SSC CGL level Question Set 11, Algebra

Fifth set of SSC CGL difficult algebra questions

Solve fifth set of SSC CGL difficult algebra questions in 12 minutes. Verify from answers. Learn how to solve the questions easy and quick from solutions.

Link to the solution set is at the end.

This is the 11th question set for SSC CGL and 5th on Algebra and can be used as a mini mock test.

Note: A number of these 10 algebra questions are tricky. 

Recommendation: To solve this question set comfortably in 12 minutes' time better go through our Comprehensive collection of Algebra problem solving techniques before taking the test at,

Basic and rich Algebraic concepts for elegant solutions of SSC CGL problems.

SSC CGL difficult algebra questions 5th set - time to solve 12 mins

Q1. If $a$, $b$ and $c$ are non-zero and $a + \displaystyle\frac{1}{b} = 1$ and  $b + \displaystyle\frac{1}{c} = 1$, the value of $abc$ is,

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

Q2. If $a + \displaystyle\frac{1}{a - 2} = 4$, then $(a - 2)^2 + \displaystyle\frac{1}{(a - 2)^2}$ is,

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

Q3. If $a + b + c = 2s$, then $\displaystyle\frac{(s - a)^2 + (s - b)^2 + (s - c)^2}{a^2 + b^2 + c^2}$ is,

1. $0$
2. $a^2 + b^2 + c^2$
3. $1$
4. $2$

Q4. If $xy(x + y) = 1$, then $\displaystyle\frac{1}{x^3y^3} - x^3 - y^3$ is,

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

Q5. If $a + b + c = 6$, $a^2 + b^2 + c^2 = 14$ and $a^3 + b^3 + c^3 = 36$, then the value of $abc$ is,

1. 3
2. 6
3. 9
4. 12

Q6. The minimum value of $(a - 2)(a - 9)$ is,

1. $\displaystyle\frac{-11}{4}$
2. $0$
3. $\displaystyle\frac{-49}{4}$
4. $\displaystyle\frac{49}{4}$

Q7. The terms $a$, $1$, and $b$ are in AP and the terms $1$, $a$ and $b$ are in GP. Find the values of $a$ and $b$, where $a\neq{b}$.

1. 4, 1
2. 2, 4
3. -2, 1
4. -2, 4

Q8. If $x\neq{0}$, $y\neq{0}$ and $z\neq{0}$, and $\displaystyle\frac{1}{x^2} + \displaystyle\frac{1}{y^2} + \displaystyle\frac{1}{z^2} = \displaystyle\frac{1}{xy} + \displaystyle\frac{1}{yz} + \displaystyle\frac{1}{zx}$, then the relation between $x$, $y$ and $z$ is,

1. $x + y = z$
2. $x + y + z = 0$
3. $x=y=z$
4. $\displaystyle\frac{1}{x} + \displaystyle\frac{1}{y} + \displaystyle\frac{1}{z} = 0$

Q9. If $a^2 - 4a - 1 = 0$, then $a^2 + \displaystyle\frac{1}{a^2} + 3a - \displaystyle\frac{3}{a}$ is,

1. 25
2. 35
3. 40
4. 30

Q10. If $\displaystyle\frac{1}{\sqrt[3]{4} + \sqrt[3]{2} + 1} = a\sqrt[3]{4} + b\sqrt[3]{2} + c$, and $a$, $b$ and $c$ are rational, find the value of $a + b + c$.

1. 3
2. 0
3. 2
4. 1

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Solutions to the questions

To know how to solve the questions quickly and easily go through the companion solution set,

SSC CGL level Solution Set 11 on Algebra.

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Answers to the fifth set of SSC CGL difficult algebra questions

Q1. Answer: Option b: $-1$.

Q2. Answer: Option d: $2$.

Q3. Answer: Option c: $1$.

Q4. Answer: Option c: $3$.

Q5. Answer: Option b: 6.

Q6. Answer: Option c: $-\displaystyle\frac{49}{4}$.

Q7. Answer: Option d: -2, 4.

Q8. Answer: Option c: $x=y=z$.

Q9. Answer: Option d: 30.

Q10. Answer: Option b: 0.

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Suresolv Algebra Reading and Practice Guide for SSC CHSL, SSC CGL, SSC CGL Tier II and Other Competitive exams.

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