## 33rd SSC CGL level Question Set, 9th on Algebra

This is the 33rd question set of 10 practice problem exercise for SSC CGL exam and 9th 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 the conceptual analytical approach.

Learning by doing is the best learning. There is no other alternative towards achieving excellence.

Before taking the test you may like to refer to our **concept tutorials** on Algebra and other related topics,

**Basic and rich Algebraic concepts for elegant solutions of SSC CGL problems,**

**More Basic and rich Algebraic concepts for elegant solutions of SSC CGL problems**

* SSC CGL level difficult Algebra problem solving by Componendo dividendo*.

### 33rd question set - 10 problems for SSC CGL exam: 9th on topic Algebra - answering time 15 mins

**Q1. **If $x = 2.361$, $y=3.263$, and $z=5.624$, then the value of $x^3 + y^3 - z^3 + 3xyz$ is,

- 35.621
- 1
- 0
- 19.277

**Q2.** If $6 + \displaystyle\frac{1}{x}=x$, then the value of $x^4 + \displaystyle\frac{1}{x^4}$ is,

- 1444
- 1442
- 1448
- 1446

**Q3.** If $x^2 + \displaystyle\frac{1}{x^2} = 66$, then the value of $\displaystyle\frac{x^2 - 1 + 2x}{x}$ is,

- $\pm{8}$
- $6, -10$
- $10, -6$
- $\pm{4}$

**Q4. **Find the minimum value of $2x^2 - (x - 3)(x + 5)$, where $x$ is real,

- 20
- 14
- -12
- 8

**Q5. **If $x+y=7$ then the value of $x^3 + y^3 + 21xy$ is,

- 243
- 143
- 443
- 343

**Q6.** If $x=\displaystyle\frac{\sqrt{3}}{2}$ then the value of $\displaystyle\frac{\sqrt{1+x} + \sqrt{1-x}}{\sqrt{1+x} - \sqrt{1-x}}$ will be,

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

** Q7.** If $p^3 + 3p^2 + 3p = 7$ then the value of $p^2 + 2p$ is,

- 3
- 4
- 5
- 6

** Q8.** If $\left(x + \displaystyle\frac{1}{x}\right)^2 = 3$ then the value of $(x^{72} + x^{66} + x^{54} + x^{36} + x^{24} + x^6 + 1)$ is,

- 4
- 2
- 3
- 1

**Q9.** If $a^2 + b^2 + c^2 = 2(a -b -c) -3$, then $4a - 3b + 5c$ is,

- 3
- 2
- 5
- 6

** Q10.** If $3x + \displaystyle\frac{1}{2x} = 5$, then the value of $8x^3 + \displaystyle\frac{1}{27x^3}$ is,

- $118\frac{1}{2}$
- $0$
- $30\frac{10}{27}$
- $1$

### Solutions to the problems

For detailed conceptual solutions with answers you should refer to the companion * SSC CGL level Solution Set 33 on Algebra* where you will get detailed explanations on easiest path to the solutions.

Watch the* quick mental solutions in the two-part video*.

**Part I: Q1 to Q5**

**Part II: Q6 to Q10**

### Guided help on Algebra in Suresolv

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