IPMAT Indore 2024 (MCQ) PYQs

Let $n$ be the number of ways in which 20 identical balloons can be distributed among 5 girls and 3 boys such that everyone gets at least one balloon and no girl gets fewer balloons than a boy does. Then

The number of values of $x$ for which $C \binom {17-x}{3x+1}$ is defined as an integer is

There are 10 points in the plane, of which 5 points are collinear and no three among the remaining are collinear. Then the number of distinct straight lines that can be formed out of these 10 points is