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_________.

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_______.

The number – 16, 2^x+3 – 2^2x-1 – 16, 2^2x-1 + 16 are in an arithmetic progression. Then x equals________.

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.

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_______.

The sum of the coefficients of all the terms in the expansion of (5x – 9)⁴ is _________.

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__________.

The area enclosed by 2|x| + 3|y| ≤ 6 is ________ sq. units.

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________.

If then the absolute value of the determinant of (A⁹ + A⁶ + A³ + A) is __________.

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_________.

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 _____________.

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___________.

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

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?

The set of real values of x for which the inequality holds is

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 ________.

In how many ways can the letters of the word MANAGEMENT be arranged such that no two vowels appear together ?

If the five digit number abcde is divisible by 6, then which of the following number is not necessarily divisible by 6 ?

The curve represented by the equation

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 ?

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. 

The set of all possible values of f(x) for which (81)^x + (81)^f(x) = 3 is

The number of four-digit integers which are greater than 1000 and divisible by both 2 and 3, but not by 5, is

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 ?

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

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

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_____________.

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 -

A set of all possible values the function f(x) = x/|x| , where x ≠ 0 takes is

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

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

The value of k for which the following lines x – y – 1 = 0, 2x + 3y – 12 = 0, 2x – 3y + k = 0 are concurrent is

The sum of the squares of all the roots of the equation x² + |x + 4| + |x – 4| – 35 = 0

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

Suppose a, b and c are integers such that a > b > c > 0, and Then the value of the determinant of A