## 57th SSC CGL level Question Set, 13th on Algebra

This is the 57th question set of 10 practice problem exercise for SSC CGL exam and 13th 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 companion 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.

Before taking the test you may like to go through 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*.

### 57th question set - 10 problems for SSC CGL exam: 13th on topic Algebra - answering time 12 mins

**Problem 1.**

If $ab + bc+ca=0$, then the value of $\left(\displaystyle\frac{1}{a^2-bc}+\displaystyle\frac{1}{b^2-ca}+\displaystyle\frac{1}{c^2-ab}\right)$ is,

- $1$
- $0$
- $a+b+c$
- $3$

**Problem 2.**

The graph of the linear equations $3x+4y=24$ is a straight line intersecting x-axis and y-axis at the points $A$ and $B$ respectively. $P (2, 0)$ and $Q \left(0, \displaystyle\frac{3}{2}\right)$ are two points on the sides OA and OB respectively of $\triangle OAB$, where O is the origin of the co-ordinate system. If $AB=10$ cm, PQ will be equal to,

- 2.5 cm
- 20 cm
- 5 cm
- 40 cm

**Problem 3.**

If $x^4+\displaystyle\frac{1}{x^4}=119$, then the positive value of $x^3-\displaystyle\frac{1}{x^3}$ is,

- 27
- 36
- 49
- 25

**Problem 4.**

If $a$, $b$, $c$ are positive real numbers and $a+b+c=1$, then the least value of $\displaystyle\frac{1}{a}+\displaystyle\frac{1}{b}+\displaystyle\frac{1}{c}$ is,

- $1$
- $5$
- $9$
- $-1$

**Problem 5.**

If $\displaystyle\frac{x-a^2}{b+c} +\displaystyle\frac{x-b^2}{c+a} +\displaystyle\frac{x-c^2}{a+b}=4(a+b+c)$, with $a$ $b$, and $c$ positive real variables, value of $x$ is,

- $a^2+b^2+c^2$
- $ab +bc +ca$
- $a^2+b^2+c^2 - ab - bc - ca$
- $(a+b+c)^2$

**Problem 6.**

Number of solutions in the two equations, $4x-y=2$ and $2y-8x+4=0$ is,

- zero
- two
- one
- infinitely too many

**Problem 7.**

Let $a=\sqrt{6}-\sqrt{5}$, $b=\sqrt{5}-2$ and $c=2-\sqrt{3}$. Then the relation between $a$, $b$ and $c$ is,

- $b \lt c \lt a$
- $b \lt a \lt c$
- $a \lt b \lt c$
- $a \lt c \lt b$

**Problem 8.**

For real $x$, the maximum value of $3x^2+\displaystyle\frac{4}{x^2}$ is,

- $2\sqrt{3}$
- $3\sqrt{2}$
- $4\sqrt{3}$
- none of the above

**Problem 9.**

If $(3x-2y):(2x+3y)=5:6$ then one of the values of $\left(\displaystyle\frac{\sqrt[3]{x}+\sqrt[3]{y}}{\sqrt[3]{x}-\sqrt[3]{y}}\right)^2$ is,

- $25$
- $5$
- $\displaystyle\frac{1}{5}$
- $\displaystyle\frac{1}{2}$

**Problem 10.**

If $\displaystyle\frac{x^{24}+1}{x^{12}}=7$, then the value of $\displaystyle\frac{x^{72}+1}{x^{36}}$ is,

- 433
- 322
- 432
- 343

### Solutions to the problems

For detailed **conceptual solutions with answers** you should refer to the companion * SSC CGL level Solution Set 57 on Algebra* where you will get detailed explanations on easiest path to the solutions.

Watch * quick solutions in two-part video*.

**Part I: Q1 to Q5**

**Part II: Q6 to Q10**

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