Practice IPMAT Indore 2026 Question Paper with Solutions

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 friends who like both Shopping and Adventure Sports is ___

Ram purchased 3 oranges at Rs. 20 each and 5 mangoes at Rs. 38 each and then sold them by offering discounts of 25% and 20% on the fixed marked prices of oranges and mangoes, respectively. If he earned a profit of 50% on selling the oranges alone, and a total profit of 32% on selling all the fruits, then the marked price of each mango was ___

The remainder when \(7^{103} + 7^{101}\) is divided by \(9\) 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 ___

If \(n\) is an integer such that \(\frac{|n+6|-|n-3|}{\sqrt{100-n^3}} \geq 0\), then the number of possible values of \(n\) is ___

In a company, initially the ratio of the foreign and domestic workers was \(5 : 8.\) When some foreign and 12 domestic workers left the company, this ratio became \(2 : 3.\) Later, when 10 more foreign workers were replaced by 10 new domestic workers, this ratio became \(3 : 7.\) The initial number of domestic workers in the company was ___

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

A man starts walking from point A to point B at 4 km/hr. After 30 minutes, a woman starts from point A at 6 km/hr. If the woman reaches point B 20 minutes earlier than the man, then the distance between A and B in km 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 ___