In the following question the symbols #, *, @. ! and = are used with the following meanings:
A # B means A is greater than B.
A * B means A is greater than or equal to B.
A @ B means A is equal to B.
A ! B means A is lesser than B.
A = B means A is lesser than or equal to B.
Now in each of the following questions, assuming the three statements to be true, find which of the two
conclusions I and II given below them is/are true. Give answer.
1) if only conclusion I is true
2) if only conclusion II is true
3) if either conclusion I or conclusion II is true
4) if neither conclusion I nor conclusion II is true
5) if both conclusions I and II are true.

Statements : P = Q, T @ R, R # P
Conclusions :
I.T = Q
II. T # Q

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?

$\left(20+3\right)\times 6+8-32=76$ 

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

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.

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.

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. $L=M II. M < L$