In all the questions that follow, different symbols have been used with different meaning. For each set of questions you have to assume given statements to be true and then decide which of the two conclusions is/are definitely true.
Give answer
The symbol $+, -, \times , ÷$ and $=$ are used with following meanings:
$\mathrm{P}+\mathrm{Q}$ means $\mathrm{P}$ is greater than $\mathrm{Q}$ .
$\mathrm{P}–\mathrm{Q}$ means $\mathrm{P}$ is greater than or equal to $\mathrm{Q}$ .
$\mathrm{P}\times \mathrm{Q}$ means $\mathrm{P}$ is equal to $\mathrm{Q}$ .
$\mathrm{P}÷\mathrm{Q}$ means $\mathrm{P}$ is smaller than $\mathrm{Q}$ .
$\mathrm{P}=\mathrm{Q}$ means $\mathrm{P}$ is either smaller than or equal to $\mathrm{Q}$ .

Statements :
$\mathrm{M} \times \mathrm{N}, \mathrm{L} ÷ \mathrm{O}, \mathrm{N} + \mathrm{X}, \mathrm{L} = \mathrm{X}$
Conclusions:
I. $\mathrm{N} + \mathrm{L}$
II. $\mathrm{X} ÷ \mathrm{O}$

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

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

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

$64\times 8÷6-4\times 2=?$  

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 

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

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

Find the relation between these two quantities.

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 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

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

$13 * 4 * 5 * 12 * 6$

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

Follow the instruction and choose the correct option.

If $\mathrm{\Delta }$ means $>$, $\square$ means $<$, $○$ means $=$ and $\#$ means $\ne$ and $\mathrm{A}○\mathrm{B} , \mathrm{C} \mathrm{\Delta } \mathrm{D}$ as well as $\mathrm{D}\square \mathrm{A}$, then which of the following is true?

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.

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.

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?

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

$15 * 3 * 5 * 16 * 41$