SSC CGL Tier II level Question Set 1, Algebra 1

1st SSC CGL Tier II level Question Set, 1st on Algebra

SSC CGL Tier 2 question set 1 algebra1

This is the 1st question set of 10 practice problem exercise for SSC CGL Tier II exam and also the 1st 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.


1st question set - 10 problems for SSC CGL exam: 1st on topic Algebra - answering time 12 mins

Q1. Find the maximum value of the expression $(p^2 +7p+13)^{-1}$.

  1. $\displaystyle\frac{5}{7}$
  2. $\displaystyle\frac{4}{3}$
  3. $20$
  4. $\displaystyle\frac{3}{7}$

Q2. If $n=7+3\sqrt{5}$, then the value of $\left(\sqrt{n} + \displaystyle\frac{1}{\sqrt{n}}\right)$ is,

  1. $\displaystyle\frac{5}{7}$
  2. $\displaystyle\frac{7}{12}$
  3. $\displaystyle\frac{9+\sqrt{5}}{2\sqrt{2}}$
  4. $\displaystyle\frac{\sqrt{5}}{2\sqrt{2}}$

Q3. If $x=20$, $y=19$, the value of $\displaystyle\frac{x^2+y^2+xy}{x^3-y^3}$ is,

  1. $35$
  2. $1$
  3. $324$
  4. $365$

Q4. If $p + \displaystyle\frac{2p}{3} + \displaystyle\frac{p}{2} +\displaystyle\frac{p}{7}=97$, then the value of $p$ is,

  1. 46
  2. 44
  3. 40
  4. 42

Q5. If $p=1+\sqrt{2}+\sqrt{3}$, then $\left(p+\displaystyle\frac{1}{p-1}\right)$ is,

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

Q6. If $(x+y) : (y+z) : (z+x) = 6 : 7 : 8$ and $x+y+z=14$, then value of $z$ is,

  1. 6
  2. 14
  3. 8
  4. 7

Q7. If $x=\displaystyle\frac{\sqrt{2}+1}{\sqrt{2}-1}$ and $xy=1$ find the value of $\displaystyle\frac{2x^2+3xy+2y^2}{2x^2-3xy+2y^2}$.

  1. $\displaystyle\frac{71}{65}$
  2. $\displaystyle\frac{7}{12}$
  3. $\displaystyle\frac{65}{71}$
  4. $\displaystyle\frac{72}{7}$

Q8. If $x=\displaystyle\frac{a+b}{1-ab}$ and $y=\displaystyle\frac{a-b}{1+ab}$ then the value of $\displaystyle\frac{x+y}{1-xy}$ is,

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

Q9. If $x+\displaystyle\frac{1}{x}=-2$, then the value of $x^{2n+1}+\displaystyle\frac{1}{2^{2n+1}}$ where $n$ is a positive integer is,

  1. $0$
  2. $2$
  3. $-5$
  4. $-2$

Q10. If $x=5^{n-1} +5^{-n-1}$ where $n$ is real, the minimum value of $x$ is,

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

Answers to the questions

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

Problem 2. Answer: Option c : $\displaystyle\frac{9+\sqrt{5}}{2\sqrt{2}}$.

Problem 3. Answer: Option b: 1.

Problem 4. Answer: Option d: 42.

Problem 5. Answer: Option a: $1+2\sqrt{3}$.

Problem 6. Answer: Option a : 6.

Problem 7. Answer: Option a: $\displaystyle\frac{71}{65}$.

Problem 8. Answer: Option c: $\displaystyle\frac{2a}{1-a^2}$.

Problem 9. Answer: Option d: -2.

Problem 10. Answer: Option d: $\displaystyle\frac{2}{5}$.


Additional help on SSC CGL Algebra

Apart from a large number of question and solution sets and a valuable article on "7 Steps for sure success on Tier 1 and Tier 2 of SSC CGL" rich with concepts and links, you may refer to our other articles specifically on Algebra,

SSC CGL Tier II level Question Set 3, Algebra 3

SSC CGL Tier II level Solution Set 3, Algebra 3

SSC CGL Tier II level Question Set 2, Algebra 2

SSC CGL Tier II level Solution Set 2, Algebra 2

SSC CGL Tier II level Solution Set 1, Algebra 1

How to solve difficult SSC CGL Algebra problems in a few steps 14

How to solve difficult SSC CGL Algebra problems in a few steps 13

How to solve difficult SSC CGL Algebra problems in a few steps 12

More rich algebraic concepts and techniques for elegant solutuions of SSC CGL problems

Basic and rich algebraic concepts for elegant Solutions of SSC CGL problems

How to solve difficult SSC CGL Algebra problems in a few steps 11

How to solve difficult SSC CGL Algebra problems in a few assured steps 10

How to solve difficult SSC CGL Algebra problems in a few steps 9

How to solve difficult SSC CGL Algebra problems in a few steps 8

How to solve difficult SSC CGL Algebra problems in a few steps 7

How to solve difficult Algebra problems in a few simple steps 6

How to solve difficult Algebra problems in a few simple steps 5

How to solve difficult surd Algebra problems in a few simple steps 4

How to solve difficult Algebra problems in a few simple steps 3

How to solve difficult Algebra problems in a few simple steps 2

How to solve difficult Algebra problems in a few simple steps 1

SSC CGL level Question Set 51, Algebra 12

SSC CGL level Solution Set 51, Algebra 12

SSC CGL level Question Set 45 Algebra 11

SSC CGL levelĀ  Solution Set 45, Algebra 11

SSC CGL level Solution Set 35 on Algebra 10

SSC CGL level Question Set 35 on Algebra 10

SSC CGL level Solution Set 33 on Algebra 9

SSC CGL level Question Set 33 on Algebra 9

SSC CGL level Solution Set 23 on Algebra

SSC CGL level Question Set 23 on Algebra

SSC CGL level Solution Set 22 on Algebra

SSC CGL level Question Set 22 on Algebra

SSC CGL level Solution Set 13 on Algebra

SSC CGL level Question Set 13 on Algebra

SSC CGL level Question Set 11 on Algebra

SSC CGL level Solution Set 11 on Algebra

SSC CGL level Question Set 10 on Algebra

SSC CGL level Solution Set 10 on Algebra

SSC CGL level Question Set 9 on Algebra

SSC CGL level Solution Set 9 on Algebra

SSC CGL level Question Set 8 on Algebra

SSC CGL level Solution Set 8 on Algebra

SSC CGL level Question Set 1 on Algebra

SSC CGL level Solution Set 1 on Algebra