SSC CGL level Question Set 64, Algebra 15 | SureSolv

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SSC CGL level Question Set 64, Algebra 15

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

ssc cgl level question set 64 algebra 15

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. $-1$
  2. $1$
  3. $0$
  4. $3$

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

  1. 24
  2. 36
  3. 18
  4. 32

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

  1. $0$
  2. $-1$
  3. $1$
  4. $2$

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

  1. 433
  2. 343
  3. 322
  4. 432

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

  1. 140
  2. 130
  3. 120
  4. 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,

  1. $0$
  2. $2$
  3. $3$
  4. $1$

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,

  1. $1000$
  2. $970$
  3. $5$
  4. $98$

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,

  1. $0$
  2. $1$
  3. $\displaystyle\frac{1}{2}$
  4. $2$

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

  1. $-124$
  2. $124$
  3. $126$
  4. $-126$

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,

  1. $-a^2-b^2-c^2$
  2. $a^2-b^2-c^2$
  3. $a^2-b^2+c^2$
  4. $a^2+b^2+c^2$

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: $a^2+b^2+c^2$.


Guided help on Algebra in Suresolv

To get the best results out of the extensive range of articles of tutorials, questions and solutions on Algebra in Suresolv, follow the guide,

Suresolv Algebra Reading and Practice Guide for SSC CHSL, SSC CGL, SSC CGL Tier II and Other Competitive exams.

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