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SSC CGL Tier II level Question Set 3, Algebra 3

Algebra questions for SSC CGL Tier II with answer Set 3

Algebra questions for SSC CGL Tier 2 Set 3 with answers

Solve 10 questions in algebra questions for SSC CGL Tier II Set 3 within 12 minutes and verify from answers given. To solve quickly, refer to solution set.

Answers to the questions and link to the solution set are at the end.

Now take the timed mini-mock test.


Set 3 of 10 Algebra questions for SSC CGL Tier 2 - answering time 12 mins

Q1. If $4y-3x=13$ and $xy=14$, then $64y^3-27x^3$ is,

  1. 8479
  2. 8400
  3. 8740
  4. 8749

Q2. If $x=(0.09)^2$, $y=\displaystyle\frac{1}{(0.09)^2}$ and $z=(1- 0.09)^2 - 1$, then which of the following relations is true?,

  1. $y \lt x$ and $x=z$
  2. $y \lt z \lt x$
  3. $z \lt x \lt y$
  4. $x \lt y$ and $x=z$

Q3. Minimum value of $x^4 +\displaystyle\frac{1}{x^4+1} - 3$ is,

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

Q4. If $\displaystyle\frac{p}{3}=\frac{q}{2}$ then the value of $\displaystyle\frac{2p+3q}{3p-2q}$ is,

  1. $1$
  2. $\displaystyle\frac{12}{5}$
  3. $\displaystyle\frac{5}{12}$
  4. $\displaystyle\frac{12}{7}$

Q5. If $(a-4)^2 + (b-9)^2+(c-3)^2=0$, then the value of $\sqrt{a+b+c}$ is,

  1. $\pm{4}$
  2. $4$
  3. $-4$
  4. $\pm{2}$

Q6. If $\displaystyle\frac{1}{x+y}=\displaystyle\frac{1}x+\displaystyle\frac{1}{y}$, where, $x \neq 0$, $y \neq 0$ and $x \neq y$, the value of $x^3-y^3$ is,

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

Q7. If $a^x=(x+y+z)^y$, $a^y=(x+y+z)^z$ and $a^z=(x+y+z)^x$ find the value of $a+b+c$ where $a \neq 0$.

  1. $0$
  2. $1$
  3. $a^3$
  4. $a$

Q8. If $\displaystyle\frac{x-a^2}{b^2+c^2} + \displaystyle\frac{x-b^2}{c^2+a^2} +\displaystyle\frac{x-c^2}{a^2+b^2} =3$ then the value of $x$ is,

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

Q9. If $ax^2+bx+c=a(x-p)^2$, then the correct relation between $a$, $b$ and $c$ would be,

  1. $2b=a+c$
  2. $b^2=4ac$
  3. $b^2=ac$
  4. $abc=1$

Q10. If $\displaystyle\frac{y}{x} - \displaystyle\frac{x}{y}=3$, then find the value of $\displaystyle\frac{x^3}{y^3} + \displaystyle\frac{y^3}{x^3}$.

  1. $10\sqrt{3}$
  2. $10\sqrt{13}$
  3. $13\sqrt{3}$
  4. $13\sqrt{10}$

Learn how to solve the questions quickly from the solution set at,

SSC CGL Tier 2 Solution Set 3 on Algebra 3.


Answers to the Algebra questions for SSC CGL Tier 2 Set 3

Problem 1: Answer: Option d: 8749.

Problem 2: Answer: Option c : $z \lt x \lt y$.

Problem 3: Answer: Option c: $-2$.

Problem 4: Answer: Option b: $\displaystyle\frac{12}{5}$.

Problem 5: Answer: Option b: 4.

Problem 6: Answer: Option a : 0.

Problem 7: Answer: Option d: $a$.

Problem 8: Answer: Option b: $a^2+b^2+c^2$.

Problem 9: Answer: Option b: $b^2=4ac$.

Problem 10: Answer: Option b: $10\sqrt{13}$.


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