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IPMAT Indore 2025 Past Year Papers with Solutions filter tool

Q1:

Given that 1+122+132+142+...=π261 + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + ... = \frac{\pi^2}{6}, the value of 1+132+152+172+...1 + \frac{1}{3^2} + \frac{1}{5^2} + \frac{1}{7^2} + ... is
Answer options
Option: 4
Correct Answer
Explanation →

Q2:

If y=a+blog⁡exy=a+b \log _{e} x then which of the following is true?
Answer options
Option: 3
Correct Answer
Explanation →

Q3:

If a1,a2,...,a8a_1, a_2, ..., a_8 are the roots of the equation x8+x7+...+x+1=0x^8 + x^7 + ... + x + 1 = 0, then the value of a12025+a22025+...+a82025a_1^{2025} + a_2^{2025} + ... + a_8^{2025} is
Answer options
Option: 3
Correct Answer
Explanation →

Q4:

Suppose a,ba, b and cc are three real numbers such that Max(a,b,c)+Min(a,b,c)=15\text{Max} (a, b, c) + \text{Min} (a, b, c) = 15, and Median(a,b,c)−Mean(a,b,c)=2\text{Median} (a, b, c) - \text{Mean} (a, b, c) = 2. Then the median of a,ba, b and cc is
Answer options
Option: 2
Correct Answer
Explanation →

Q5:

If log⁡25[5log⁡3(1+log⁡3(1+2log⁡2x))]=12\log_{25} [5 \log_3 (1+\log_3(1+2\log_2x))] = \frac12 then xx is:
Answer options
Option: 2
Correct Answer
Explanation →

Q6:

A natural number nn lies between 100100 and 400400, and the sum of its digits is 1010. The probability that nn is divisible by 44, is
Answer options
Option: 2
Correct Answer
Explanation →

Q7:

In triangle ABC,AB=AC=x,∠ABC=θABC, AB = AC = x, ∠ABC = \theta and the circumradius is equal to yy. Then xy\frac{x}{y} equals
Answer options
Option: 4
Correct Answer
Explanation →

Q8:

If 8x2−2kx+k=08x^2 - 2kx + k = 0 is a quadratic equation in xx, such that one of its roots is pp times the other, and p,kp, k are positive real numbers, then kk equals
Answer options
Option: 3
Correct Answer
Explanation →

Q9:

Let A(1,3)A(1,3) and B(5,1)B(5,1) be two points. If a line with slope mm intersects ABAB at an angle of 45°45°, then the possible values of mm are
Answer options
Option: 3
Correct Answer
Explanation →

Q10:

Let P(x)P(x) be a quadratic polynomial such that
∣P(0)P(1)P(0)P(2)∣=0\left|\begin{array}{ll} P(0) & P(1) \\ P(0) & P(2) \end{array}\right|=0
Let P(0)=2P(0)=2 and P(1)+P(2)+P(3)=14P(1)+P(2)+P(3)=14. Then P(4)P(4) equals
Answer options
Option: 3
Correct Answer
Explanation →

Q11:

A circle touches the y-axis at (0,4)(0, 4) and passes through the point (−2,0)(-2, 0). Then the radius of the circle is
Answer options
Option: 2
Correct Answer
Explanation →

Q12:

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
Answer options
Option: 2
Correct Answer
Explanation →

Q13:

Anindita invests a total of 11 lakh rupees distributed across three schemes A, B and C for a period of two years. These schemes offer an interest rate of 10%10\%, 8%8\% and 12%12\% per annum, respectively, each compounded annually. If the initial investment amount in scheme A is 3000030000 rupees and the total interest earned from all the three schemes during the first year is 1060010600 rupees, then the total interest earned, in rupees, from all the three schemes for the second year is
Answer options
Option: 2
Correct Answer
Explanation →

Q14:

Let f(x)=a2x2+2bx+cf(x) = a^2x^2 + 2bx + c where, a≠0a \neq 0, b,cb, c are real numbers and xx is a real variable then
Answer options
Option: 2
Correct Answer
Explanation →

Q15:

The area of the triangle, formed by the straight lines y=0,12x−5y=0,y = 0, 12x - 5y = 0, and 3x+4y=73x + 4y = 7 is
Answer options
Option: 2
Correct Answer
Explanation →

Q16:

Area of a regular octagon inscribed in a circle of radius 1 unit is:
Answer options
Option: 1
Correct Answer
Explanation →

Q17:

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
Answer options
Option: 1
Correct Answer
Explanation →

Q18:

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
Answer options
Option: 2
Correct Answer
Explanation →

Q19:

The set of all values of xx satisfying the inequality log⁡x+12[log⁡2(x+2)]>0\log_{\frac{x+1}{2}} [\log_2(x+2)] > 0 is
Answer options
Option: 4
Correct Answer
Explanation →

Q20:

Let S1={100,105,110,115,...} S_1 = \{100, 105, 110, 115, ... \} and S2={100,95,90,85,...} S_2 = \{100, 95, 90, 85, ... \} be two series in arithmetic progression. If ak a_k and bk b_k are the k k -th terms of S1 S_1 and S2 S_2 , respectively, then ∑k=120akbk \sum_{k=1}^{20} a_k b_k equals __________.
Answer options
Option: 2
Correct Answer
Explanation →

Q21:

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
Answer options
Option: 2
Correct Answer
Explanation →

Q22:

Which of the following numbers is divisible by 310+23^{10} + 2?
Answer options
Option: 4
Correct Answer
Explanation →

Q23:

Let A and B be two finite sets such that n(A−B)n(A - B), n(A∩B)n(A\cap B), n(B−A)n(B - A) are in an arithmetic progression. Here n(X)n(X) denotes the number of elements in a finite set XX. If n(A∪B)=18n(A\cup B) = 18, then n(A)+n(B)n(A) + n(B) is ____
Answer options
Option: 1
Correct Answer
Explanation →

Q24:

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
Answer options
Option: 1
Correct Answer
Explanation →

Q25:

The remainder when 111011+10111111^{1011} + 1011^{11} is divided by 99 is
Answer options
Option: 2
Correct Answer
Explanation →

Q26:

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 (in lakhs of rupees) and the value of products returned (in lakhs of rupees).
\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline
Month Sales (in lakhs of rupees) Value of products returned (as a percentage of sales)
Apparel Footwear Electronics Apparel Footwear Electronics
January26210428913%7%2%
February27911338716%9%3%
March23612128320%7%2%
April2585832516%8%1%
May2496935912%6%4%
June23011132119%5%3%
July24411934117%9%4%
August2526033616%6%2%
September28811835510%9%5%
October22210838315%8%2%
November2289328214%9%4%
December2218626818%10%1%
Which month had highest percentage decline in monthly sales as compared to previous month for the Apparel category?
Answer options
Option: 4
Correct Answer
Explanation →

Q27:

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 (in lakhs of rupees) and the value of products returned (in lakhs of rupees).
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Month Sales (in lakhs of rupees) Value of products returned (as a percentage of sales)
Apparel Footwear Electronics Apparel Footwear Electronics
January26210428913%7%2%
February27911338716%9%3%
March23612128320%7%2%
April2585832516%8%1%
May2496935912%6%4%
June23011132119%5%3%
July24411934117%9%4%
August2526033616%6%2%
September28811835510%9%5%
October22210838315%8%2%
November2289328214%9%4%
December2218626818%10%1%
For which categories the value of the products returned (as a percentage of sales) increased for three consecutive months?
Answer options
Option: 2
Correct Answer
Explanation →

Q28:

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 (in lakhs of rupees) and the value of products returned (in lakhs of rupees).
\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline
Month Sales (in lakhs of rupees) Value of products returned (as a percentage of sales)
Apparel Footwear Electronics Apparel Footwear Electronics
January26210428913%7%2%
February27911338716%9%3%
March23612128320%7%2%
April2585832516%8%1%
May2496935912%6%4%
June23011132119%5%3%
July24411934117%9%4%
August2526033616%6%2%
September28811835510%9%5%
October22210838315%8%2%
November2289328214%9%4%
December2218626818%10%1%
By what percentage the net sales for June increased as compared to May in the Footwear category?
Answer options
Option: 1
Correct Answer
Explanation →

Q29:

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 (in lakhs of rupees) and the value of products returned (in lakhs of rupees).
\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline
Month Sales (in lakhs of rupees) Value of products returned (as a percentage of sales)
Apparel Footwear Electronics Apparel Footwear Electronics
January26210428913%7%2%
February27911338716%9%3%
March23612128320%7%2%
April2585832516%8%1%
May2496935912%6%4%
June23011132119%5%3%
July24411934117%9%4%
August2526033616%6%2%
September28811835510%9%5%
October22210838315%8%2%
November2289328214%9%4%
December2218626818%10%1%
Among the following four months, for which month the contribution of the Apparel category in the total monthly sales was the highest?
Answer options
Option: 2
Correct Answer
Explanation →

Q30:

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 (in lakhs of rupees) and the value of products returned (in lakhs of rupees).
\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline\newline
Month Sales (in lakhs of rupees) Value of products returned (as a percentage of sales)
Apparel Footwear Electronics Apparel Footwear Electronics
January26210428913%7%2%
February27911338716%9%3%
March23612128320%7%2%
April2585832516%8%1%
May2496935912%6%4%
June23011132119%5%3%
July24411934117%9%4%
August2526033616%6%2%
September28811835510%9%5%
October22210838315%8%2%
November2289328214%9%4%
December2218626818%10%1%
Among the following four months, for which month the value of the Footwear returned (in lakhs of rupees) was the highest?
Answer options
Option: 2
Correct Answer
Explanation →

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

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Our free resources include handwritten solutions for all questions, making it easier to understand the concepts and approach. Use these PYQs to assess your preparation level and identify areas that need more focus. No login required. We have created handwritten solutions for all IPMAT Indore questions for free!