SSC CGL level Question Set 51, Algebra 12 | SureSolv

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SSC CGL level Question Set 51, Algebra 12

51st SSC CGL level question Set, 12th on Algebra

SSC CGL question set 51 algebra12

This is the 51st question set of 10 practice problem exercise for SSC CGL exam and 12th on topic Algebra.

For maximum gains, the test should be taken first, that is obvious. But more importantly, to absorb the concepts, techniques and deductive reasoning elaborated through these solutions, one must solve many problems in a systematic manner using this conceptual analytical approach.

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Before taking the test you may like to go through our concept tutorials on Algebra and other related topics,

Basic and rich Algebraic concepts for elegant solutions of SSC CGL problems,

More Basic and rich Algebraic concepts for elegant solutions of SSC CGL problems

SSC CGL level difficult problem solving by Componendo dividendo.


51st question set - 10 problems for SSC CGL exam: 12th on topic Algebra - answering time 15 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. $\displaystyle\frac{4}{3}$

Answers to the questions

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: $\displaystyle\frac{3}{4}$.


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.

Watch quick solutions on two-part video.

Part I: Q1 to Q5

Part II: Q6 to Q10


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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