In the following questions some symbols @, © , $, % and # are used with the following meaning as illustrated below:
'Y @ Z' means 'Y is not greater than Z'.
'Y © Z' means 'Y is not smaller than Z'.
'Y $ Z' means 'Y is neither smaller than nor equal to Z'.
'Y % Z' means 'Y is neither greater than nor equal to Z'.
'Y # Z' means 'Y is neither smaller than nor greater than Z'.
Now in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given below them is/are definitely true and give your answer accordingly.

Statements:
W©V, V$U, U%C, C@Y, Y©D

Conclusions:
I. YU
II. V%C
III. D#V

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

$64\times 8÷6-4\times 2=?$  

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

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

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

The interchange of which of the given numbers or signs in the alternatives will make the given equation meaningful?

$\left(20+3\right)\times 6+8-32=76$ 

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.

Two equations are given, you have to solve both the equations and should get the answer:

$\left(i\right) X^2-15X+56=0$

$\left(ii\right) Y=\sqrt{64}$

When $- \& =, 60 \& 20$ are interchanged, find which one of the following equations will be correct?

Quantity $1$: A pipe alone can fill a cistern in $60$ minutes. But due to leakage pipe filled only $80\%$ of the cistern in $60$ minutes. $"X"$ is the capacity of the cistern in litres and due to leakage $60$ litres were leaked out in $1$ hour.

Quantity $2$: $250$ litres.

Two equations are given, you should solve both the equations and get the answer:

$\left(i\right) X^2-11X+24=0$

$\left(ii\right) Y^2+14Y-45+0$

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

Find the relation between these two quantities.

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

$\left(i\right) 2X^2-4X+2=0$

$\left(ii\right) 2Y^2-Y-1=0$

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

$\left(i\right) X^2-X-6=0$

$\left(ii\right) Y^2-6Y+8=0$

I. Simple interest for $3 \mathrm{years}$  at $11\%$ rate on $\mathrm{x}$.

II. Compound interest for $3 \mathrm{years}$  at $10\%$ rate on $\mathrm{x}$.

Find the relation between these two quantities.

Directions:

If $\vee$ stands for $\times$, $\wedge$ stands for $+$, $\forall$ stands for $-$ and $A$ stands for $÷$.

Then, which of the following will be the correct equation? 

In each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II given below is/are definitely true.Give answer1. If only conclusion I is true. $2$. If only conclusion II is true. $3$. If either conclusion I or II is true. $4$. If neither conclusion I nor II is true. $5$. If both conclusions I and II are true.

Statements: $Z>Y,Y>L, L>M, M<N, N<Q$

Conclusions: I. $L=M II. M < L$