Get access to the detailed solutions to the previous years questions asked in IIM IPMAT exam
2 IPMAT 2022 - Quantitative Aptitude
Aruna purchases a certain number of apples for INR 20 each and a certain number of mangoes for INR 25 each. If she sells all the apples at 1% profit and all the mangoes at 20% loss, overall she makes neither profit nor loss. Instead, if she sell all the apples at 20% loss and all the mangoes at 10% profit, overall she makes a loss of INR 150. Then the number of apples purchased by Aruna is_________.
3 IPMAT 2022 - Quantitative Aptitude
Let P(X) denote power set of a set X. If A is the null set, then the number of elements in P(P(P(P(A)))) is_______.
4 IPMAT 2022 - Quantitative Aptitude
The number – 16, 2x+3 – 22x-1 – 16, 22x-1 + 16 are in an arithmetic progression. Then x equals________.
5 IPMAT 2022 - Quantitative Aptitude
When Geeta increases her speed from 12 km/hr to 20 km/hr. she takes one hour less than the usual time to cover the distance between her home and office. The distance between her home and office is______ km.
6 IPMAT 2022 - Quantitative Aptitude
Given that f(x) = |x| = 2|x – 1| + |x – 2| + |x – 4| + |x – 6| + 2|x – 10|, x ∈ (– ∞, ∞) the minimum value of f(x) is_______.
7 IPMAT 2022 - Quantitative Aptitude
The sum of the coefficients of all the terms in the expansion of (5x – 9)4 is _________.
8 IPMAT 2022 - Quantitative Aptitude
The number of triangles that can be formed by choosing points from 7 points on a line and 5 points on another parallel line is__________.
9 IPMAT 2022 - Quantitative Aptitude
The area enclosed by 2|x| + 3|y| ≤ 6 is ________ sq. units.
10 IPMAT 2022 - Quantitative Aptitude
A new sequence is obtained from the sequence of positive integers (1, 2, 3…) by deleting all the perfect squares. Then the 2022nd term of the new sequence is________.
12 IPMAT 2022 - Quantitative Aptitude
If 
then the absolute value of the determinant of (A9 + A6 + A3 + A) is __________.
13 IPMAT 2022 - Quantitative Aptitude
Let 50 distinct positive integers be chosen such that the highest among them is 100, and the average of the largest 25 integers among them exceeds the average of the remaining integers by 50. Then the maximum possible value of the sum of all the 50 integers is_________.
14 IPMAT 2022 - Quantitative Aptitude
The 3rd, 14th and 69th terms of an arithmetic progression form three distinct and consecutive terms of a geometric progression. If the next term of the geometric progression is the nth terms of the arithmetic progression, then n equals _____________.
15 IPMAT 2022 - Quantitative Aptitude
Mrs. and Mr. Sharma, and Mrs. and Mr. Ahuja along with four other persons are to be seated at a round table for dinner. If Mrs. and Mr. Sharma are to be seated next to each other, and Mrs. and Mr. Ahuja are not to be seated next to each other, then the total number of seating arrangements is___________.
16 IPMAT 2022 - Quantitative Aptitude
When the square of the difference of two natural numbers is subtracted from the square of the sum of the same two numbers and the result is divided by four, we get
the square of the product of the two numbers
the product of the LCM and HCF of the two numbers
the HCF of the two numbers
the LCM of the two numbers
17 IPMAT 2022 - Quantitative Aptitude
In a 400-metre race, Ashok beats Bipin and Chandan respectively by 15 seconds and 25 seconds. If Ashok beats Bipin by 150 metres, by how many metres does Bipin beat Chandan in the race?
150
50
100
80
18 IPMAT 2022 - Quantitative Aptitude
The set of real values of x for which the inequality 
holds is
[2, 81)
[2, 81]
(2, 27)
(2, 27]
19 IPMAT 2022 - Quantitative Aptitude
If f[x2 + f(y)] = xf(x) + y for all non – negative integers x and y, then the value of [f(0)]2 + f(0) equals ________.
1
0
6
3
20 IPMAT 2022 - Quantitative Aptitude
In how many ways can the letters of the word MANAGEMENT be arranged such that no two vowels appear together ?
21600
75600
37800
25200
21 IPMAT 2022 - Quantitative Aptitude
If the five digit number abcde is divisible by 6, then which of the following number is not necessarily divisible by 6 ?
eee
edcba
cdbae
bbadcacede
22 IPMAT 2022 - Quantitative Aptitude
The curve represented by the equation 
an ellipse with the foci on the y-axis
an ellipse with the foci on the x-axis
a hyperbola with the foci on the x-axis
a hyperbola with the foci on the y-axis
24 IPMAT 2022 - Quantitative Aptitude
In a bowl containing 60 ml orange juice, 40 ml of water is poured. Thereafter, 100 ml of apple juice is poured to make a fruit punch. Madhu drinks 50 ml of this fruit punch and comments that the proportion of orange juice needs to be higher for better taste. How much orange juice should be poured into the fruit punch that remained, in order to bring up the level of orange juice to 50 percentage ?
80 ml
100 ml
40 ml
60 ml
25 IPMAT 2022 - Quantitative Aptitude
Ayesha is standing stop a vertical tower 200m high and observes a car moving away from the lower on a straight, horizontal road from the foot of the tower. At 11 : 00 AM, she observes the angle of depression of the car to be 45°. At 11 : 02 AM, she observes the angle of depression of the car to be 30°. The speed at which the car is moving is approximately.
6.3 km per hour
4.39 km per hour
10.6 km per hour
8.45 km per hour
26 IPMAT 2022 - Quantitative Aptitude
The set of all possible values of f(x) for which (81)x + (81)f(x) = 3 is
(−∞, 4)
(3, 4)
(−∞, 0.25)
(0.25, 3)
27 IPMAT 2022 - Quantitative Aptitude
The number of four-digit integers which are greater than 1000 and divisible by both 2 and 3, but not by 5, is
1333
1200
1500
1666
28 IPMAT 2022 - Quantitative Aptitude
Let A= {1, 2, 3} and B = {a, b}. Assuming all relations from set A to set B are equally likely, what is the probability that a relation from A to B is also a function ?
1/2
32/26
1
1/8
30 IPMAT 2022 - Quantitative Aptitude
In a right-angled triangle ABC, the hypotenuse AC is of length 13 cm. A line drawn connecting the midpoints D and E of sides AB and AC is found to be 6 cm in length. The length of BC is
1.5 cm
2.8 cm
2√3 cm
12 cm
31 IPMAT 2022 - Quantitative Aptitude
In a room, there are n persons whose average height is 160 cm. If m more persons, whose average height is 172 cm, enter the room, then the average height of all persons in the room becomes 164 cm. then m : n is
1 : 3
1 : 2
2 : 1
3 : 1
32 IPMAT 2022 - Quantitative Aptitude
If one of the factors of the number 3728173 is randomly chosen, then the probability that the chosen factor will be a perfect square is_____________.
5/32
1/12
3/40
5/36
33 IPMAT 2022 - Quantitative Aptitude
The lengths of the sides of a triangle are x, 21 and 40, where x is the shortest side. A possible value of x is -
20
19
16
18
34 IPMAT 2022 - Quantitative Aptitude
A set of all possible values the function f(x) = x/|x| , where x ≠ 0 takes is
{1, 0, – 1}
{1}
{1, 0}
{1, – 1}
35 IPMAT 2022 - Quantitative Aptitude
The sum of the first 15 terms in an arithmetic progression is 200, while the sum of the next 15 terms is 350. Then the common difference is
2/3
7/9
4/9
1/3
36 IPMAT 2022 - Quantitative Aptitude
The cost of a piece of jewellery is proportional to the square of its weight. A piece of jewellery weighing 10 grams is INR 3600. The cost of a piece of jewellery of the same kind weighing 4 grams is
INR 576
INR 600
INR 1440
INR 1220
37 IPMAT 2022 - Quantitative Aptitude
The value of k for which the following lines x – y – 1 = 0, 2x + 3y – 12 = 0, 2x – 3y + k = 0 are concurrent is
– 1
12
1
0
38 IPMAT 2022 - Quantitative Aptitude
The sum of the squares of all the roots of the equation x2 + |x + 4| + |x – 4| – 35 = 0
175
74
50
148
39 IPMAT 2022 - Quantitative Aptitude
Let A and B be two sets such that the Cartesian product A × B consists of four elements. If two elements of A × B are (1, 4) and (4, 1), then
? ∈ A × B
A × B ≠ B × A
A × B = B × A
None of these
40 IPMAT 2022 - Quantitative Aptitude
Suppose a, b and c are integers such that a > b > c > 0, and 
Then the value of the determinant of A
is positive
is negative
is zero
can be positive or negative