## 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: $\displaystyle\frac{2}{5}$.

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