A nested function in R is a function that is defined within another function. It is created and exists within the scope of the outer function. The nested function can access variables from the outer function and can only be called from within the outer function.

The plotrix package in R provides enhanced functionalities for creating pie charts. It offers additional options and customizations beyond the basic pie() function, allowing for more advanced and specialized pie chart visualizations.

The apply() function in R can be used to apply a function to each element of a vector or columns of a data frame. The apply() function simplifies repetitive operations by iterating over the elements or columns and applying the specified function.

To calculate the mode of a factor in R, you can apply the table() function to the factor. The table() function counts the frequencies of each level in the factor, allowing you to identify the most frequent level as the mode.

To customize the appearance of an R bar chart, you can use the col parameter to change the colors of the bars, the names.arg parameter to add labels to the bars, and the legend() function to add a legend. These options allow you to customize the colors, labels, and legend to suit your visualization needs.

R uses lexical scoping, also known as static scoping. In lexical scoping, variables are resolved based on their order of definition in the source code. When a variable is referenced within a function, R first looks for that variable within the function's local environment. If not found, it then looks in the environment of the function that called it, and so on, until it reaches the global environment. This scoping behavior ensures that global variables can be accessed within functions but can be overridden by variables with the same name defined within the local environment.

R determines the max or min of a character vector based on lexicographic order. It compares the characters based on their ASCII values, considering factors such as uppercase and lowercase letters and special characters.

The 'print()' function is the basic function used to display the output in R. It prints its argument and returns it invisibly. This is useful for displaying the results of computations or the values of variables.

In R, the lapply() function can be used to apply a function to each element of a list. It returns a new list where the specified function has been applied to each element of the input list. The lapply() function is particularly useful for performing operations or calculations on each element of a list in a concise and efficient manner.

The str() function in R provides a compact, human-readable description of any R data structure, which makes it easier to understand the structure and content of large and complex lists. It displays the internal structure of an R object in a way that's compact and informative.