IPMAT Indore 2026

Painter A can paint a building in 12 days while Painter B can paint it in 16 days. If A and B work on alternate days, and A starts the work on the first day, then the number of days required to paint the building is

Gita starts from point A and walks 1000 m east. She then walks 800 m north, followed by 640 m west and 512 m south, reaching point B. After this, she continues moving in the same cyclic order: east, north, west, south, with each successive movement 20% shorter than the previous one. After infinitely many such moves, approximately how far in meters will Gita be from her starting point A?

The number of ways in which coins of denominations of rupees 2, 5 and, 10 can be combined to make a value of rupees 50 is

Let ABCD be a rectangle with AB = 72 cm and BC = 30 cm. A circle passing through points A and C cuts the side AB at P such that AP = 56 cm. The radius, in cm, of the circle is

The equation $2^x - x^2 = 0$ has

Three dice are thrown simultaneously and the sum of the three numbers appearing on the top faces of the dice is found to be 10. The probability that these three numbers are distinct, is

The number of values $a$ can take such that $x^4 + ax^3 + (3a - 4)x^2 + 2(a - 1)x - 4$ can be expressed as a product of two quadratic polynomials, $x^2 + px + 2$ and $x^2 + qx - 2$, where $p$ and $q$ are real, is

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

The number of integer solutions $(x, y)$ of the inequality $x^2 + y^2 \leq 10$ is

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

A fair die is rolled repeatedly. The probability that the cumulative sum is at least 17 in the third trial is

Let the circle $x^2 + y^2 = 2ax + 2by$ intersect the x-axis at point $A(\alpha, 0)$ and y-axis at point $B(0, \beta)$, where $\alpha\beta \neq 0$. If the point $C(p, q)$ lies on the chord AB, then $\frac{p+\alpha}{a} + \frac{q+\beta}{b}$ equals

The possible values of $x$ in the set $\{1, 5, 13\}$ for which the mean of eight observations $5, 8, 3x + 2, 15, 27, 29, 36, 5x - 2$ equals their median are

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

Two locations A and B are at diametrically opposite ends of a circular track. Rekha starts running along the track from location A in the clockwise direction. Sajal starts running simultaneously along the track in the anticlockwise direction from location B. If the length of the circular track is 14 km, and the speeds of Rekha and Sajal are in the ratio 5: 2, then the distance, in km, travelled by Rekha, when they meet at location B for the first time, 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 approximate value of the expression $2\log_3 3n - \log_3(n^2 + 1)$ for a sufficiently large $n$ is

If $x$ is a real number such that $\max(\min(x, 2 - x), x - 4, 2x - 8) = \pi - 3$, then the number of possible values of $x$ is

Positive reals $x, y$ satisfy $x \neq y$ and $\frac{x^2 + y^2}{xy} = k$. If replacing $x$ by $x + y$ and $y$ by $|x - y|$ leaves the value of $k$ unchanged, then $k$ equals

Let $S = \{1, 2, \ldots, 180\}$. Define $A$ as the set of all multiples of 4 in $S$, $B$ as the set of all multiples of 6 in $S$, and $C$ as the set of all multiples of 9 in $S$. The number of elements in $S$ that belong to exactly one of $A, B, C$ is

A circle of non-zero radius has origin as its centre. If it passes through the point of intersection of two curves $y^2 = 4ax$ and $x^2 = 4ay$, then its equation is

A person walks one lap along a circle at a speed $v$. Thereafter, he runs one lap along the boundary of the largest square that can be inscribed in the circle at a speed $3v$. The ratio of the time he walks to the time he runs is

If $m$ is a positive integer then the values of $k$ for which $6m + k$ cannot be a perfect square are

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 $a$, $b$, and $c$ are three prime numbers such that $abc = 23(a + b + c)$, then the maximum possible value of $a + b - c$ is

If two servings of Milk are part of the daily diet plan, then the minimum number of servings of any other single item that can satisfy the MDR of all three nutrients is

The food item(s) that can satisfy at least half of the MDR for all the three nutrients using up to seven servings of that single item alone is

If only $x$ servings of Milk and $y$ servings of Rice are included in the diet plan, then the minimum value of $x + y$ that will satisfy the MDR of all three nutrients is

When one serving of each of the five items is included in the diet plan, the nutrient with the least percentage of MDR satisfied is

The number of food items that can satisfy at least 15% of the MDR for at least two nutrients in one serving is