List of top Questions asked in IPMAT- 2025

The remainder when \( 11^{1011} + 1011^{11} \) is divided by 9 is
A natural number n lies between 100 and 400, and the sum of its digits is 10. The probability that n is divisible by 4, is ________
Suppose a, b and c are three real numbers such that Max(a, b, c) + Min(a, b, c) = 15, and Median(a, b, c) - Mean(a, b, c) = 2. Then the median of a, b and c is
Let A(1,3) and B(5,1) be two points. If a line with slope m intersects AB at an angle of 45\(^\circ\), then the possible values of m are
Consider a triangle with side lengths 4 meters, 6 meters, and 9 meters. A dog runs around the triangle in such a way that the shortest distance of the dog from the triangle is exactly 1 meter. The total distance covered (in meters) by the dog in one round is
If the sum of the first 21 terms of the sequence \( \ln \frac{a}{b}, \ln \frac{a^2}{b^3}, \ln \frac{a^3}{b^5}, \dots \) is \( \ln \frac{a^m}{b^n} \), then the value of \( m + n \) is ________
Arpita and Nikita, working together, can complete an assigned job in 12 days. If Arpita works initially to complete 40% of the job, and the remaining job is completed by Nikita alone, then it takes 24 days to complete the job. The possible number of days that Nikita requires to complete the entire job, working alone, is ________
Eight teams take part in a tournament where each team plays against every other team exactly once. In a particular year, one team got suspended after playing 3 matches, due to a disciplinary issue. The organizers decide to proceed, nonetheless, with the remaining matches. The total number of matches that were played in the tournament that year is ________
If a, b, c are three distinct natural numbers, all less than 100, such that \( |a - b| + |b - c| = |c - a| \), then the maximum possible value of b is ________
The number of factors of \( 3^5 \times 5^8 \times 7^2 \) that are perfect squares is ________
A circle touches the y-axis at (0, 4) and passes through the point (-2, 0). Then the radius of the circle is
In triangle ABC, AB = AC = x, \( \angle ABC = \theta \) and the circumradius is equal to y. Then \( \frac{x}{y} \) equals
If \( \log_3(x^2 - 1) \), \( \log_3(2x^2 + 1) \) and \( \log_3(6x^2 + 3) \) are the first three terms of an arithmetic progression, then the sum of the next three terms of the progression is ________
English exam and Math exam were conducted separately for a class of 120 students. The number of students who did not appear for the English exam is twice the number of students who did not appear for the Math exam. The number of students who passed the Math exam is twice the number of students who appeared but failed the English exam. If the number of students who passed the English exam is twice the number of students who appeared but failed the Math exam, then the number of students who appeared but failed the English exam is ________
If \( A = \begin{bmatrix} 2 & n \\ 1 & 4 \end{bmatrix} \) such that \( A^3 = 27 \begin{bmatrix} 4 & q \\ p & r \end{bmatrix} \), then \( p + q + r \) equals ________
If the polynomial \( ax^2 + bx + 5 \) leaves a remainder 3 when divided by \( x - 1 \), and a remainder 2 when divided by \( x + 1 \), then \( 2b - 4a \) equals ________
If m and n are two positive integers such that \( 7m + 11n = 200 \), then the minimum possible value of m + n is ________
A circle of radius 13 cm touches the adjacent sides AB and BC of a square ABCD at M and N, respectively. If AB = 18 cm and the circle intersects the other two sides CD and DA at P and Q, respectively, then the area, in sq. cm, of triangle PMD is ________
Monica, who is 18 years old, is one-third the age of her father. The age at which she will be half the age of her father is ________