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SSC CGL level Question Set 74, Algebra 16

Hard algebra questions for SSC CGL Set 74

Hard algebra questions for SSC CGL Set 74: Use algebra problem solving techniques

10 Hard algebra questions for SSC CGL Set 74 to be solved in 12 minutes.

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16th set of 10 hard algebra questions for SSC CGL 74 - answering time 12 mins

Q1. If $a:b=2:3$ and $b:c=4:5$, find $a^2:b^2:bc$.

  1. $16:36:20$
  2. $4:9:45$
  3. $4:36:40$
  4. $16:36:45$

Q2. If $a+b+c=4\sqrt{3}$ and $a^2+b^2+c^2=16$, then the ratio of $a:b:c$ is,

  1. $1:\sqrt{2}:\sqrt{3}$
  2. $1:2:3$
  3. $1:1:1$
  4. None of these

Q3. If $x^2+y^2+z^2=2(x+z-1)$, then the value of $x^3+y^3+z^3$ is,

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

Q4. If $a+b+c=0$, then the value of $2b^2c^2+2c^2a^2+2a^2b^2 - a^4-b^4-c^4$ is,

  1. 7
  2. 0
  3. 28
  4. 14

Q5. If $\displaystyle\frac{a}{b}=\frac{2}{3}$ and $\displaystyle\frac{b}{c}=\frac{4}{5}$ then the value of the ratio $\displaystyle\frac{a+b}{b+c}$ is,

  1. $\displaystyle\frac{20}{27}$
  2. $\displaystyle\frac{8}{6}$
  3. $\displaystyle\frac{6}{8}$
  4. $\displaystyle\frac{27}{20}$

Q6. If $U_n=\displaystyle\frac{1}{n}-\displaystyle\frac{1}{n+1}$, then the value of $U_1+U_2+U_3+U_4+U_5$ is,

  1. $\displaystyle\frac{1}{2}$
  2. $\displaystyle\frac{1}{3}$
  3. $\displaystyle\frac{5}{6}$
  4. $\displaystyle\frac{2}{5}$

Q7. If $a*b=2a+3b-ab$, then the value of $(3*5+5*3)$ is,

  1. 2
  2. 4
  3. 6
  4. 10

Q8. If $\displaystyle\frac{x}{2x^2+5x+2}=\frac{1}{6}$,  then the value of $x+\displaystyle\frac{1}{x}$ is,

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

Q9. If $x=\displaystyle\frac{\sqrt{3}+1}{\sqrt{3}-1}$, and $y=\displaystyle\frac{\sqrt{3}-1}{\sqrt{3}+1}$, then the value of $x^2+y^2$ is,

  1. $13$
  2. $0$
  3. $14$
  4. $15$

Q10. If $\displaystyle\frac{2x-y}{x+2y}=\displaystyle\frac{1}{2}$, then the value of $\displaystyle\frac{3x-y}{3x+y}$ is,

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

To know how to solve the questions quick read the solutions at,

SSC CGL level Solution Set 74, Algebra 16.


Answers to the hard algebra questions for SSC CGL Set 74

Problem 1. Answer: Option d: $16:36:45$.

Problem 2. Answer: Option c : $1:1:1$.

Problem 3. Answer: Option c: 2.

Problem 4. Answer: Option b: 0.

Problem 5. Answer: Option a: $\displaystyle\frac{20}{27}$.

Problem 6. Answer: Option c : $\displaystyle\frac{5}{6}$.

Problem 7. Answer: Option d: 10.

Problem 8. Answer: Option d: $\displaystyle\frac{1}{2}$.

Problem 9. Answer: Option c: $14$.

Problem 10. Answer: Option b: $\displaystyle\frac{3}{5}$.


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