:
Simplified equation: 1 Mark
Name of expression: 1 Mark
The given equation is:
$(3x-8y+4)-(x-y)$
$=3x-8y+4-x+y$
$=2x-7y+4$
where $2x,7y$ and $4$ are the three terms.
So, the simplified equation is a trinomial.

:
$-2(3y+6)=(-2\times 3y)+(-2\times 6)$
$=-6y+(-12)$
$=-6y-12$

:
Forming equation: 1 Mark
Steps: 1 Mark
Answer: 1 Mark
Value: 1 Mark
Here while adding the algebraic expressions we need to know that we can only add the like terms.
Like terms are those terms which have the same algebraic factors.
Sum
$=(t-t^2-14)+(15t^3+13+9t-8t^2)+(12t^2-19-24t)+(4t-9t^2+19t^3)$
$=t-t^2-14+15t^3+13+9t-8t^2+12t^2-19-24t+4t-9t^2+19t^3$
$=(t+9t-24t+4t)+(-t^2-8t^2+12t^2-9t^2)+(-14+13-19)+(15t^3+19t^3)$
$=-10t-6t^2-20+34t^3$
Hence, the required expression is $-10t-6t^2-20+34t^3$.
Given that:
$t=-1$
On substituting the values we get:
$-10t-6t^2-20+34t^3$
$=-10\times (-1)-6\times (-1{)}^2-20+34\times (-1{)}^3$
$=10-6-20-34$
$=-50$

:
Visualizing the question and forming equation: 2 Marks
Steps: 1 Mark
Answer: 1 Mark
According to question:
$=\left[\right(2x^2+3y)+(5x^2+3x\left)\right]-(8y^2+3x^2+2x+3y)$
$=[2x^2+3y+5x^2+3x]-(8y^2+3x^2+2x+3y)$
$=[7x^2+3y+3x]-(8y^2+3x^2+2x+3y)$
$=[7x^2+3y+3x-8y^2-3x^2-2x-3y$
$=4x^2+x-8y^2$
Hence, the expression represented by the above symbols is$4x^2+x-8y^2$.

:
Forming the equation: 1 Mark
Steps: 1 Mark
Result: 1 Mark
According to question,
= (3x - y + 11) + (- y - 11) - (3x - y - 11)
= 3x - y + 11 - y - 11 - 3x + y + 11
= 3x - 3x - y - y + y + 11 - 11 + 11
= (3 - 3)x - (1 + 1 - 1)y + 11 + 11 -11
= 0x - y + 11
= -y +11
The required expression is-y +11.

:
Final number of leaves by both: 2 Mark
Steps: 1 Mark
Answer: 1 mark
The first case, Sonu collected 12 leaves and Raju collected x leaves.
Sum of leaves collected by Sonu = 12
Sum of leaves collected by Raju = $x$
After some time, Sonu lost 3 leaves and Raju collected $2x$leaves.
Sum of leaves collected by Sonu = 12 - 3 = 9
Sum of leaves collected by Raju $=2x+x=3x$
Algebraic expression for the total number leaves collected by both $=9+3x$
It is given that, both of them collected equalnumberof leaves,
So, $3x=9$
Or$x=9÷3=3$
Hence, the value of$x$ is $3$.

:
Numerical Coefficients: 1 Mark
Sum: 1 Mark
The numerical coefficient of $4x^2$ = 4
The numerical coefficient of $12xy$ = 12
The numerical coefficient of $-5y^2$ = -5
The numerical coefficient of $-11y$ = -11
Sum of the coefficients = 4 + 12 - 5 - 11 = 0
Hence, the sum of all the numerical coefficients in the above expression is zero.

Answer: Option A. -> 12x,x
:
A
The terms which have the same variable raised to the same powerbut may only differ in numerical coefficient are calledlike terms.
For example:
$\left(i\right)3mand-7m\text{are like terms.}$
$\left(ii\right)zand\frac{3}{2}z\text{are like terms.}$
So, amongthe given set of terms,
$12xandx\text{are like terms.}$

Answer: Option B. -> False
:
B
An algebraic expression which contains two unlike terms is called a binomial. For example, 8 + x, xy - 4 are binomials.
An algebraic expression which contains three unlike terms is called trinomial. For example, 8 + x + y, xy - 4x + y, etc.
So, the expression,$5x^2+5x+5$, is a trinomial as this expression contains three unlike terms, which are, $5x^2$, 5x and 5.
Hence the given statement is false.

Answer: Option A. -> 6mn+33x
:
A
In order to findthe sum of $2mn+11xand22x+4mn$, we need to group the like terms first (we can add only the like terms).
$\Rightarrow (2mn+11x)+(22x+4mn)$
$=2mn+11x+22x+4mn$
$=(2mn+4mn)+(11x+22x)$
$=6mn+33x$
Hence, the sum is
$6mn+33x$.