:
Steps: 1 Mark
Answer: 1 Mark
The value of the polynomial $a^3+3a^{2}b+2ab-b^2$at a = -2 and b = 3
$a^3+3a^{2}b+2ab-b^2$
On substituting the values of a and b in the above expression we get:
$=(-2{)}^3+3\times (-2{)}^2\times 3+2\times (-2)\times 3-3^2$
$=-8+36-12-9=7$
So, thevalue of the polynomial $a^3+3a^{2}b+2ab-b^2$ at $a=-2$ and $b=3$ is 7.

Answer: Option A. -> True
:
A
A single term or a combination of two or more terms joined by operators such as plus (+) or minus (-) signs forms an algebraic expression. E.g., 58 - y , 6xy + z etc.
$So,\frac{1}{x}isanalgebraicexpression.$

:
Definition: 1 Mark
Classification: 3 Marks
Monomials: An expression with only one term is called monomial.
Binomial: An expression with two, unlike terms, is called a binomial.
Trinomial: An expression with three, unlike terms, is called a trinomial.
$\begin{array}{ccc}S.NO& Expression& TypeofPolynomial\\ \left(i\right)& 4y-7z& Binomial\\ \left(ii\right)& y^2& Monomial\\ \left(iii\right)& x+y-xy& Trinomial\\ \left(iv\right)& 100& Monomial\\ \left(v\right)& ab-a-b& Trinomial\\ \left(vi\right)& 5-3t& Binomial\\ \left(vii\right)& 4p^{2}q-4p{q}^2& Binomial\\ \left(viii\right)& 7mn& Monomial\\ \left(ix\right)& z^2-3z+8& Trinomial\\ \left(x\right)& a^2+b^2& Binomial\\ \left(xi\right)& z^2+z& Binomial\\ \left(xii\right)& 1+x+x^2& Trinomial\end{array}$

:
Coefficients and terms: 0.5 Mark each
Value of the expression: 1 Mark
Coefficients of $x^2$and $x$ are 10 and - 5 respectively
Terms are $10x^2$, $-5x$ and $-6$
We have to find the value of the expression at $x=2$ is
$10\times 2\times 2-5\times 2-6$
= $40-10-6$
= $24$
Hence, the value of the expression at $x=2is24$

:
Forming the equation: 1 Mark
Sum: 1 Mark
Value: 1 Mark
We have to find the sum of the expressions
$2a+3b+c+d,-a+b-c-d$
and $3a-4b-2c-2d$.
$(2a+3b+c+d)+(-a+b-c-d)+(3a-4b-2c-2d)$
$2a+3b+c+d-a+b-c-d+3a-4b-2c-2d$
$2a-a+3a+3b+b-4b+c-c-2c+d-d-2d$
$4a+0\times b-2c-2d$
Sum $=4a-2c-2d$
As per question ,
a = 2, b = 3, c = 4, d = 5
So, on substituting the values we get,
Sum = $4\times 2-2\times 4-2\times 5$
=$8-8-10$
= $-10$
The value of the expression is $-10$.

:
Forming the equation: 1 Mark
Steps: 2 Marks
Result: 1 Mark
Given that:
Total amount Aliyah had $=Rs.24$
Total number of pencils Aliyah bought $=7$
Total amount left after buying pencil $=Rs.10$
Total amount she spent
$=Rs.24-Rs.10=Rs.14$
Total money spenton pencil = Rs 14
Let the cost each pencil be $x$
$7x=Rs.14$
Cost of each pencil ,$x=\frac{14}{7}=Rs.2$
The cost of each pencil is $Rs2$.

:
Steps: 2 Marks
Answer: 1 Mark
Steps to be followed to decide whether the given terms are like or not are as followed:
i) Ignore the numerical coefficients.
ii) Check the variables in the terms. They must be same otherwise they are unlike terms.
iii) Next, check the powers of each variable in the terms. They should be the same and if they are not then they are not like terms.
We have to check if $x^{2}andxy$ are like terms.
The variables in both these expressions are $xandy$.
The power of $y$ is equal in both the expressions.
But the power of $x$ in the term $x^{2}y$ is 2, while in the term $xy$ it is one.
$\therefore$ The terms are not like.

:
Forming the equation: 1 Mark
Steps: 2 Marks
Result: 1 Mark
As per the question,
The amount of money given by Remits' mother$Rs3x{y}^2$.
The amount of money given by Remits'father$Rs5(x{y}^2+2)$.
Total amount $=3x{y}^2+5x{y}^2+10=3x{y}^2+5x{y}^2+10=8x{y}^2+10$
Total amount Remit spent $=10-3x{y}^2$
Amount of money left $=(8x{y}^2+10)-(10-3x{y}^2)=8x{y}^2+10-10+3x{y}^2=Rs.11x{y}^2$
Now if $x=2andy=3$, then on substituting the values we get,
Amount of money left with
= $11\times 2\times \times 3\times 3$ = $Rs198$
Hence, the amount of money left with Remit is$Rs198$.

:
Forming the expression: 1 Mark
Value of expression: 1 Mark
The product of two numbers, m, and n is
m$\times$n.
Three times the product is 3mn.
Adding 5to three times the product
=5 + 3mn
The expression formed is5 + 3mn
The value of the product at m = 4 and n = 5
$=5+3\times 4\times 5=65$
Hence, thevalue of the expression if m = 4 and n = 5 is 65.

Answer: Option B. -> 5+3mn
:
B
Analgebraic expressionis a mathematical phrase that can contain ordinary numbers, variables $\left(likexory\right)$and operators. According to the given question,
Three times the product of two numbers $m$ and $n$ is $3mn.$
5 is added to three times the product of two numbers $m$ and $n.$
The equation that represents this statement is $5+3mn.$