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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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,
- 3
- -1
- 1
- -3
Q2. If $a + \displaystyle\frac{1}{a - 2} = 4$, then $(a - 2)^2 + \displaystyle\frac{1}{(a - 2)^2}$ is,
- 4
- 0
- -2
- 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,
- $0$
- $a^2 + b^2 + c^2$
- $1$
- $2$
Q4. If $xy(x + y) = 1$, then $\displaystyle\frac{1}{x^3y^3} - x^3 - y^3$ is,
- $1$
- $-1$
- $3$
- $-3$
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,
- 3
- 6
- 9
- 12
Q6. The minimum value of $(a - 2)(a - 9)$ is,
- $\displaystyle\frac{-11}{4}$
- $0$
- $\displaystyle\frac{-49}{4}$
- $\displaystyle\frac{49}{4}$
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 $a\neq{b}$.
- 4, 1
- 2, 4
- -2, 1
- -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,
- $x + y = z$
- $x + y + z = 0$
- $x=y=z$
- $\displaystyle\frac{1}{x} + \displaystyle\frac{1}{y} + \displaystyle\frac{1}{z} = 0$
Q9. If $a^2 - 4a - 1 = 0$, then $a^2 + \displaystyle\frac{1}{a^2} + 3a - \displaystyle\frac{3}{a}$ is,
- 25
- 35
- 40
- 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 $a + b + c$.
- 3
- 0
- 2
- 1
Solutions to the problems
For detailed conceptual solutions with answers you should refer to the companion SSC CGL level Solution Set 11 on Algebra.
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