IPM Indore 2019 Question Paper

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 31), and (31, 0) is

Two small insects, which are x metres apart, take u minutes to pass each other when they are flying towards each other, and v minutes to meet each other when they are flying in the same direction. Then, the ratio of the speed of the slower insect to that of the faster insect is

An alloy P has copper and zinc in the proportion of 5: 2 (by weight), while another alloy Q has the same metals in the proportion of 3: 4 (by weight). If these two alloys are mixed in the proportion of a : b (by weight), a new alloy R is formed, which has equal contents of copper and zinc. Then, the proportion of copper and zinc in the alloy S, formed by mixing the two alloys P and Q in the proportion of b : a (by weight) is

How many different numbers can be formed by using only the digits 1 and 3 which are smaller than 3000000?

There are numbers $$a_{1}, a_{2}, a_{3}, ....,an$$ each of them being +1 or -1. If it is known that $$a_{1}a_{2} + a_{2}a_{3} + a_{3}a_{4} +⋯ a_{n−1}a_{n} + a_{n}a_{1} + = 0$$ then

Average annual exports for the given period 2006-2017) was approximately

The percentage decline in exports during the period 2006-2011 is more than the percentage decline in exports during 2012-2017 by approximately

The maximum difference between imports and exports is

Balance of trade is defined as imports subtracted from exports ( = exports - imports). Which of the following blocks of three years has witnessed the largest average negative balance of trade?

The percentage increase in imports over the previous year is maximum during