IPMAT Indore 2026 Question Paper

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

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

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

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

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

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 $$x$$ 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

The approximate value of the expression $$2\log_3 3n - \log_3(n^2 + 1)$$ for a sufficiently large $$n$$ is