SSC CGL level Question Set 9, Algebra

3rd set of MCQ Algebra questions for SSC CGL

MCQ algebra questions with answers for SSC CGL exams sets 3. Selected for variety. Take the timed test and verify answers. Clear doubts from solutions.

A number of these 10 are hard algebra questions. But don't hesitate. Go ahead and try them.

This forms the 9th question set for SSC CGL and 3rd on Algebra and can be used as a mini mock test.

Before taking the test you may like to refer to the following concept tutorial on Algebra that has a good collection of basic to powerful algebra problem solving techniques,

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

MCQ Algebra Questions 3rd set - 10 problems for SSC CGL exam - time to solve 12 mins

Q1. If $a -2b = 4$, then the value of the expression $a^3 - 8b^3 -24ab -64$ is,

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

Q2. If $x + \displaystyle\frac{1}{x} = 4$, then $x^4 + \displaystyle\frac{1}{x^4}$ is,

1. 124
2. 194
3. 64
4. 81

Q3. If $x^2 = y + z$, $y^2= z + x$ and $z^2 = x + y$, then the value of $\displaystyle\frac{1}{x + 1} + \displaystyle\frac{1}{y + 1}  + \displaystyle\frac{1}{z + 1} $ is,

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

Q4. If $x = 7 - 4\sqrt{3}$, then $x^{\frac{1}{2}} + x^{\frac{-1}{2}}$ is, 

1. $4$
2. $3\sqrt{3}$
3. $7$
4. $2\sqrt{3}$

Q5. $(y -z)^3 + (z -x)^3 + (x -y)^3$ is equal to,

1. $(x - y)(y + z)(x - z)$
2. $(y - z)(z + x)(y - x)$
3. $(y - z)(z - x)(x - y)$
4. $3(y - z)(z - x)(x - y)$

Q6. The sum of $\displaystyle\frac{a}{b}$ and its reciprocal is 1 and $a\neq{0}$, $b\neq{0}$. The value of $a^3 + b^3$ is,

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

Q7. If $ x = b + c - 2a$, $y = c + a - 2b$ and $z = a + b -2c$, then the value of $x^2 + y^2 - z^2 + 2xy$ is,

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

Q8. If $x = \displaystyle\frac{4ab}{a + b}$, where $a\neq{b}$, then the value of, $\displaystyle\frac{x + 2a}{x - 2a} + \displaystyle\frac{x + 2b}{x - 2b}$ is,

1. a
2. 2
3. 2ab
4. b

Q9. If $x = 3 + 2\sqrt{2}$ then the value of $\left(\sqrt{x} - \displaystyle\frac{1}{\sqrt{x}}\right)$ is,

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

Q10. If $x = 2 - 2^{\frac{1}{3}}  + 2^{\frac{2}{3}}$, then the value of $x^3 - 6x^2 + 18x + 18$ is,

1. 40
2. 33
3. 22
4. 45

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Answers to the 10 MCQ algebra questions for SSC CGL 3rd set

Q1. Answer: Option a: 0.

Q2. Answer: Option b: 194.

Q3. Answer: Option d: 1.

Q4. Answer: Option a: $4$.

Q5. Answer: Option d: $3(y - z)(z - x)(x - y)$.

Q6. Answer: Option b: 0.

Q7. Answer: Option b: 0.

Q8. Answer: Option b: 2.

Q9. Answer: Option c: 2.

Q10. Answer: Option a: 40.

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Solutions to the problems

For detailed conceptual solutions with answers you should refer to the companion SSC CGL level Solution Set 9 on Algebra.

Video

You may watch the solutions in the two-part video.

Part I Q1 to Q5

Part II: Q6 to Q10

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Guided help on Algebra in Suresolv

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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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