In the following questions the symbols $\$, @, *, **$and $\#$ are used with the following meanings:
$\text{'}\mathrm{A}\$\mathrm{B}\text{'}$ means 'A is greater than B'.
$\text{'}\mathrm{A}@\mathrm{B}\text{'}$ means 'A is either greater than or equal to B'.
$\text{'}\mathrm{A}*\mathrm{B}\text{'}$ means 'A is equal to B'.
$\text{'}\mathrm{A}**\mathrm{B}\text{'}$ means 'A is smaller than B'.
$\text{'}\mathrm{A}\#\mathrm{B}\text{'}$ means 'A is either smaller than or equal to B'.

Statements: $\mathrm{G} \$ \mathrm{H}, \mathrm{J} \# \mathrm{K}, \mathrm{H} * \mathrm{K}$
Conclusions:
$$\begin{gathered} \mathrm{I}. \mathrm{H} \$ \mathrm{J} \\ \mathrm{II}. \mathrm{J} * \mathrm{H} \end{gathered}$$

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

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 

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?

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

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

Statements:

I. All Napkins are Towels.

II. All Rags are Napkins.

Conclusions:

I. Some Towels are Rags.

II. All Rags are Towels.

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?

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?

Statements

I. All watches are ornaments.

II. All clocks are watches.

Conclusions

I. All ornaments are clocks.

II. All clocks are ornaments.

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 two statements are given and these statements are followed by two conclusions numbered I and II. You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts.

Statements:
No wire is cable.
No coil is a wire.

Conclusions:
I. No cable is coil.
II. Some coils are cables.

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

In the following question below are two statements followed by two conclusions numbered I and II. You have to take the two given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

Statements:
All chains are ropes.
Some links are chains.

Conclusions:
I. Some ropes are links.
II. All links are ropes.

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

$15 * 3 * 5 * 16 * 41$