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IPMAT Indore 2025 Past Year Papers with Solutions filter tool

Q1:

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
20
Correct Answer
Explanation →

Q2:

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 \newline - Every team has at least 2 members from each of the three skill sets. \newline - Teams C and D have 6 biologists each, and Team A has 6 geologists. \newline - Every team except A has more biologists than explorers. \newline - 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 _____
4
Correct Answer
Explanation →

Q3:

If a, b, c are three distinct natural numbers, all less than 100, such that ∣a−b∣+∣b−c∣=∣c−a∣|a - b| + |b - c| = |c - a|, then the maximum possible value of b is ______
98
Correct Answer
Explanation →

Q4:

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
24
Correct Answer
Explanation →

Q5:

If the sum of the first 2121 terms of the sequence: ln⁡ab,ln⁡abb,ln⁡ab2,ln⁡ab2b,…\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⁡ambn\ln \frac{a^{m}}{b^{n}}, then the value of m+nm+n is \qquad
147
Correct Answer
Explanation →

Q6:

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 ________
40
Correct Answer
Explanation →

Q7:

If A=[2n41]A = \begin{bmatrix} 2 & n \\ 4 & 1 \end{bmatrix} such that A3=27[4qpr]A^3 = 27 \begin{bmatrix} 4 & q \\ p & r \end{bmatrix}, then p+q+rp + q + r equals _________
12
Correct Answer
Explanation →

Q8:

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 \newline - Every team has at least 2 members from each of the three skill sets. \newline - Teams C and D have 6 biologists each, and Team A has 6 geologists. \newline - Every team except A has more biologists than explorers. \newline - 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 ______
2
Correct Answer
Explanation →

Q9:

If log⁡3(x2−1)\log_3(x^2 - 1), log⁡3(2x2+1)\log_3(2x^2 + 1) and log⁡3(6x2+3)\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
15
Correct Answer
Explanation →

Q10:

A circle of radius 1313 cm touches the adjacent sides AB and BC of a square ABCD at M and N, respectively. If AB = 1818 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
153
Correct Answer
Explanation →

Q11:

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 ____
36
Correct Answer
Explanation →

Q12:

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 \newline - Every team has at least 2 members from each of the three skill sets. \newline - Teams C and D have 6 biologists each, and Team A has 6 geologists. \newline - Every team except A has more biologists than explorers. \newline - The number of explorers in each team is distinct and decreases in the order A, B, C, D, and E.
The median number of biologists across five teams is
6
Correct Answer
Explanation →

Q13:

If mm and nn are two positive integers such that 7m+11n=2007m + 11n = 200, then the minimum possible value of m+nm + n is
20
Correct Answer
Explanation →

Q14:

The number of factors of 35×58×723^5 \times 5^8 \times 7^2 that are perfect squares is
30
Correct Answer
Explanation →

Q15:

If the polynomial ax2+bx+5ax^2 + bx + 5 leaves a remainder 33 when divided by x−1x - 1, and a remainder 22 when divided by x+1x + 1, then 2b−4a2b - 4a equals
11
Correct Answer
Explanation →

IPMAT Indore 2025 SA - Past Year Questions (Free PDF Download)

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