## 64th SSC CGL level Question Set, 15th on Algebra

This is the 64th question set of 10 practice problem exercise for SSC CGL exam and the 15th 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.

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*.

### 64th question set - 10 problems for SSC CGL exam: 15th on topic Algebra - answering time 12 mins

**Q1. **If $a$, $b$, and $c$ are real numbers and $a^2+b^2+c^2=2(a-b-c)-3$ then the value of $(a+b+c)$ is,

- $-1$
- $1$
- $0$
- $3$

**Q2.** If $p^4=119-\displaystyle\frac{1}{p^4}$, then the value of $p^3-\displaystyle\frac{1}{p^3}$ is,

- 24
- 36
- 18
- 32

**Q3. **If $a+b=1$, then the value of $a^3+b^3-ab-(a^2-b^2)^2$ is,

- $0$
- $-1$
- $1$
- $2$

**Q4. **If $\displaystyle\frac{x^{24}+1}{x^{12}}=7$, then the value of $\displaystyle\frac{x^{72}+1}{x^{36}}$ is,

- 433
- 343
- 322
- 432

**Q5. **If $x^2+x=5$, then the value of $(x+3)^3+\displaystyle\frac{1}{(x+3)^3}$ is,

- 140
- 130
- 120
- 110

**Q6.** If $\displaystyle\frac{p^2}{q^2}+\displaystyle\frac{q^2}{p^2}=1$, then the value of $(p^6+q^6)$ is,

- $0$
- $2$
- $3$
- $1$

** Q7.** If $x=\displaystyle\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$, then the value of $x^3+\displaystyle\frac{1}{x^3}$ is,

- $1000$
- $970$
- $5$
- $98$

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

- $0$
- $1$
- $\displaystyle\frac{1}{2}$
- $2$

**Q9.** If $m=-4$, and $n=-2$, then the value of $m^3-3m^2+3m+3n+3n^2+n^3$ is equal to,

- $-124$
- $124$
- $126$
- $-126$

** Q10.** If $\displaystyle\frac{p-a^2}{b^2+c^2}+\displaystyle\frac{p-b^2}{c^2+a^2}+\displaystyle\frac{p-c^2}{a^2+b^2}=3$, then the value of $p$ is,

- $-a^2-b^2-c^2$
- $a^2-b^2-c^2$
- $a^2-b^2+c^2$
- $a^2+b^2+c^2$

The detailed conceptual solutions are in * SSC CGL Solution set 64 Algebra 15*, and the video solutions are in the two-part video below.

**Part 1: Q1 to Q5**

**Part 2: Q6 to Q10**

### Answers to the Questions

Q1. **Answer:** Option a: $-1$.

Q2. **Answer:** Option b : 36.

Q3. **Answer:** Option a: 0.

Q4. **Answer:** Option c: 322.

Q5. **Answer:** Option d: 110.

Q6. **Answer:** Option a : 0.

Q7. **Answer:** Option b: 970.

Q8. **Answer:** Option b: $1$.

Q9. **Answer:** Option d: $-126$.

Q10. **Answer: **Option d: $a^2+b^2+c^2$.

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