3rd SSC CGL Tier II level Question Set, 3rd on Algebra
This is the 3rd question set of 10 practice problem exercise for SSC CGL Tier II exam and also the 3rd 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.
3rd question set - 10 problems for SSC CGL exam: 3rd on topic Algebra - answering time 12 mins
Q1. If $4y-3x=13$ and $xy=14$, then $64y^3-27x^3$ is,
- 8479
- 8400
- 8740
- 8749
Q2. If $x=(0.09)^2$, $y=\displaystyle\frac{1}{(0.09)^2}$ and $z=(1- 0.09)^2 - 1$, then which of the following relations is true?,
- $y \lt x$ and $x=z$
- $y \lt z \lt x$
- $z \lt x \lt y$
- $x \lt y$ and $x=z$
Q3. Minimum value of $x^4 +\displaystyle\frac{1}{x^4+1} - 3$ is,
- $0$
- $-1$
- $-2$
- $-3$
Q4. If $\displaystyle\frac{p}{3}=\frac{q}{2}$ then the value of $\displaystyle\frac{2p+3q}{3p-2q}$ is,
- $1$
- $\displaystyle\frac{12}{5}$
- $\displaystyle\frac{5}{12}$
- $\displaystyle\frac{12}{7}$
Q5. If $(a-4)^2 + (b-9)^2+(c-3)^2=0$, then the value of $\sqrt{a+b+c}$ is,
- $\pm{4}$
- $4$
- $-4$
- $\pm{2}$
Q6. If $\displaystyle\frac{1}{x+y}=\displaystyle\frac{1}x+\displaystyle\frac{1}{y}$, where, $x \neq 0$, $y \neq 0$ and $x \neq y$, the value of $x^3-y^3$ is,
- $0$
- $2$
- $1$
- $-1$
Q7. If $a^x=(x+y+z)^y$, $a^y=(x+y+z)^z$ and $a^z=(x+y+z)^x$ find the value of $a+b+c$ where $a \neq 0$.
- $0$
- $1$
- $a^3$
- $a$
Q8. If $\displaystyle\frac{x-a^2}{b^2+c^2} + \displaystyle\frac{x-b^2}{c^2+a^2} +\displaystyle\frac{x-c^2}{a^2+b^2} =3$ then the value of $x$ is,
- $a^2+b^2$
- $a^2+b^2+c^2$
- $a^2+b^2-c^2$
- $a^2-b^2-c^2$
Q9. If $ax^2+bx+c=a(x-p)^2$, then the correct relation between $a$, $b$ and $c$ would be,
- $2b=a+c$
- $b^2=4ac$
- $b^2=ac$
- $abc=1$
Q10. If $\displaystyle\frac{y}{x} - \displaystyle\frac{x}{y}=3$, then find the value of $\displaystyle\frac{x^3}{y^3} + \displaystyle\frac{y^3}{x^3}$.
- $10\sqrt{3}$
- $10\sqrt{13}$
- $13\sqrt{3}$
- $13\sqrt{10}$
For detailed conceptual solution to the questions, refer to SSC CGL Tier II level Solution set 3 Algebra 3.
Watch quick solutions in the two-part video.
Part I: Q1 to Q5
Part II: Q6 to Q10
Answers to the questions
Problem 1: Answer: Option d: 8749.
Problem 2: Answer: Option c : $z \lt x \lt y$.
Problem 3: Answer: Option c: $-2$.
Problem 4: Answer: Option b: $\displaystyle\frac{12}{5}$.
Problem 5: Answer: Option b: 4.
Problem 6: Answer: Option a : 0.
Problem 7: Answer: Option d: $a$.
Problem 8: Answer: Option b: $a^2+b^2+c^2$.
Problem 9: Answer: Option b: $b^2=4ac$.
Problem 10: Answer: Option b: $10\sqrt{13}$.
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.
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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.
