Relation and Function — NDA Mathematics PYQs

Consider the following for the two (02) items that follow :
Let the function $y=(1-\cos x{)}^{-1}$, where $x\ne 2n\pi$ and $n$ is an integer.

What is the range of the function?

Consider the following for the two (02) items that follow :
Let the curve $f(x)=|x-3|$.

What is the domain of the function $f(x)$?

Consider the following for the two (02) items that follow :
Let $f=\{(1,1),(2,4),(3,7),(4,10)\}$.

If $f(x)=px+q$, then what is the value of $(p+q)$?

Consider the following for the two (02) items that follow :
Let $f=\{(1,1),(2,4),(3,7),(4,10)\}$.

Consider the following statements :
I. $f$ is one-one function.
II. $f$ is onto function if the codomain is the set of natural numbers.
Which of the statements given above is/are correct?

Consider the following for the two (02) items that follow :
The function $f(x)$ satisfies $f\left(\frac{x}{y}\right)=\frac{f(x)}{f(y)}$ for all positive real values of $x$ and $y$, and $f(2)=3$.

What is $f(16)$ equal to?

Consider the following for the two (02) items that follow :
The function $f(x)$ satisfies $f\left(\frac{x}{y}\right)=\frac{f(x)}{f(y)}$ for all positive real values of $x$ and $y$, and $f(2)=3$.

What is $f(1)\cdot f(4)$ equal to?

Consider the following for the two (02) items that follow :
A function $f$ is such that $f(xy)=f(x+y)$ for all real values of $x$ and $y$, and $f(5)=10$.

What is $f(0)$ equal to?

Consider the following for the two (02) items that follow :
A function $f$ is such that $f(xy)=f(x+y)$ for all real values of $x$ and $y$, and $f(5)=10$.

What is $f(20)+f(-20)$ equal to?

Let $A=\{-3,-2,-1,0,1,2,3\}$ and $B=\{0,1,4,9\}$. How many elements does the subset of $A\times B$ corresponding to the relation $R=\{(x,y):|x|<y\}$ have, where $x\in A$ and $y\in B$?

Consider the following for the two (02) items that follow :
Consider the function $f(x)=\frac{x}{1-x}$ $(x>0,x\ne 1)$.

What is $\frac{f(x)}{f(x+1)}$ equal to?