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SSC CGL level Question Set 64, Algebra 15

Submitted by Atanu Chaudhuri on Fri, 28/04/2017 - 14:00

Hard algebra questions SSC CGL Set 64

Varieties of hard algebra questions SSC CGL Set 64 with answers

Solve 10 various types of hard algebra questions SSC CGL Set 64 in 12 minutes. Check solutions from answers. Learn to solve quickly from paired solutions.

Answers to the questions and link to the quick solutions are at the end.

10 hard algebra questions SSC CGL Set 64 - 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. $a^2+b^2+c^2$

Learn how to solve the questions quickly at,

SSC CGL Solution set 64 Algebra 15.

Answers to the hard algebra questions SSC CGL Set 64

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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