✅ IPMAT Indore 2025 Complete Question Paper with Solutions
- Anshu Agarwal
- Jul 23
- 10 min read
Updated: Aug 2
In this post, we’ve shared fully solved, slot-wise solutions of IPMAT Indore 2025 — prepared by Anshu Agarwal Sir, India’s top educator for IPM aspirants (99.97%ile CAT QA & XAT QA Topper). These are not just correct answers but concept-based, detailed explanations that help you understand why an option is right or wrong.
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🟩 IPMAT Indore 2025 QA Questions & Solutions [Short Answers]
If a, b, c are three distinct natural numbers, all less than 100, such that
|a - b| + |b - c| = |c - a|, then maximum possible value of b is:
If the sum of first 21 terms of the sequence ln(a/b), ln(a/(b√b)), ln(a/b²), ln(a/(b²√b)), … is ln ( aᵐ / bⁿ ), then 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
If the polynomial ax² + 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:
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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 ________
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 ________
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 ______
The number of factors of 3⁵ × 5⁸ × 7² that are perfect squares is:
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If A = [[2, n], [4, 1]] such that A³ = 27 × [[4, q], [p, r]], then p + q + r equals:
If log₃(x² - 1), log₃(2x² + 1) and log₃(6x² + 3) are the first three terms of an AP, then the sum of the next three terms of the progression is:
Directions [13 – 15]:
5 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: Biologist, Geologist and Explorer. However, the number of members from each skill set varies by team, and each member has only one specialty. 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.
Team C and Team 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:
The median number of biologists across five teams is:
The number of teams having more geologists than biologists is:
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🟩 IPMAT Indore 2025 QA Questions & Solutions [MCQ]
1. Consider a triangle with side lengths 4 meters, 6 meters and 9 meters. A dog runs around 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:
(a) 19 + 2π
(b) 22
(c) 22 − 2π
(d) 22 + 2π
2. A natural number n lies between 100 and 400, the sum of the digits is 10. Probability that n is divisible by 4 is:
(a) 7⁄27
(b) 1⁄3
(c) 1⁄4
(d) 2⁄9
3. The remainder when 11¹⁰¹¹ + 1011¹¹ is divided by 9 is:
(a) 7
(b) 0
(c) 9
(d) 8
4. The set of all values of x satisfying the inequality
log₍ₓ + 1⁄ₓ₎ [ log₂ ((x − 1)⁄(x + 2)) ] > 0
(a) (5, ∞)
(b) (2, 5)
(c) (−5, −2)
(d) Null set
5. Which of the following number is divisible by 3¹⁰ + 2 ?
(a) 3³⁰ + 2
(b) 3²⁰ + 4
(c) 3²⁰ + 8
(d) 3³⁰ + 8
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6. The sum of 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) 48
(b) −24
(c) −48
(d) 24
7. If a₁, a₂, …, a₈ are the roots of the equation
x⁸ + x⁷ + … + x + 1 = 0,
then the value of
a₁²⁰²⁵ + a₂²⁰²⁵ + … + a₈²⁰²⁵ is:
(a) 8
(b) 2
(c) 0
(d) 4
8. Let A and B be two finite sets such that n(A − B), n(A ∩ B), n(B − A) are in arithmetic progression . Here n(X) denotes the number of elements in set X.
If n(A ∪ B) = 18, then n(A) + n(B) is:
(a) 30
(b) 36
(c) 27
(d) 24
9. If 1/1² + 1/2² + 1/3² + … up to ∞ = π²⁄6, then the value of 1/1² + 1/3² + 1/5² + … up to ∞ is:
(a) π²⁄6 − 1
(b) π²⁄8
(c) π⁄6
(d) π²⁄12
Short Explanation
10. A circle touches y-axis at (0, 4) and passes through the point (−2, 0). Then the radius of the circle is:
(a) 6
(b) 5
(c) 4
(d) 7
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11. 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:
(a) 9.5
(b) 10
(c) 11
(d) 10.5
Short Explanation
12. 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
(a) 180
(b) 120
(c) 276
(d) 240
Short Explanation
13. If log₂₅[5 log₃(1 + log₃(1 + 2 log₂x))] = ½ then x is:
(a) 16
(b) 2
(c) 8
(d) 4
Short Explanation
14. Area of a regular octagon inscribed in a circle of radius 1 unit is
(a) √10
(b) 9⁄(2√2)
(c) 2 + √2
(d) 2√2
Short Explanation
15. 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:
(a) 22348
(b) 10308
(c) 19708
(d) 11748
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16. 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 _____
(a) 7
(b) 6
(c) 8
(d) 5
Short Explanation
17. Let f(x) = a²x² + 2bx + c where a ≠ 0, b, c are real numbers and x is a real variable then:
(a) f(x) has a maximum and no minimum
(b) f(x) has a maximum and a minimum
(c) f(x) has no minimum and no maximum
(d) f(x) has a minimum and no maximum
Short Explanation
18. In triangle ABC, AB = AC = x, ∠ABC = θ and the circumradius is equal to y. Then x/y equals:
(a) 2 sin θ
(b) 2 cos θ
(c) sin θ
(d) cos θ
Short Explanation
19. Let A(1, 3) and B(5, 1) be two points. If a line with slope m intersects AB at an angle 45°, then the possible value of m are:
(a) 5, −1⁄5
(b) −3, 1⁄3
(c) 7, 1⁄7
(d) 3, 1⁄3
Short Explanation
20. The area of the triangle, formed by the straight lines y = 0, 12x − 5y = 0 and 3x + 4y = 7, is:
(a) 35⁄27
(b) 28⁄9
(c) 35⁄54
(d) 14⁄9
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21. If y = a + b logₑx
(a) y − a is proportional to xᵇ
(b) logₑy is proportional to x
(c) 1⁄(y − a) is proportional to xᵇ
(d) eʸ is proportional to xᵇ
Short Explanation
22. Let S₁ = {100, 105, 110, 115, …} and S₂ = {100, 95, 90, 85, …} be two series in arithmetic progression. If aₖ and bₖ are the kᵗʰ terms of S₁ and S₂ respectively, then ∑ₖ₌₁²⁰ (aₖ × bₖ) equals:
(a) 137275
(b) 137225
(c) 135375
(d) 138250
23. Let P(x) be a quadratic polynomial such that
‖ P(0) P(1) ‖
‖ P(0) P(2) ‖ = 0.
Let P(0) = 2 and P(1) + P(2) + P(3) = 14. Then P(4) equals:
(a) 16
(b) −6
(c) −14
(d) 30
24. If 8x² − 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:
(a) 2(√p + 1⁄√p)²
(b) p + 1⁄p
(c) 2(p + 1⁄p)
(d) (√p + 1⁄√p)²
Short Explanation
25. 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
(a) 10⁄19
(b) 9⁄19
(c) ½
(d) ⅔
Short Explanation
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Directions [26 – 30]:
The table given below provides the details of monthly sales (in lakhs of rupees) and the value of products returned by the customers (as a percentage of sales) of an e-commerce company for three product categories for the year 2024.
Net sales (in lakhs of rupees) is defined as the difference between sales and value of products returned (in lakhs).
Month | Apparel | Footwear | Electronics | Apparel (%) | Footwear (%) | Electronics (%) |
January | 262 | 104 | 289 | 13% | 7% | 2% |
February | 279 | 113 | 387 | 16% | 9% | 3% |
March | 236 | 121 | 283 | 20% | 7% | 2% |
April | 258 | 58 | 325 | 16% | 8% | 1% |
May | 249 | 69 | 359 | 12% | 6% | 4% |
June | 230 | 111 | 321 | 19% | 5% | 3% |
July | 244 | 119 | 341 | 17% | 9% | 4% |
August | 252 | 60 | 336 | 16% | 6% | 2% |
September | 288 | 118 | 355 | 10% | 9% | 5% |
October | 222 | 108 | 383 | 15% | 8% | 2% |
November | 228 | 93 | 282 | 14% | 9% | 4% |
December | 221 | 86 | 268 | 18% | 10% | 1% |
26. Among the following four months, for which month the value of the Footwear returned (in lakhs of rupees) was the highest?
(a) March
(b) September
(c) June
(d) July
27. For which categories did the value of products returned (as a percentage of sales) increase for three consecutive months?
(a) Both Apparel and Footwear
(b) Only Apparel
(c) Only Footwear
(d) Only Electronics
28. Among the following four months, for which month the contribution of the Apparel category in the total monthly sales was the highest?
(a) January
(b) August
(c) December
(d) April
29. By what percentage did the net sales for June increase as compared to May in the Footwear category?
(a) 60.87 percent
(b) 7.21 percent
(c) 62.58 percent
(d) 18.97 percent
30. Which month had the highest percentage decline in monthly sales as compared to the previous month for the Apparel category?
(a) October
(b) December
(c) June
(d) March
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