SSC CGL level Question Set 35, Algebra

Hard algebra questions with answers SSC CGL Set 35

Solve 10 hard algebra questions of SSC CGL Set 35 in 15 minutes. Verify your solutions from answers. Learn to solve quickly from paired solutions.

Answers and the link to the solution set are at the end.

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10 hard algebra questions SSC CGL Set 35 - answering time 15 mins

Q1. Two numbers $a$ and $b$ (where $a \gt b$) are such that their sum is three times their difference. The value of $\displaystyle\frac{3ab}{4(a^2-b^2)}$ is then,

1. $\frac{1}{3}$
2. $\frac{1}{2}$
3. $1\frac{1}{4}$
4. $\frac{5}{6}$

Q2. If $\displaystyle\frac{\sqrt{3+x} + \sqrt{3-x}}{\sqrt{3+x} - \sqrt{3-x}}=2$, then $x$ is,

1. $\displaystyle\frac{12}{5}$
2. $\displaystyle\frac{5}{12}$
3. $\displaystyle\frac{5}{7}$
4. $\displaystyle\frac{7}{5}$

Q3. If $a+b=1$, $c+d=1$ and $a-b=\displaystyle\frac{d}{c}$ then the value of $c^2-d^2$ is,

1. $1$
2. $\displaystyle\frac{a}{b}$
3. $\displaystyle\frac{b}{a}$
4. $-1$

Q4. If $x + \displaystyle\frac{1}{x} = \sqrt{3}$, then the value of $x^{18} + x^{12} + x^6 + 1$ is,

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

Q5. If $a$ and $b$ are two real numbers and the expression $ax^3 + 3x^2 -8x + b$ is exactly divisible by the expressions $(x + 2)$ and $(x-2)$ then the values of $a$ and $b$ are,

1. $a=-2$; $b=12$
2. $a=2$; $b=12$
3. $a=12$; $b=2$
4. $a=2$; $b=-12$

Q6. If $(a^2+b^2)^3 = (a^3+b^3)^2$ then $\displaystyle\frac{b}{a} + \displaystyle\frac{a}{b}$ will be equal to,

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

Q7. $\left(x + \displaystyle\frac{1}{x}\right)\left(x - \displaystyle\frac{1}{x}\right)\left(x^2 + \displaystyle\frac{1}{x^2} -1\right)\left(x^2 + \displaystyle\frac{1}{x^2} +1\right)$ is equal to,

1. $\left(x^6 + \displaystyle\frac{1}{x^6}\right)$
2. $\left(x^6 - \displaystyle\frac{1}{x^6}\right)$
3. $\left(x^8 + \displaystyle\frac{1}{x^8}\right)$
4. $\left(x^8 - \displaystyle\frac{1}{x^8}\right)$

Q8. If $x+y=a$ and $xy=b^2$ then the value of $x^3 - x^2y - xy^2 + y^3$ in terms of $a$ and $b$ is,

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

Q9. If $x=99999$, the value of $\displaystyle\frac{4x^3-x}{(2x+1)(6x-3)}$ is,

1. 11111
2. 66666
3. 33333
4. 22222

Q10. The length of the intercept of the graph of the equation $9x -12y = 108$ between x and y axes is,

1. 12 units
2. 18 units
3. 9 units
4. 15 units

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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 35 on Algebra where you will get detailed explanations on easiest path to the solutions.

Answers to the hard algebra questions SSC CGL Set 35

Q1. Answer: Option b: $\displaystyle\frac{1}{2}$.

Q2. Answer: Option a : $\displaystyle\frac{12}{5}$.

Q3. Answer: Option c: $\displaystyle\frac{b}{a}$.

Q4. Answer: Option c: 0.

Q5. Answer: Option d: $a=2$; $b=-12$.

Q6. Answer: Option a : $\displaystyle\frac{2}{3}$.

Q7. Answer: Option b: $\left(x^6 - \displaystyle\frac{1}{x^6}\right)$.

Q8. Answer: Option a: $a^3 -4b^2a$.

Q9. Answer: Option c: 33333.

Q10. Answer: Option d: 15 units.

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