Question

What is a variable?
A. A symbol that takes the fixed numerical value.
B. A symbol that takes various numerical values.
C. A symbol sometimes fixed and sometimes variable.
D. cannot be determined.

Answer 1

Hint: Variable are those variables whose values are not fix like $\sin x$ is a variable for $x = 0$$ \Rightarrow \sin x = 0$
For $x = 30$$ \Rightarrow \sin x = \dfrac{1}{2}$. So as it all depends on the value of $x$ therefore it is a variable.

Complete step-by-step answer:
Variable and constant are the two symbols which help to write any expression. So variable is the symbol which takes various numerical values and the symbol having the fixed numerical value is known as the constant. Variables are generally denoted by the letters $x,y,z,a,b,c$ and the constant term comprises the numbers like $1,2, - 1,\pi $, etc.
The combination of the constant and the variables from the other variables.
Let us understand by taking the suitable examples like here we are given the expression like
1. $12{x^2} + x + 1$
2. $12abc$
3. $2x + 5 = 10$
Here we have 3 examples.
In the example 1 which is $12{x^2} + x + 1$ we have two variables ${x^2},x$ and so we can say that there is only one variable $x$ as ${x^2}$ is also dependent on the \[x\] and hence by changing the value of $x$ we get different values of $12{x^2} + x + 1$. So here $x$ is the variable and 12, 1 are the constant terms.
In example 2 we have been given the equation $12abc$ so here we can say that there are three variables $a,b,c$as by changing the values of each one of them we will get the different values of $12abc$ and here also 12 is the constant term.
In example three we are given $2x + 5 = 10$ and hence here $x$ is the variable in which we put the different numbers and we can assign the values to the variables.
Therefore we can conclude that variable is the symbol that takes various numerical values.
So B is the appropriate option.

Note: As we know that constants are the fixed numbers and variables are varying in some situations varying numbers are also treated as the constants. In such situations it is presumed that the particular varying number will take the fixed value.