for excellence on SSC CGL Tier II exam.
- Concept articles are particularly valuable for learning the concepts and techniques, whereas How to solve in a few steps articles show how the techniques are applied to actually solve specially selected problems from real exam.
- Finally, each of the large number of question sets should certainly be used as a timed mini-mock test for analysis of your difficulties in answering followed by clarification of doubts from the corresponding solution set.

Wish you all the sure success.