## 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.

### 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,

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

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