IIM Bangalore UG 13th Dec 2025

In how many ways can three letters (not necessarily distinct from one another) be selected from the letters of the word PARALLELOGRAMS ?

Let $$A = \left\{a_{1}, a_{2}, ...a_{i}, ... \right\}$$ be an arithmetic progression, and let $$B = \left\{b_{1}, b_{2}, ...b_{i}, ... \right\}$$ be a geometric progression.
The commom difference for A is 2.
The commom ratio for B is 0.2 and b_{1} = 0.8
The infinite sum of the products $$a_{i}b_{i}$$ is 1, where i = 1, 2, 3, ....
What is $$a_{1}$$?

Which of the following functions is a one-to-one and onto function from real numbers to real numbers (R to R).

Let A, B and C be the three mutually independent events with their probabilities equal to x, y and z respectively. Then the probability that exactly two of these events occur is

25000 blood donors were registered with Red Cross in a city. The number of donors increased at the rate of 10% every 6 months. Find the total time (in years) at the end of which the total number of blood donors becomes 33275.

In Saroja's sari shop, the marked price of each sari is x% above the cost of its procurement. She sells each sari after a discount of 25%. In addition, if someone buys a dozen saris, she offers an extra sari for free, and still makes a profit of 8% over their cost of procurement. If Saroja had sold the saris without discounting, but with the offer of an extra saree for every dozen sold, then her profit percentage would have been:

Assume the population of Panchagarh in 2016 is 450000. Then the combined non-male population of cities P, Q and T is approximately what percent more/less than the combined male populations of cities R, S and T?

Assume the population of Panchagarh in 2016 was 1.5 lakh. In 2017, the population of city P increased by 15%, while that of city S increased by 20%. What is the ratio of the male population of city P to that of city S in 2017?

Assume the total population of Panchagarh state in 2016 is 350000. Then find the average female population of cities P, Q, and S in 2016.

Assume the population of city R was 96000 in 2016. Then, in percentage terms, by how much was it more than the male population of city T?