SSC CGL level Question Set 45, Algebra 11 | SureSolv

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SSC CGL level Question Set 45, Algebra 11

45th SSC CGL level Question Set, 11th on Algebra

SSC CGL question set 45 algebra11

This is the 45th question set of 10 practice problem exercise for SSC CGL exam and 11th 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 the solutions, one must solve many problems in a systematic manner using this conceptual analytical approach.

Learning by doing is the best learning. There is no other alternative towards achieving excellence.

Before taking the test you may like to refer to 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 Algebra problem solving by Componendo dividendo.


45th question set - 10 problems for SSC CGL exam: 11th on topic Algebra - answering time 15 mins

Problem 1.

If $\displaystyle\frac{5x}{2x^2+5x+1}=\frac{1}{3}$, then the value of $\left(x+\displaystyle\frac{1}{2x}\right)$ is,

  1. 5
  2. 10
  3. 15
  4. 20

Problem 2.

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

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

Problem 3.

If $x^3+\displaystyle\frac{3}{x}=4(a^3+b^3)$ and $3x+\displaystyle\frac{1}{x^3}=4(a^3-b^3)$ then $a^2-b^2$ is equal to,

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

Problem 4.

If $ab + bc+ca=0$, then the value of $\displaystyle\frac{1}{a^2-bc} +\displaystyle\frac{1}{b^2-ac}+\displaystyle\frac{1}{c^2-ab}$ is,

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

Problem 5.

If $x$ is a rational number and $\displaystyle\frac{(x+1)^3-(x-1)^3}{(x+1)^2-(x-1)^2}=2$ then the sum of numerator and denominator of $x$ is,

  1. $7$
  2. $4$
  3. $5$
  4. $3$

Problem 6.

If $a+b+c=0$ then the value of $(a+b-c)^2+(b+c-a)^2+(c+a-b)^2$ will be equal to,

  1. $4(a^2+b^2+c^2)$
  2. $4(ab+bc+ca)$
  3. $0$
  4. $8abc$

Problem 7.

If $x^2+y^2=5xy$, ,then the value of $\left(\displaystyle\frac{x^2}{y^2}+\displaystyle\frac{y^2}{x^2}\right)$ is equal to,

  1. $32$
  2. $16$
  3. $-23$
  4. $23$

Problem 8.

If $x+\displaystyle\frac{2}{x}=1$, then tne value of $\displaystyle\frac{x^2+x+2}{x^2(x-1)}$ is,

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

Problem 9.

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 numbers, then $a+b+c$ is equal to,

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

Problem 10.

If $x=7+4\sqrt{3}$ then the value of $\left(\sqrt{x}+\displaystyle\frac{1}{\sqrt{x}}\right)$ is,

  1. $2\sqrt{3}$
  2. $-2\sqrt{3}$
  3. $4$
  4. $-4$

Answers to the questions

Problem 1. Answer: Option a: 5.

Problem 2. Answer: Option b : $-2$.

Problem 3. Answer: Option a: $1$.

Problem 4. Answer: Option a: $0$.

Problem 5. Answer: Option b: $4$.

Problem 6. Answer: Option a : $4(a^2+b^2+c^2)$.

Problem 7. Answer: Option d: $23$.

Problem 8. Answer: Option c: $-1$.

Problem 9. Answer: Option c: 0.

Problem 10. Answer: Option a: $4$.


Solutions to the problems

For detailed conceptual solutions with answers you should refer to the companion SSC CGL level Solution Set 45 on Algebra where you will get detailed explanations on easiest path to the solutions.

Watch the video solutions for the ten problems in the 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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