## 1st SSC CGL Tier II level Question Set, 1st on Algebra

This is the 1st question set of 10 practice problem exercise for SSC CGL Tier II exam and also the 1st 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.

### 1st question set - 10 problems for SSC CGL exam: 1st on topic Algebra - answering time 12 mins

**Q1. **Find the maximum value of the expression $(p^2 +7p+13)^{-1}$.

- $\displaystyle\frac{5}{7}$
- $\displaystyle\frac{4}{3}$
- $20$
- $\displaystyle\frac{3}{7}$

**Q2.** If $n=7+3\sqrt{5}$, then the value of $\left(\sqrt{n} + \displaystyle\frac{1}{\sqrt{n}}\right)$ is,

- $\displaystyle\frac{5}{7}$
- $\displaystyle\frac{7}{12}$
- $\displaystyle\frac{9+\sqrt{5}}{2\sqrt{2}}$
- $\displaystyle\frac{\sqrt{5}}{2\sqrt{2}}$

**Q3.** If $x=20$, $y=19$, the value of $\displaystyle\frac{x^2+y^2+xy}{x^3-y^3}$ is,

- $35$
- $1$
- $324$
- $365$

**Q4. **If $p + \displaystyle\frac{2p}{3} + \displaystyle\frac{p}{2} +\displaystyle\frac{p}{7}=97$, then the value of $p$ is,

- 46
- 44
- 40
- 42

**Q5. **If $p=1+\sqrt{2}+\sqrt{3}$, then $\left(p+\displaystyle\frac{1}{p-1}\right)$ is,

- $1 +2\sqrt{3}$
- $2\sqrt{3}-1$
- $2+\sqrt{3}$
- $3+\sqrt{2}$

**Q6.** If $(x+y) : (y+z) : (z+x) = 6 : 7 : 8$ and $x+y+z=14$, then value of $z$ is,

- 6
- 14
- 8
- 7

** Q7.** If $x=\displaystyle\frac{\sqrt{2}+1}{\sqrt{2}-1}$ and $xy=1$ find the value of $\displaystyle\frac{2x^2+3xy+2y^2}{2x^2-3xy+2y^2}$.

- $\displaystyle\frac{71}{65}$
- $\displaystyle\frac{7}{12}$
- $\displaystyle\frac{65}{71}$
- $\displaystyle\frac{72}{7}$

** Q8.** If $x=\displaystyle\frac{a+b}{1-ab}$ and $y=\displaystyle\frac{a-b}{1+ab}$ then the value of $\displaystyle\frac{x+y}{1-xy}$ is,

- $\displaystyle\frac{a}{1+b^2}$
- $\displaystyle\frac{2a}{1+b}$
- $\displaystyle\frac{2a}{1-a^2}$
- $\displaystyle\frac{2a}{1+a^2}$

**Q9.** If $x+\displaystyle\frac{1}{x}=-2$, then the value of $x^{2n+1}+\displaystyle\frac{1}{x^{2n+1}}$ where $n$ is a positive integer is,

- $0$
- $2$
- $-5$
- $-2$

** Q10.** If $x=5^{n-1} +5^{-n-1}$ where $n$ is real, the minimum value of $x$ is,

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

The detailed conceptual solutions may be referred to at, **SSC CGL Tier II level Solution set 1 Algebra 1.**

**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 b: $\displaystyle\frac{4}{3}$.

**Problem 2.** **Answer:** Option c : $\displaystyle\frac{9+\sqrt{5}}{2\sqrt{2}}$.

**Problem 3.** **Answer:** Option b: 1.

**Problem 4.** **Answer:** Option d: 42.

**Problem 5.** **Answer:** Option a: $1+2\sqrt{3}$.

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

**Problem 7.** **Answer:** Option a: $\displaystyle\frac{71}{65}$.

**Problem 8.** **Answer:** Option c: $\displaystyle\frac{2a}{1-a^2}$.

**Problem 9.** **Answer:** Option d: -2.

**Problem 10.** **Answer: **Option d: $\displaystyle\frac{2}{5}$.

### 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.