SSC CGL Tier II level Question Set 14, Algebra 5

14th SSC CGL Tier II level Question Set, 5th on Algebra

This is the 14th question set of 10 practice problem exercise for SSC CGL Tier II exam and the 5th on topic Algebra.

To solve such problems quickly, identification of inherent patterns and use of associated methods are necessary. The corresponding solution set encapsulates the approach.

It is recommended that you take the test first and then only refer to its solution set. Taking the test will enable you to appreciate the pattern based solution process better. The answers and link of the corresponding solution set are available at the end.

---

14th question set - 10 problems for SSC CGL Tier II exam: 5th on topic Algebra - answering time 15 mins

Q1. If $x=\displaystyle\frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}-\sqrt{11}}$, and $y=\displaystyle\frac{1}{x}$, then the value of $3x^2-5xy+3y^2$ is,

1. 1771
2. 1717
3. 1177
4. 1171

Q2. If $x=7+4\sqrt{3}$ find the value of $\displaystyle\frac{3x^6+2x^4+4x^3+2x^2+3}{x^4+x^3+x^2}$ is,

1. $\displaystyle\frac{8238}{15}$
2. $\displaystyle\frac{8138}{15}$
3. $\displaystyle\frac{8338}{15}$
4. $\displaystyle\frac{8138}{17}$

Q3. The value of the expression $\displaystyle\frac{(x^2-y^2)^3+(y^2-z^2)^3+(z^2-x^2)^3}{(x-y)^3+(y-z)^3+(z-x)^3}$  is,

1. $(x^2-y^2)(y^2-z^2)(z^2-x^2)$
2. $3(x+y)(y+z)(z+x)$
3. $(x+y)(y+z)(z+x)$
4. $3(x-y)(y-z)(z-x)$

Q4. If $a+b+c=5$, $ab+bc+ca=7$ and $abc=3$ find the value of $\left(\displaystyle\frac{a}{b}+\displaystyle\frac{b}{a}\right)+\left(\displaystyle\frac{b}{c}+\displaystyle\frac{c}{b}\right)+\left(\displaystyle\frac{c}{a}+\displaystyle\frac{a}{c}\right)$.

1. $9\displaystyle\frac{2}{3}$
2. $8\displaystyle\frac{2}{3}$
3. $8\displaystyle\frac{1}{3}$
4. $7\displaystyle\frac{2}{3}$

Q5. If $a \neq b \neq c$, then the value of $\displaystyle\frac{a^2+b^2+c^2}{ab+bc+ca}$ is,

1. greater than 1
2. equal to 1
3. less than 1
4. can't be defined

Q6. If $x+y=4$ and $x^2+y^2=14$, where $x \gt y$, the values of $x$ and $y$ respectively are,

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

Q7. If $a^2+b^2+c^2=2(2a-3b-5c)-38$, then the value of $(a-b-c)$ is,

1. $12$
2. $10$
3. $9$
4. $11$

Q8. The expression, $a^2+\displaystyle\frac{1}{a^2} -13a+\displaystyle\frac{13}{a}+34$ converted to product of factors is,

1. $\left(a+\displaystyle\frac{1}{a}-4\right)\left(a+\displaystyle\frac{1}{a}+9\right)$
2. $\left(a-\displaystyle\frac{1}{a}-4\right)\left(a-\displaystyle\frac{1}{a}-9\right)$
3. $\left(a-\displaystyle\frac{1}{a}+4\right)\left(a-\displaystyle\frac{1}{a}+9\right)$
4. $\left(a+\displaystyle\frac{1}{a}+4\right)\left(a-\displaystyle\frac{1}{a}+9\right)$

Q9. If $a+b+c=0$, then $\displaystyle\frac{2a^2}{b^2+c^2-a^2}+\displaystyle\frac{2b^2}{c^2+a^2-b^2}+\displaystyle\frac{2c^2}{a^2+b^2-c^2}+3$ is equal to,

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

Q10. If $a=2+\sqrt{3}$, then the value of $\displaystyle\frac{a^3}{a^6+3a^3+1}$ is,

1. $55$
2. $\displaystyle\frac{3}{55}$
3. $\displaystyle\frac{1}{55}$
4. $\displaystyle\frac{1}{40}$

To know how to solve the problems quickly in a few steps, refer to the corresponding solution set,

SSC CGL Tier II Solution set 14, Algebra 5.

Watch the quick solutions in two-part video.

Part I: Q1 to Q5

Part II: Q6 to Q10

---

Answers to the questions

Problem 1. Answer: Option b: 1717.

Problem 2. Answer: Option b : $\displaystyle\frac{8138}{15}$.

Problem 3. Answer: Option c: $(x+y)(y+z)(z+x)$.

Problem 4. Answer: Option b: $8\displaystyle\frac{2}{3}$.

Problem 5. Answer: Option a: greater than 1.

Problem 6. Answer: Option c : $2+\sqrt{3}$, $2-\sqrt{3}$.

Problem 7. Answer: Option b: $10$.

Problem 8. Answer: Option b: $\left(a-\displaystyle\frac{1}{a}-4\right)\left(a-\displaystyle\frac{1}{a}-9\right)$.

Problem 9. Answer: Option d: $0$.

Problem 10. Answer: Option b: $\displaystyle\frac{1}{55}$.

---

Other resources that you may find valuable

Concept tutorials on Algebra and other related topics

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

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

SSC CGL level difficult Algebra problem solving by Componendo dividendo

Proof of least value of sum of reciprocals for any number of positive variables

How to factorize 25 selected quadratic equations quickly by factor analysis

General guidelines for successful performance in SSC CGL test

7 Steps for sure success in SSC CGL tier 1 and tier 2 competitive tests

Difficult algebra problem solving using high power methods

How to solve difficult algebra problems in a few steps

SSC CGL Tier II level question and solution sets on Algebra

SSC CGL Tier II level Solution Set 17, Algebra 6

SSC CGL Tier II level Question Set 17, Algebra 6

SSC CGL Tier II level Solution Set 14, Algebra 5

SSC CGL Tier II level Question Set 14, Algebra5

SSC CGL Tier II level Question Set 9, Algebra 4

SSC CGL Tier II level Solution Set 9, Algebra 4

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 Question Set 1 Algebra 1

SSC CGL Tier II level Solution Set 1, Algebra 1

SSC CGL level question and solution sets on Algebra

SSC CGL level Question Set 81, Algebra 17

SSC CGL level Solution Set 81, Algebra 17

SSC CGL level Question Set 74, Algebra 16

SSC CGL level Solution Set 74, Algebra 16

SSC CGL level Question Set 64, Algebra 15

SSC CGL level Solution Set 64, Algebra 15

SSC CGL level Question Set 58, Algebra 14

SSC CGL level Solution Set 58, Algebra 14

SSC CGL level Question Set 57, Algebra 13

SSC CGL level Solution Set 57, Algebra 13

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 level Solution Set 45, Algebra 11

SSC CGL level Question Set 35, Algebra 10

SSC CGL level Solution Set 35, Algebra 10

SSC CGL level Question Set 33, Algebra 9

SSC CGL level Solution Set 33, Algebra 9

SSC CGL level Question Set 23, Algebra 8

SSC CGL level Solution Set 23, Algebra 8

SSC CGL level Question Set 22, Algebra 7

SSC CGL level Solution Set 22, Algebra 7

SSC CGL level Question Set 13, Algebra 6

SSC CGL level Solution Set 13, Algebra 6

SSC CGL level Question Set 11, Algebra 5

SSC CGL level Solution Set 11, Algebra 5

SSC CGL level Question Set 10, Algebra 4

SSC CGL level Solution Set 10, Algebra 4

SSC CGL level Question Set 9, Algebra 3

SSC CGL level Solution Set 9, Algebra 3

SSC CGL level Question Set 8, Algebra 2

SSC CGL level Solution Set 8, Algebra 2

SSC CGL level Question Set 1, Algebra 1

SSC CGL level Solution Set 1, Algebra 1

Getting content links in your mail

You may get link of any content published

• from this site by site subscription or,
• on competitive exams by exams subscription.

---