SSC CGL level Question Set 74, Algebra 16

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.

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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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