SSC CGL Tier II level Question Set 9, Algebra 4

9th Set of Algebra questions for SSC CGL Tier 2 with answers

Solve 10 selected algebra questions for SSC CGL tier 2 Set 9 in 12 mins. Verify results from given answers. Learn to solve quick from linked solutions.

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

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10 Algebra questions for SSC CGL Tier 2 Set 9 - answering time 12 mins

Q1. If $x+\displaystyle\frac{2}{x}=1$, then the value of $\displaystyle\frac{x^2+x+2}{x^2(1-x)}$ is,

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

Q2. If $4x+5y=83$, and $3x : 2y=21 : 22$, then $(y-x)$ equals to,

1. 4
2. 7
3. 3
4. 11

Q3. If $\displaystyle\frac{3-5x}{2x} + \displaystyle\frac{3-5y}{2y} + \displaystyle\frac{3-5z}{2z}=0$, then the value of $\displaystyle\frac{2}{x}+\displaystyle\frac{2}{y}+\displaystyle\frac{2}{z}$ is,

1. 10
2. 5
3. 20
4. 15

Q4. If $\displaystyle\frac{2p}{p^2-2p+1}=\frac{1}{4}$ then the value of $\left(p+\displaystyle\frac{1}{p}\right)$ is,

1. $1$
2. $10$
3. $\displaystyle\frac{2}{5}$
4. $7$

Q5. If $2x=\sqrt{a}+\displaystyle\frac{1}{\sqrt{a}}$, and $a \gt 0$, then the value of $\displaystyle\frac{\sqrt{x^2-1}}{x-\sqrt{x^2-1}}$ is,

1. $a+1$
2. $a-1$
3. $\frac{1}{2}(a-1)$
4. $\frac{1}{2}(a+1)$

Q6. If $x^2+y^2+z^2=xy+yz+zx$, then the value of $\displaystyle\frac{3x^4+7y^4+5z^4}{5x^2y^2+7y^2z^2+3z^2x^2}$ is,

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

Q7. If $\displaystyle\frac{a^2-bc}{a^2+bc}+\displaystyle\frac{b^2-ca}{b^2+ca}+\displaystyle\frac{c^2-ab}{c^2+ab}=1$, then the value of $\displaystyle\frac{a^2}{a^2+bc}+\displaystyle\frac{b^2}{b^2+ca}+\displaystyle\frac{c^2}{c^2+ab}$ is,

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

Q8. If $2\left(x^2+\displaystyle\frac{1}{x^2}\right) - \left(x-\displaystyle\frac{1}{x}\right) -7 =0$ then the two valid values of $x$ are,

1. $0$, $1$
2. $\frac{1}{2}$, $1$
3. $1$, $2$
4. $2$, $-\frac{1}{2}$

Q9. If $x=\sqrt[3]{a+\sqrt{a^2+b^3}}+\sqrt[3]{a-\sqrt{a^2+b^3}}$, then $x^3+3bx$ is equal to,

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

Q10. If $bc+ca+ab=abc$, then the value of $\displaystyle\frac{b+c}{bc(a-1)} + \displaystyle\frac{c+a}{ca(b-1)}+\displaystyle\frac{a+b}{ab(c-1)}$ is,

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

For detailed conceptual solutions to the questions refer to SSC CGL Tier II level Solution set 9 Algebra 4.

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Answers to the algebra questions for SSC CGL Tier 2 Set 9

Problem 1: Answer: Option c: 1.

Problem 2: Answer: Option a : 4.

Problem 3: Answer: Option a: 10.

Problem 4: Answer: Option b: 10.

Problem 5: Answer: Option c: $\frac{1}{2}(a-1)$.

Problem 6: Answer: Option b : $1$.

Problem 7: Answer: Option a: $2$.

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

Problem 9: Answer: Option d: $2a$.

Problem 10: Answer: Option b: $1$.

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