MATHS M.C.Q. [1 Marks Each]

Since, the value of a variable is not fixed.
So, variable means that it can take different values.
Hence, $(a)$ is correct option.

Since, the product of $x$ and $y = xy$
So, the expression when the product is decreased by $4$ is written as $xy - 4$

Given equation is $x - 4 = -2$
$\Rightarrow x = -2 + 4$
$\Rightarrow x = 2$
Hence, $(b)$ is correct option.

The constant in the polynomial $x + 5$ is $5.$

Given, in algebra, $a \times b = ab$, which means a is multiplied by $b.$
Also, in arithmetic, $3 \times 5$ means $3$ is multiplied by $5.$
$3 \times 5 = 15$
Hence, $(c)$ is correct option.

Given equations $4x = 16$
$\Rightarrow\frac{4\text{x}}{4}=\frac{16}{4}$
$\Rightarrow\text{x}=4$
Verification
Put $x = 4$ in Eq. $(i)$ then we get
$4 \times 4 = 16 \Rightarrow 16 = 16$
Therefore, value of $x$ is $4.$
Hence, $(a)$ is correct option.

Constant term has zero degree of polynomial. Because the constant term in an expression or equation has a fixed value and does not contain variables.
Example: $p(x) = k$ Where $k$ is a constant.

$\Rightarrow\frac{1}{3}\text{x}+5=8$
$\Rightarrow\frac{1}{3}\text{x}+5-5=8-5$ [Substracting 5 from both sides]
$\Rightarrow\frac{1}{3}\text{x}\times3=3\times3$ [Multiplying both sides by $3]$
$\text{x}=9$

$\frac{\text{x}}{5}=1$
$\Rightarrow\frac{\text{x}}{5}\times5=1\times5$ [Multiplying both the side by $5]$
$x = 5$

=As, the sum of $a$ and $b = a + b$
And, the product of $a$ and $b = ab$
So, the expression when the product is added to the sum $= a + b + ab$

Here, side $= x$
We know that, area of square = Side $\times$ Side
Area of square $= x \times x$
Hence, $(a)$ correct option.

We know that, an equation which contains only numbers is called a numerical equation.
Since, equation $\frac{4}{2}=2$ contains only numbers, so it is a numerical equation.
Hence,$ (a)$ is correct option.

We know that, an expression with a variable, constants and the sign of equality $(=)$ is called an equation.
So, $x - 1 = 0$ is an equation.
Hence, $(c)$ is correct option.

Since, $9$ less than $x$ is written as $x - 9$

$\big(\frac{\text{y}}{3}\big)=5$
$\Rightarrow \text{y} = 5 \times 3 = 15$

All the terms in the expression $-5xyz$ barring $x$ will be the coefficient of $x$, i.e. $-5yz.$

Using $a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)$
Using $a^3 + b^3 + c^3 - 3abc = 0 \times (a^2 + b^2 + c^2 - ab - bc - ca)$
Using $a^3 + b^3 + c^3 = 3abc$
Here if $a + b + c$ is $0$ then answer will be $3abc$

Given, each matchbox contains $50$ matchsticks.
Then, total number of matchsticks in n boxes = Matchsticks in one box $\times $ Total boxes
$= 50 \times n = 50n$
Hence, $(b)$ is correct option.

Given equation is $\frac{\text{q}}{2}=3$
$\Rightarrow\frac{\text{q}}{2}\times2=3\times2$
$\Rightarrow\text{q}=6$
Hence, $(a)$ is correct option.

In $5xy - 4x + 8$
$\therefore$ The constant term is $= +8.$

As, the sum of $a$ and $b = (a + b)$
So, the required expression representing the given statement $= (a + b)(a + b - 5)$

$3\text{z} = 9 $
$\Rightarrow \text{z} =\big(\frac { 9 }{ 3 }\big) = 3$

Given, $\text{A}=\pi(\text{R}^2-\text{r}^2)$
Therefore $\text{A}=\pi\text{R}^2-\pi\text{r}^2\Rightarrow\text{A}+\pi\text{r}^2=\pi\text{R}^2$
$\Rightarrow\text{R}^2={\frac{\text{A}+\pi\text{r}^2}{\pi}}$
$\Rightarrow\text{R}=\sqrt{\frac{\text{A}+\pi\text{r}^2}{\pi}}$

A variable is a symbol or letter, such as $x$ or $y$, that represents a value.
In algebraic equations, the value of one variable is often dependent on the value of
another. Hence its a symbol that takes various numerical values.
e.g. in the polynomial $x+5, x$ is a variable.

Let $a$ and $b$ be two integers, then in commutative property
$a + b = b + a$
Here, $x$ and $y$ are integers.
Then, $x + y = y + x$
Hence, $(a)$ is correct option.