SSC CGL level Question Set 11, Algebra

Eleventh SSC CGL level Question Set, topic Algebra

This is the eleventh Question set of 10 practice problems on topic Algebra for SSC CGL exam as well as school students interested in elegant problem solving. Students must complete this question set in prescribed time first and then only refer to the corresponding solution set.

This exercise set containing 10 problems highlights the need of solving the problems using powerful strategies rather than brute force conventional deduction methods. 

Some of these questions are a bit advanced in nature and require a few new types of algebraic patttern recognition and abilities to be used.

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Recommended reading of Tutorials

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SSC CGL level difficult Algebra problem solving by Componendo dividendo

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Eleventh question set on Algebra - 10 problems for SSC CGL exam - time 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 $\displaystyle\frac{(s - a)^2 + (s - b)^2 + (s - c)^2+s^2}{a^2 + b^2 + c^2}$ 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 problems

For detailed conceptual solutions with answers you should refer to the companion SSC CGL level Solution Set 11 on Algebra.

Video

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

Part 1: Q1 to Q5

Part II: Q6 to Q10

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Guided help on Algebra in Suresolv

To get the best results out of the extensive range of articles of tutorials, questions and solutions on Algebra in Suresolv, follow the guide,

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

The guide list of articles includes ALL articles on Algebra in Suresolv and is up-to-date.

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