SSC CGL level Question Set 33, Algebra

Submitted by Atanu Chaudhuri on Sun, 03/07/2016 - 13:07

33rd SSC CGL level Question Set, 9th on Algebra

SSC CGL question set 33 algebra9

This is the 33rd question set of 10 practice problem exercise for SSC CGL exam and 9th 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 the 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.

33rd question set - 10 problems for SSC CGL exam: 9th on topic Algebra - answering time 15 mins

Q1. If $x = 2.361$, $y=3.263$, and $z=5.624$, then the value of $x^3 + y^3 - z^3 + 3xyz$ is,

35.621
1
0
19.277

Q2. If $6 + \displaystyle\frac{1}{x}=x$, then the value of $x^4 + \displaystyle\frac{1}{x^4}$ is,

1444
1442
1448
1446

Q3. If $x^2 + \displaystyle\frac{1}{x^2} = 66$, then the value of $\displaystyle\frac{x^2 - 1 + 2x}{x}$ is,

$\pm{8}$
$6, -10$
$10, -6$
$\pm{4}$

Q4. Find the minimum value of $2x^2 - (x - 3)(x + 5)$, where $x$ is real,

Q5. If $x+y=7$ then the value of $x^3 + y^3 + 21xy$ is,

Q6. If $x=\displaystyle\frac{\sqrt{3}}{2}$ then the value of $\displaystyle\frac{\sqrt{1+x} + \sqrt{1-x}}{\sqrt{1+x} - \sqrt{1-x}}$ will be,

$-\sqrt{3}$
$1$
$\sqrt{3}$
$-1$

Q7. If $p^3 + 3p^2 + 3p = 7$ then the value of $p^2 + 2p$ is,

Q8. If $\left(x + \displaystyle\frac{1}{x}\right)^2 = 3$ then the value of $(x^{72} + x^{66} + x^{54} + x^{36} + x^{24} + x^6 + 1)$ is,

Q9. If $a^2 + b^2 + c^2 = 2(a -b -c) -3$, then $4a - 3b + 5c$ is,

Q10. If $3x + \displaystyle\frac{1}{2x} = 5$, then the value of $8x^3 + \displaystyle\frac{1}{27x^3}$ is,

$118\frac{1}{2}$
$0$
$30\frac{10}{27}$
$1$

Solutions to the problems

For detailed conceptual solutions with answers you should refer to the companion SSC CGL level Solution Set 33 on Algebra where you will get detailed explanations on easiest path to the solutions.

Watch the quick mental solutions in the two-part video.

Part I: Q1 to Q5

Part II: Q6 to Q10

Guided help on Suresolv Algebra

All Suresolv Algebra articles are listed with links at the end, but it is unguided list.

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

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

Basically, it is how to read and practice Suresolv Algebra guide.

This contains even list of puzzles or even high school math articles on Algebra.

Wish you all the sure success.

Resources on Suresolv 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 listed on latest shown first basis,