SSC CGL level Question Set 23, Algebra

10 tricky algebra questions for SSC CGL to solve in 12 mins

Solve 10 algebra questions for SSC CGL Set 8 in 12 minutes. Score your efforts from answers and learn to solve quickly from the paired solution set.

For best results, take the timed test, from answers score your efforts with 1 mark for each correct answer and minus 0.25 for each wrong one. Finally learn to solve these questions in minimum steps by algebra problem solving techniques from the paired solution set.

Answers and the link to the solutions are at the end.

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10 algebra questions for SSC CGL Set 8 - answering time 12 mins

Q1. If $x = \sqrt[3]{a + \sqrt{a^2 + b^3}} + \sqrt[3]{a - \sqrt{a^2 + b^3}}$, then the value of $x^3 + 3bx$ is,

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

Q2. If $x = 2015$, $y = 2014$ and $z = 2013$ then the value of $x^2 + y^2 + z^2 - xy - yz -zx$ is,

1. 4
2. 3
3. 2
4. 6

Q3. The area in square unit of triangle formed by the graphs of $x=4$, $y=3$ and $3x + 4y= 12$ is,

1. 12
2. 8
3. 10
4. 6

Q4. If $2\left(x^2 + \displaystyle\frac{1}{x^2}\right) - \left(x - \displaystyle\frac{1}{x}\right) - 7 = 0$, then the two values of $x$ are,

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

Q5. If $\left(x + \displaystyle\frac{1}{x}\right)^2 = 3$ then the value of,

$x^{206} + x^{200} + x^{90} + x^{84} + x^{18} $

$\hspace{24mm} + x^{12} + x^6 + 1$ is,

1. 0
2. 1
3. 206
4. 84

Q6. If $1.5x=0.04y$ then the value of $\displaystyle\frac{y^2 - x^2}{y^2 + 2xy + x^2}$ will be,

1. $\frac{73}{77}$
2. $\frac{74}{77}$
3. $\frac{73}{770}$
4. $\frac{730}{77}$

Q7. If $x + \displaystyle\frac{1}{x} = 3$ then the value of $x^5 + \displaystyle\frac{1}{x^5}$ is,

1. 322
2. 113
3. 123
4. 126

Q8. If $\|a\|$ is the greatest integer equal to or less than $a$, then the value of $\|-\frac{1}{4}\| + \|4\frac{1}{4}\| + \|3\|$ is,

1. 4
2. 5
3. 7
4. 6

Q9. One of the factors of $(a^2 - b^2)^3 + (b^2 - c^2)^3 + (c^2 - a^2)^3$ is,

1. $(b - c)(b - c)$
2. $(a + b)(a - b)$
3. $(a + b)(a + b)$
4. $(a - b)(a - b)$

Q10. If $x^2 + y^2 + z^2 = xy + yz + zx$, then the value of $\displaystyle\frac{z + x}{y}$ is,

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

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Solution to the problems

Learn to solve these questions in minimum steps from the paired solutions,

SSC CGL level Solution Set 23 on Algebra.

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Answers to the 10 tricky algebra questions for SSC CGL Set 8

Problem 1. Answer: Option d: 2a.

Problem 2. Answer: Option b : 3.

Problem 3. Answer: Option d: 6.

Problem 4. Answer: Option a: $2$, $-\frac{1}{2}$.

Problem 5. Answer: Option a: 0.

Problem 6. Answer: Option a : $\frac{73}{77}$.

Problem 7. Answer: Option c: 123.

Problem 8. Answer: Option d: 6.

Problem 9. Answer: Option b: $(a + b)(a - b)$.

Problem 10. Answer: Option a: 2.

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