In this question the symbols @, #, $, *, ⊙ 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 is/are definitely true and mark your answer accordingly.

Statements: J $*$ E, D $@$ E, E $\$$ K, K $\odot$ T

Conclusions:

1. J $\$$ D

2. J $*$ D

3. E $\$$ T

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

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

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

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

$64\times 8÷6-4\times 2=?$  

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.

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

Find the relation between these two quantities.

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?

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

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

$13 * 4 * 5 * 12 * 6$

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 $a^{2}x\alpha byz, czx\alpha b^{2}y$ 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?

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?

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

$15 * 3 * 5 * 16 * 41$