IPMAT Indore 2026 Question Paper

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 _________

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 that like Countryside Sightseeing is ____

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 friends who like both Shopping and Adventure Sports is ____

Let ABCD be a cyclic quadrilateral with AB = 15, BC = 20, CD = 24 and AC = 25. Then AD equals_________

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 _________

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 Celsius scale of temperature can be converted to Fahrenheit scale using the relationship $$F = 1.8C + 32$$, where $$F$$ and $$C$$ are temperature recorded in degrees Fahrenheit and Celsius, respectively. Ajay noted down the temperature of a chemical reaction as $$x$$ degrees Fahrenheit but reported it as $$x$$ degrees Celsius by mistake. If this led to a recording of the temperature that was 144% higher than the actual temperature in Celsius scale, then $$x$$ equals ____

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 ____

Let $$M = \begin{bmatrix} 1 & 1 & 1 \\ a & b & c \\ a^2 & b^2 & c^2 \end{bmatrix}$$ where $$a, b$$ and $$c$$ are real numbers such that $$a + b + c = 0$$ and $$abc \neq 0$$. If $$\det M = 0$$, then the maximum possible value of $$\frac{a^2 + b^2}{c^2}$$ is ____