Solution Set of Inequations on Number Line

Some relationships have been expressed through symbols which are explained below:

X = greater than
? = not less than
# = not equal to
^ = equal to
+ = not greater than
@ = less than

If a @ b @ c, which of the following does not imply?

Directions- In each of the following questions the symbols $\mathrm{\alpha }$, $\mathrm{\beta }$, $\gamma$, $\mathrm{\delta }$ and $Q$ have been used having their meaning as-
$\mathrm{M} \mathrm{\alpha } \mathrm{N}$ means $\mathrm{M}$ is greater than $\mathrm{N}$.
$\mathrm{M} \mathrm{\beta } \mathrm{N}$ means $\mathrm{M}$ is smaller than$\mathrm{N}$.
$\mathrm{M} \mathrm{\gamma } \mathrm{N}$ means $\mathrm{M}$ is not greater than $\mathrm{N}$.
$\mathrm{M} \mathrm{\delta } \mathrm{N}$ means $\mathrm{M}$ is not smaller than $\mathrm{N}$.
$M Q N$ means $\mathrm{M}$ is equal to $\mathrm{N}$.
Assuming the statement given in each of the following questions as true, deduce, which of the given five alternatives is definitely true ?

Statement: $4\mathrm{C} \mathrm{\delta } 3\mathrm{A}, \mathrm{B} \mathrm{\alpha } \mathrm{C}$

In these questions the symbols %, ©, ^, @ and # are used with different meanings as follows:
A % B means A is not greater than B.
A © B means A is neither greater than nor equal to B.
A ^ B means A is not smaller than B.
A @ B means A is neither smaller than nor equal to B.
A # B means A is neither greater than nor smaller than B.
Now in each of the following questions assuming the given statements to be true, find out which of the conclusions I, II, III given below them is/are definitely true and mark your answer accordingly.

Statements:
A ^ B,
C % B,
B @ D,
D # E
Conclusions:
I. A @ C
II. A # C
III. B @ E

In the question, two equations numbered I and II with variables $x$ and $y$ are given. You have to solve both the equations to find the value of $x$ and $y$. Give answer:
A. If $x>y$
B. If $x\ge y$
C. If $x<y$
D. If $x\le y$
E. If $x=y$ or relationship between $x$ and $y$ cannot be determined.

I. $12x^2-41x+35=0$
II. $4y^2-17y+15=0$

Directions- In each of the following questions the symbols $\mathrm{\alpha }$, $\mathrm{\beta }$, $\mathrm{\gamma }$, $\mathrm{\delta }$ and $\mathrm{Q}$ have been used having their meaning as-
$\mathrm{M} \mathrm{\alpha } \mathrm{N}$means $\mathrm{M}$ is greater than $\mathrm{N}$.
$\mathrm{M} \mathrm{\beta } \mathrm{N}$ means $\mathrm{M}$ is smaller than $\mathrm{N}$.
$\mathrm{M} \mathrm{\gamma } \mathrm{N}$ means $\mathrm{M}$is not greater than $\mathrm{N}$.
$\mathrm{M} \mathrm{\delta } \mathrm{N}$ means $\mathrm{M}$ is not shorter than $\mathrm{N}$.
$\mathrm{M} \mathrm{Q} \mathrm{N}$ means $\mathrm{M}$ is equal to $\mathrm{N}$.
Assuming the statement given in each of the following questions as true, deduce, which of the given five alternatives is definitely true ?

Statement: $2\mathrm{A} \mathrm{\alpha } 4\mathrm{C}, 4\mathrm{A} \mathrm{Q} 6\mathrm{B}$

Largest integral value of $x$ satisfying $\frac{x^2+2x-4}{x^2-4x+5}>3$ is 

If $\frac{\left|x+3\right|+x}{x+2}>1, \text{then} x\in$

The solution set of $2\left(x-2\right)>x-5$ is given by

Solution set of $\frac{2}{x}<3$ is 

The solution set of the inequality $-2\le \frac{3x+2}{2}<7$ is

The set of values of $k\left(k\in R\right),$ for which the equation $x^2-4\left|x\right|+3-\left|k-1\right|=0$ will have exactly four real roots is 

The solution set of the inequality $\frac{1}{x-2}-\frac{1}{x}⩽\frac{2}{x+2}$ is $(-\alpha ,\beta ]\cup \left(\gamma ,\alpha \right)\cup [\delta ,\infty )$ then 

The set of all real numbers satisfying the inequality $x-2<1$ is

Which of the following is an example of  'quadratic inequality in one variable' ?

Quantity I: ${\left(x-18\right)}^2=0$

Quantity II: $y^2=324$

If $2\le 3x-4\le 5,x\in R$, then $x$ belongs to the interval

For what range of values of ' $\mathrm{x}$ ' will be the inequality

$15 \mathrm{x}-\left(\frac{2 }{ \mathrm{x}}\right)>1$?

The domain of the function $\mathrm{f}\left(\mathrm{x}\right)={\log }_7\left\{{\log }_3\left({\log }_5\right.\right.$ $\left.\left.\left(20\mathrm{x}-{\mathrm{x}}^2-91\right)\right)\right\}$ is: 

The set of values of $x$ which satisfy the inequality $0.7^{2x^2-3x+4}<0.343$ is

On solving the inequalities $2x+5y\le 20,3x+2y\le 12,x\ge 0,y\ge 0$, we get the following situation