The computer that functions by taking discrete numbers and performing mathematic...

The question is asking about a type of computer that works by using specific numbers to perform mathematical calculations. The options given are mainframe, digital, hybrid, and analogue.

A mainframe computer is a large and powerful computer used by organizations for tasks like processing large amounts of data. It is not specifically designed to work with discrete numbers and perform mathematical calculations, so option A is incorrect.

A digital computer is a type of computer that uses binary digits (0s and 1s) to represent and process data. It is capable of performing mathematical calculations using discrete numbers, so option B could be a possibility.

A hybrid computer is a computer system that combines the features of both analog and digital computers. It can process both continuous and discrete data, making it capable of performing mathematical calculations using discrete numbers. So, option C, hybrid, is the correct answer.

An analog computer, on the other hand, works with continuous data and represents numbers using physical quantities such as voltage or currents. It is not specifically designed to work with discrete numbers and perform mathematical calculations, so option D is incorrect.

In summary, out of the given options, the computer that functions by taking discrete numbers and performing mathematical calculations is called a hybrid computer.