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:
Z % Y,
Y © X,
X # W,
W © V
Conclusions:
I. V % X
II. Z # W
III. Z © W

Consider the following statements:
(i) When $0<\mathrm{x}<1$, then $\frac{1}{1+\mathrm{x}}<1-\mathrm{x}+{\mathrm{x}}^2$.

(ii) When $0<\mathrm{x}<1$, then $\frac{1}{1+\mathrm{x}}>1-\mathrm{x}+{\mathrm{x}}^2$.

(iii) When $-1<\mathrm{x}<0$, then $\frac{1}{1+\mathrm{x}}<1-\mathrm{x}+{\mathrm{x}}^2$.

(iv) When $-1<\mathrm{x}<0$, then $\frac{1}{1+\mathrm{x}}>1-\mathrm{x}+{\mathrm{x}}^2$.

Then the correct statements are

In the given below question substitutes for various mathematical symbols, followed by a question involving the calculation of an expression is given. Put the real signs in the given equations and solve the question.

If $+$ means $÷$, $÷$ means $-$, $-$ means $\times$, $\times$ means $+$, then

$64\times 8÷6-4\times 2=?$  

I.$(7{)}^{450}>(9{)}^{300}$

II .${\left(2\right)}^{900}>{\left(7\right)}^{450}$

$\mathrm{Quantity} \mathrm{I}=18 {\mathrm{x}}^3{\mathrm{y}}^3, \mathrm{Quantity} \mathrm{II}=12 {\mathrm{x}}^4{\mathrm{y}}^4, \mathrm{if} \mathrm{x}>0 \& \mathrm{y}<0$

Find the relation between these two quantities.

The speed of a boat in still water and the speed of the current is in ratio $5:1$. If the difference between distances covered by the boat in going $2 \mathrm{hours}$ upstream and $2 \mathrm{hours}$  downstream is $8 \mathrm{km}$.

I. Quantity I - Speed of boat in still water

II. Quantity II -A cyclist goes $30 \mathrm{km}$ in $3 \mathrm{hours}$ 

Find the relation between these two quantities.

Consider the following inequalities:

$$\begin{gathered} 1. \frac{a^2-b^2}{a^2+b^2}>\frac{a-b}{a+b}, \text{where} a>b>0 \\ 2. \frac{a^3+b^3}{a^2+b^2}>\frac{a^2+b^2}{a+b}, \text{where} a>b>0 \end{gathered}$$

Which of the above is/ are correct?

To get the correct equation, choose which set of signs from the given alternatives to be substituted sequentially in place of $\left(*\right)$

$13 * 4 * 5 * 12 * 6$

Two equations are given, you have to solve the both the equations:

$\left(i\right) X^2=196$

$\left(ii\right) Y^2+2y-48=0$

To get the correct equation, choose which set of signs from the given alternatives to be substituted sequentially in place of $\left(*\right)$

$15 * 3 * 5 * 16 * 41$