Relation and Function — NDA Mathematics PYQs

Let $R$ be a relation on the set $\mathbb{N}$ of natural numbers defined by $R=\{(x,y):x,y\in \mathbb{N}\text{ and }x=y^3\}$. Which of the following statements is/are correct ?
I. $R$ is symmetric relation
II. $R$ is transitive relation
Select the answer using the code given below :

If $2f(x)+f(1-x)=x$, then what is $f(x)$ equal to ?

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?