List of top Questions asked in IPMAT- 2025

Art can be _____________________ because it encourages individuals to express their emotions through a creative outlet, allowing them to process complex feelings, reduce stress, and _____________________ self-awareness.
On the first day of January 2025, the Indian Meteorological Department [IMD] announced that 2024 was the hottest year on record. A study by the Council on Energy, Environment and Water shows that nearly eight out of ten Indians live in districts that are at risk of either a flood, a cyclone, or a drought. Nearly twenty three States in India are heatwave-prone. In the summer of 2024, India recorded more than 44,000 cases of heatstroke and over 300 heat-related mortalities, as per the bulletin of the Ministry of Health and Family Welfare. Water reservoirs and the energy demand that keeps India powered are impacted too. During a ten-day long heatwave in Delhi, peak power demand was 16% higher than the previous year.
As globalization held sway over the world, communities, which used to live in relative isolation, sought access to the wider world, and in the process, they parted with their own language and adopted a new lingua franca. The loss of language, however, does not merely mean the loss of a mode of communication or the loss of a few thousand words. _____________________. So, when a language dies, a way of thinking dies with it.
There are so many instances of one or more deer crossing the road, or just standing in the middle of the road, or else _____________________; it is like the deer cannot hear the noise of the engines or see the headlights.
We hope that the government's new policies will _____________________ a period of economic growth.
When she inherited some jewellery from a distant relative, she had no idea of its worth and decided _____________________.
The labourers who were fired broke into the office building and destroyed some of the machinery. Rather than finding a solution to their problems, they _____________________.
Without a doubt, the widespread use of renewable energy is a key solution to climate change. However, it is not a _____________________ as efforts in conservation are equally crucial.
Everyone wondered how the travel vlogger could go around the world all through the year and _____________________.
Deepak is an unpleasant person, but we all _____________________ because his sister is a close friend of ours.
If \( a_1, a_2, \dots, a_8 \) are the roots of the equation \( x^8 + x^7 + \dots + x + 1 = 0 \), then the value of \( a_1^{2025} + a_2^{2025} + \dots + a_8^{2025} \) is
The area of the triangle, formed by the straight lines \( y = 0 \), \( 12x - 5y = 0 \), and \( 3x + 4y = 7 \), is ________
Given that \( 1 + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \dots = \frac{\pi^2}{6} \), the value of \( 1 + \frac{1}{3^2} + \frac{1}{5^2} + \frac{1}{7^2} + \dots \) 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 an arithmetic 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 ________
Area of a regular octagon inscribed in a circle of radius 1 unit is
The number of integers greater than 5000 and divisible by 5 that can be formed with the digits 1, 3, 5, 7, 8, 9 where no digit is repeated is
Let \( f(x) = a^2x^2 + 2bx + c \) where, a \( \neq \) 0, b, c are real numbers and x is a real variable then
Anindita invests a total of 1 lakh rupees distributed across three schemes A, B and C for a period of two years. These schemes offer an interest rate of 10%, 8% and 12% per annum, respectively, each compounded annually. If the initial investment amount in scheme A is 30000 rupees and the total interest earned from all the three schemes during the first year is 10600 rupees, then the total interest earned, in rupees, from all the three schemes for the second year is ________
Let P(x) be a quadratic polynomial such that \( \begin{vmatrix} P(0) & P(1) \\ P(0) & P(2) \end{vmatrix} = 0 \). Let P(0) = 2 and P(1) + P(2) + P(3) = 14. Then P(4) equals
If \( 8x^2 - 2kx + k = 0 \) is a quadratic equation in x, such that one of its roots is p times the other, and p, k are positive real numbers, then k equals
The sum of the first 5 terms of a geometric progression is the same as the sum of the first 7 terms of the same progression. If the sum of the first 9 terms is 24, then the 4th term of the progression is
A and B take part in a rifle shooting match. The probability of A hitting the target is 0.4, while the probability of B hitting the target is 0.6. If A has the first shot, post which both strike alternately, then the probability that A hits the target before B hits it is
Two swimmers, Ankit and Bipul, start swimming from the opposite ends of a swimming pool at the same time. Ankit can cover the length of the pool once in 10 minutes. Bipul can cover the length of the pool once in 15 minutes. They swim back and forth for 80 minutes without stopping. The number of times they meet each other is ________
Let \( S_1 = \{100, 105, 110, 115, \dots\} \) and \( S_2 = \{100, 95, 90, 85, \dots \} \) be two series in arithmetic 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 ________