SSC CGL Tier II level Question Set 9, Algebra 4 | SureSolv

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SSC CGL Tier II level Question Set 9, Algebra 4

9th SSC CGL Tier II level Question Set, 4th on Algebra

SSC-CGL Tier 2 question set 9 algebra 4

This is the 9th question set of 10 practice problem exercise for SSC CGL Tier II exam and the 4th 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.

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


9th question set - 10 problems for SSC CGL exam: 4th on topic Algebra - answering time 12 mins

Q1. If $x+\displaystyle\frac{2}{x}=1$, then the value of $\displaystyle\frac{x^2+x+2}{x^2(1-x)}$ is,

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

Q2. If $4x+5y=83$, and $3x : 2y=21 : 22$, then $(y-x)$ equals to,

  1. 4
  2. 7
  3. 3
  4. 11

Q3. If $\displaystyle\frac{3-5x}{2x} + \displaystyle\frac{3-5y}{2y} + \displaystyle\frac{3-5z}{2z}=0$, then the value of $\displaystyle\frac{2}{x}+\displaystyle\frac{2}{y}+\displaystyle\frac{2}{z}$ is,

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

Q4. If $\displaystyle\frac{2p}{p^2-2p+1}=\frac{1}{4}$ then the value of $\left(p+\displaystyle\frac{1}{p}\right)$ is,

  1. $1$
  2. $10$
  3. $\displaystyle\frac{2}{5}$
  4. $7$

Q5. If $2x=\sqrt{a}+\displaystyle\frac{1}{\sqrt{a}}$, and $a \gt 0$, then the value of $\displaystyle\frac{\sqrt{x^2-1}}{x-\sqrt{x^2-1}}$ is,

  1. $a+1$
  2. $a-1$
  3. $\frac{1}{2}(a-1)$
  4. $\frac{1}{2}(a+1)$

Q6. If $x^2+y^2+z^2=xy+yz+zx$, then the value of $\displaystyle\frac{3x^4+7y^4+5z^4}{5x^2y^2+7y^2z^2+3z^2x^2}$ is,

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

Q7. If $\displaystyle\frac{a^2-bc}{a^2+bc}+\displaystyle\frac{b^2-ca}{b^2+ca}+\displaystyle\frac{c^2-ab}{c^2+ab}=1$, then the value of $\displaystyle\frac{a^2}{a^2+bc}+\displaystyle\frac{b^2}{b^2+ca}+\displaystyle\frac{c^2}{c^2+ab}$ is,

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

Q8. If $2\left(x^2+\displaystyle\frac{1}{x^2}\right) - \left(x-\displaystyle\frac{1}{x}\right) -7 =0$ then the two valid values of $x$ are,

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

Q9. If $x=\sqrt[3]{a+\sqrt{a^2+b^3}}+\sqrt[3]{a-\sqrt{a^2+b^3}}$, then $x^3+3bx$ is equal to,

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

Q10. If $bc+ca+ab=abc$, then the value of $\displaystyle\frac{b+c}{bc(a-1)} + \displaystyle\frac{c+a}{ca(b-1)}+\displaystyle\frac{a+b}{ab(c-1)}$ is,

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

For detailed conceptual solutions to the questions refer to SSC CGL Tier II level Solution set 9 Algebra 4.

Watch quick solutions in two-part video.

Part I: Q1 to Q5

Part II: Q6 to Q10


Answers to the questions

Problem 1: Answer: Option c: 1.

Problem 2: Answer: Option a : 4.

Problem 3: Answer: Option a: 10.

Problem 4: Answer: Option b: 10.

Problem 5: Answer: Option c: $\frac{1}{2}(a-1)$.

Problem 6: Answer: Option b : $1$.

Problem 7: Answer: Option a: $2$.

Problem 8: Answer: Option d: $2$, $-\frac{1}{2}$.

Problem 9: Answer: Option d: $2a$.

Problem 10: Answer: Option b: $1$.


Additional help on Suresolv Algebra

To use the extensive range of articles on quick algebra problem solving, follow the guide,

5 step Suresolv Algebra Reading and Practice Guide for SSC CGL Tier II.

You will get step by step recommended actions for success in SSC CGL Tier II and other relevant competitive exams along with the full list of articles on Algebra with links.

The list includes: ALL Concept articles on Algebra, ALL articles on How to solve difficult Algebra problems in a few steps, ALL Question and Solution Sets for SSC CGL and ALL Question and Solution sets for SSC CGL Tier II.

Important points to remember

  • SSC CGL problem solving builds the foundation for excellence on SSC CGL Tier II exam.
  • Concept articles are particularly valuable for learning the concepts and techniques, whereas How to solve in a few steps articles show how the techniques are applied to actually solve specially selected problems from real exam.
  • Finally, each of the large number of question sets should certainly be used as a timed mini-mock test for analysis of your difficulties in answering followed by clarification of doubts from the corresponding solution set.

Wish you all the sure success.


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