SSC CGL level Question Set 51, Algebra 12

Hard Algebra practice questions for SSC CGL set 12 with answers

Solve the hard algebra practice questions for SSC CGL 12th set in 12 minutes. Verify correctness from answers and learn how to solve quick from solutions.

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

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Basic and advanced algebra concepts and techniques for SSC CGL.

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12th set of Hard Algebra practice questions for SSC CGL - time to answer 12 mins

Problem 1.

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

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

Problem 2.

If $a^2+b^2+c^2+3=2(a+b+c)$ then the value of $(a+b+c)$ is,

1. 2
2. 3
3. 5
4. 4

Problem 3.

If $a^2-4a-1=0$, then the value of $a^2+\displaystyle\frac{1}{a^2}+3a-\displaystyle\frac{3}{a}$ is,

1. 40
2. 35
3. 30
4. 25

Problem 4.

If $x+\displaystyle\frac{1}{x}=99$, find the value of $\displaystyle\frac{100x}{2x^2+102x+2}$.

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

Problem 5.

If $\sqrt{1+\displaystyle\frac{x}{961}}=\displaystyle\frac{32}{31}$, then the value of $x$ is,

1. 63
2. 64
3. 61
4. 65

Problem 6.

If $1.5a=0.04b$ then the value of $\displaystyle\frac{b-a}{b+a}$ will be equal to,

1. $\displaystyle\frac{73}{77}$
2. $\displaystyle\frac{75}{2}$
3. $\displaystyle\frac{2}{75}$
4. $\displaystyle\frac{77}{33}$

Problem 7.

The value of the expression, $\displaystyle\frac{(a-b)^2}{(b-c)(c-a)}+\displaystyle\frac{(b-c)^2}{(a-b)(c-a)}+\displaystyle\frac{(c-a)^2}{(a-b)(b-c)}$ is,

1. $2$
2. $3$
3. $0$
4. $\displaystyle\frac{1}{3}$

Problem 8.

If $9\sqrt{x}=\sqrt{12}+\sqrt{147}$, then $x$ is,

1. 5
2. 2
3. 3
4. 4

Problem 9.

If $p:q=r:s=t:u=2:3$ then $(mp+nr+ot):(mq+ns+ou)$ is equal to,

1. 2 : 3
2. 3 : 2
3. 2 : 1
4. 1 : 2

Problem 10.

If $\displaystyle\frac{1}{a+1}+\displaystyle\frac{1}{b+1}+\displaystyle\frac{1}{c+1}=2$ then $a^2+b^2+c^2$ is,

1. $\displaystyle\frac{3}{4}$
2. $\displaystyle\frac{1}{3}$
3. $\displaystyle\frac{27}{16}$
4. $\displaystyle\frac{4}{3}$

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Answers to the 12th set of hard algebra practice questions for SSC CGL

Problem 1. Answer: Option a: $1$.

Problem 2. Answer: Option b : 3.

Problem 3. Answer: Option c: 30.

Problem 4. Answer: Option b: $\displaystyle\frac{1}{3}$.

Problem 5. Answer: Option a: 63.

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

Problem 7. Answer: Option b: $3$.

Problem 8. Answer: Option c: 3.

Problem 9. Answer: Option a: 2 : 3.

problem 10. Answer: Option a: $\displaystyle\frac{3}{4}$.

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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 51 on Algebra 12 where you will get detailed explanations on easiest path to the solutions.

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