Practice IPMAT Indore 2025 Quantitative Ability (Short Answer) PYQs

Five teams-A, B, C, D, and E — each consisting of 15 members, are going on expeditions to five different locations. Each team includes members from three different skill sets: biologists, geologists, and explorers. However, the number of members from each skill set varies by team and each member has only one speciality. The total number of biologists, geologists, and explorers are equal.

The following additional information is available

- Every team has at least 2 members from each of the three skill sets.

- Teams C and D have 6 biologists each, and Team A has 6 geologists.

- Every team except A has more biologists than explorers.

- The number of explorers in each team is distinct and decreases in the order A, B, C, D, and E.

The number of biologists in team E 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 ______

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 the sum of the first \(21\) terms of the sequence: \(\ln \frac{a}{b}, \ln \frac{a}{b \sqrt{b}}, \ln \frac{a}{b^{2}},\) \(\ln \frac{a}{b^{2} \sqrt{b}}, \ldots\) is \(\ln \frac{a^{m}}{b^{n}}\), then the value of \(m+n\) is \(\qquad\)

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 \(A = \begin{bmatrix} 2 & n \\ 4 & 1 \end{bmatrix}\) such that \(A^3 = 27 \begin{bmatrix} 4 & q \\ p & r \end{bmatrix}\), then \(p + q + r\) equals _________

Five teams-A, B, C, D, and E — each consisting of 15 members, are going on expeditions to five different locations. Each team includes members from three different skill sets: biologists, geologists, and explorers. However, the number of members from each skill set varies by team and each member has only one speciality. The total number of biologists, geologists, and explorers are equal.

The following additional information is available

- Every team has at least 2 members from each of the three skill sets.

- Teams C and D have 6 biologists each, and Team A has 6 geologists.

- Every team except A has more biologists than explorers.

- The number of explorers in each team is distinct and decreases in the order A, B, C, D, and E.

The number of teams having more geologists than biologists is ______

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

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 ____