There are 60 questions in a question paper. If no two students solve the same combination of questions but solve equal number of questions, then the maximum number of student who appeared in the examination, is

Options

A. `""^(60)C_(29)`
B. `""^(60)C_(30)`
C. `""^(60)C_(50)`
D. none of these

Explanation

To solve the problem step by step, we need to determine the maximum number of students who can appear in the examination, given that no two students solve the same combination of questions and each student solves an equal number of questions.

### Step 1: Understand the Problem
We have a total of 60 questions in the question paper. Each student solves a certain number of questions (let's denote this number as \( x \)). The goal is to find the maximum number of students who can solve a unique combination of \( x \) questions.

### Step 2: Use Combinations
The number of ways to choose \( x \) questions from 60 questions is given by the combination formula \( \binom{n}{r} \), which represents the number of ways to choose \( r \) items from \( n \) items without regard to the order of selection. In our case, it is \( \binom{60}{x} \).

...