In the following question, some symbols $@, \$, \copyright , \#$ and $\%$ are used with the following meaning as illustrated below:
'A$@$B' means 'A is not greater than B'.
'A$\$$B' means 'A is neither smaller than nor equal to B'.
'A$\copyright$B' means 'A is not smaller than B'.
'A$\#$B' means 'A is neither greater than nor equal to B'
'A$\%$B' means 'A is neither smaller than nor greater than B'.
Now the following question, assuming the given statements to be true, find which of the two conclusions $\mathrm{I}$ and $\mathrm{II}$ given below is/are definitely true.

Statements: R$\copyright$G, K$\#$Z, K$\$$G, V$\#$Z

Conclusions: $\mathrm{I}.$ V$@$K                       $\mathrm{II}.$ R$\%$Z

A clock is so placed that at $12$ Noon its minute hand points towards West. The mathematical operators have been placed at the minute hand position at particular time given below:

$\text{'}<\text{'}$ at fifteen minutes before noon
$\text{'}=\text{'}$ at ten minutes past two
$\text{'}>\text{'}$ at half past six
$\text{'}\times \text{'}$ at twenty minutes past seven
$\text{'}+\text{'}$ at quarter past eight
$\text{'}-\text{'}$ at nine o’ clock
$\text{'}+\text{'}$ at five minutes to ten

Which is the correct mathematical expression based on above information?

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.

In this question, $\text{'}∆\text{'}$ means "Greater than" $\square$ means "Less than",$\text{'}\varphi \text{'}$  means "equal to" $\oplus$ means "not equal to"
If $\mathrm{C}∆\mathrm{A}$, $\mathrm{A}\square \mathrm{B}$, $\mathrm{D\varphi B}$ and $\mathrm{B}\oplus \mathrm{C}$, then choose the correct option in the following

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

$64\times 8÷6-4\times 2=?$  

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

In the following question choose the correct alternative assuming $\alpha$ stands for $=$; $\beta$ stands for $>$; $\gamma$ stands for $<$ and $\delta$ stands for $\ne$.

If $ax\gamma by, bx\alpha cz$ and $b^2\alpha ac$ then

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.

In the following question choose the correct alternative assuming $\alpha$ stands for $=$; $\beta$ stands for $>$; $\gamma$ stands for $<$ and $\delta$ stands for $\ne$.

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

$13 * 4 * 5 * 12 * 6$

In the following question choose the correct alternative assuming $\alpha$ stands for $=$; $\beta$ stands for $>$; $\gamma$ stands for $<$ and $\delta$ stands for $\ne$.

If $a^{2}x\alpha byz, czx\alpha b^{2}y$ and $c^{2}z\alpha axy$, then

In a coded language, the mathematical operators have been placed in clock. The position of operator is the position of minute hand. The coding is as follows $\text{'}+\text{'}$ at $7:25$, $\text{'}\times \text{'}$ at $5:15$, $\text{'}÷\text{'}$ at $9:00$, $\text{'}<\text{'}$ at $10:55$, $\text{'}>\text{'}$ at $3:30$, $\text{'}=\text{'}$ at $1:05$, $\text{'}-\text{'}$ at $11:25$. If positions of $\text{'}+\text{'}, \text{'}–\text{'}, \text{'}\times \text{'}, \text{'}÷\text{'}, \text{'}<\text{'}, \text{'}>\text{'}, \text{'}=\text{'}$ changed by rotation of angle $30°, 60°, 90°, 120°, 150°, 180°, 210°$ in the clockwise and anti-clockwise alternatively, then which of the following is correct statement?

In the following question choose the correct alternative assuming $\alpha$ stands for $=$; $\beta$ stands for $>$; $\gamma$ stands for $<$ and $\delta$ stands for $\ne$.

If $6x\alpha 5y$ and $2y\beta 3z$, then 

If 

$\text{'}+\text{'}$ implies $\text{'}\mathrm{go}\text{'}$

$\text{'}-\text{'}$ implies $\text{'}\mathrm{to}\text{'}$

$\text{'}\times \text{'}$ implies $\text{'}\mathrm{walk}\text{'}$

$\text{'}=\text{'}$ implies $\text{'}\mathrm{early}\text{'}$

$\text{'}<\text{'}$ implies $\text{'}\mathrm{before}\text{'}$

$\text{'}>\text{'}$ implies $\text{'}\mathrm{Sun}\text{'}$

$\text{'}÷\text{'}$ implies $\text{'}\mathrm{rise}\text{'}$

then, identify the correct expression:

In the following question choose the correct alternative assuming $\alpha$ stands for $=$; $\beta$ stands for $>$; $\gamma$ stands for $<$ and $\delta$ stands for $\ne$.

If $abxy\alpha c^{2}z, bx\beta ay$ and $b^2\alpha ac$, then

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.

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

$15 * 3 * 5 * 16 * 41$