IPMAT Indore 2026 Question Paper

The number of ways in which three distinct integers can be chosen from the set {1, 2, …, 9} such that their product is divisible by 4, is_________

Five friends A, B, C, D, and E go on a trip together. Each of them likes at least one of the following three activities: Countryside Sightseeing, Shopping, and Adventure Sports such that:

• No two friends like exactly the same set of activities.
• A, B and E like exactly two activities each.
• D likes only Countryside Sightseeing.
• C likes more number of activities compared to D.

The number of ways in which a pair of friends can be chosen for a trip from those who like Adventure Sports is ____

Savitri borrowed 10000 rupees from a bank for a period of two years at a fixed interest rate of 10% per annum, compounded semi-annually, and paid back 5025 rupees at the end of first year. Then, the amount, in rupees, to be paid at the end of second year is_________

If $$x, y$$ are real numbers and equations $$x^2 - 12x + 35 = 0$$ and $$x^2 + ax + 105 = 0$$ have at least one common root, then the minimum possible value of $$y^2 + 4y - 5a$$ is ____

Let $$S$$ denote an arithmetic progression whose first term is either 132 or 158, and the common difference is an even integer less than 10. If the $$n^{\text{th}}$$ term of $$S$$ is 174, then the number of possible distinct values of $$n$$ is ____

If $$\log_{18} 24 = p$$, then $$\log_{96} 108$$ equals

A certain number of people contributed to a charity. The first person contributed one rupee. The rule for contribution was that the next person would contribute double the amount already raised. If the total money raised for the charity was 2187 rupees, then the number of people who contributed to the charity is

If $$A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$$, then the determinant of $$A + A^2 + A^3 + \cdots + A^{13}$$ is

In a class, 25% of all students read news from the Internet. Moreover, 45% of all students read news from printed newspaper. Further, 20% of all students read news from both the Internet and printed newspaper and they do not play video games. It is also known that 30% of the students who do not read news play video games. The minimum percentage of students who do not play video games is

The number of integers $$n$$ such that $$1 \leq n \leq 10^7$$ and $$\gcd(n, 10^7) = 10^3$$ is ____