IIM Bangalore UG 13th Dec 2025

Two rectangles are drawn on line segments of fixed widths. When the heights are 7 m and 8 m respectively, their areas sum up to 156 $$m^{2}$$. But if these heights are 5 m and 7 m respectively, then their areas sum up to 123 $$m^{2}$$. Find the sum of the areas of the squares (in $$m^{2}$$) drawn on the line segments.

The centroid of a triangle with vertices (2a,b),(-b,a) and (b,3a) is (4,11). The area of the triangle is ___ square units.

Let b and c be two real numbers such that the numbers 3, b, c are in geometric progression. For the matrix 

$$A = \begin{bmatrix}1 & 1 & 1 \\3 & b & c \\9 & b^{2} & c^{2} \end{bmatrix}$$, if $$\text{det}\mid A \mid = 162$$, then the value of c is

The proportions of gold in three alloys are 40%, 50% and 80% respectively. These alloys are mixed in certain proportions to obtain 30 kg of a new alloy, which has 55% gold. If the amount of the first alloy is 9 kg, what is the amount in kg of the third alloy used?

A sportsperson could be an expert in badminton and / or squash. Given that someone is a squash expert, the probability that they are expert at badminton as well is 0.8. There are twice as many badminton experts as there are squash experts. Given that Saina is a badminton expert, what is the likelihood that she is an expert in squash?

Two positive integers m and n satisfy HCF (m, n) = 14 and LCM (m, n) = 168. If m < n and m divides 84, what is the maximum possible value of m?

In 2012, if 10% of visitors in Region E were foreign tourists, then how many domestic tourists (in thousands) visited Region E in that year?

Foreign visitors to Region B form 15%, 20% and 25% of the tourist visits during 2010, 2011 and 2012 respectively. Assume that each foreign tourist spends ₹ 7,000, while each domestic tourist spends ₹ 3,000. What is the total revenue (in ₹ crores) from tourist spends during 2010-2012?

In 2010, the total spending per tourist in Region E was ₹6,000, and it increased by 10% in each successive year, while arrivals decreased as per the graph. What was the total spending (in ₹ crore) from Region E across 2010-2012?

In which region was the highest average tourist arrival recorded during 2010-2012?