IPM Indore 2025 Question Paper

Area of a regular octagon inscribed in a circle of radius 1 unit is:

Two swimmers, Ankit and Bipul, start swimming from the opposite ends of aswimming pool at the same time. Ankit can cover the length of the pool once in 10minutes. Bipul can cover the length of the pool once in 15 minutes. They swim backand forth for 80 minutes without stopping. The number of times they meet each other is

The sum of the first 5 terms of a geometric progression is the same as the sum of thefirst 7 terms of the same progression. If the sum of the first 9 terms is 24, then the4th term of the progression is

The set of all values of x satisfying the inequality $$\log_{\left(x + \frac{1}{x}\right)}\left[\log_2 \left(\frac{x-1}{x+2}\right)\right]>0$$ is

Let $$S_1 = \left\{100, 105, 110, 115, ...\right\}$$ and $$S_2 = \left\{100, 95, 90, 85, ...\right\}$$ be two series inarithmetic progression. If $$a_k$$ and $$b_k$$ are the k-th terms of
$$S_1$$ and $$S_2$$, respectively, then $$\sum_{k=1}^{20}a_k b_k$$ equals ____________.

A and B take part in a rifle shooting match. The probability of A hitting the target is0.4, while the probability of B hitting the target is 0.6. If A has the first shot, postwhich both strike alternately, then the probability that A hits the target before B hits it is

Which of the following numbers is divisible by $$3^{10} + 2$$

Let A and B be two finite sets such that $$n(A - B), n(A \cap B), n(B - A)$$ are in anarithmetic progression. Here n(X) denotes the number of elements in a finite set X. If $$n(A \cup B) = 18$$, then $$n(A) + n(B)$$ is __________

The number of integers greater than 5000 and divisible by 5 that can be formed withthe digits 1, 3, 5, 7, 8, 9 where no digit is repeated is

The remainder when $$11^{1011} + 1011^{11}$$ is divided by 9 is