List of top Questions asked in IPMAT- 2024

The number of integer solutions of the equation $x_1 + x_2 + x_3 + x_4 = 50$, where $x_1 \ge 1$, $x_2 \ge 2$, $x_3 \ge 0$, and $x_4 \ge 0$, is: 

The number of factors of 1800 that are multiple of 6 is …………. .

In a group of 150 students, 52 like tea, 48 like juice, and 62 like coffee. If each student in the group likes at least one among tea, juice, and coffee, then the maximum number of students that like more than one drink is _______________.

The sentences given below, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the most logical order and enter the sequence of numbers in the space provided. Only numbers are to be entered in the space provided for the answer, and no letters, characters, or spaces should be entered. For example, a response such as 3412 is valid, and responses such as 3412. or 3 41 2 are invalid. 
1. In this microgravity environment, your blood also tends to move towards the heart and head. 
2. Both effects are only short-lived and, after a brief period of readjustment on arriving back home, the heart and spine return to normal. 
3. The heart interprets this as an increase in the amount of blood in the body and that it needs to pump less, so it shrinks. 
4. In space with less gravitational force than on Earth, there's less pressure on your spine and so it'll get a bit longer, effectively making you as much as two inches taller.

The number of real solutions of the equation \((x^2 - 15x + 55)^{x^2 - 5x + 6} = 1\) is __________.

Let \( ABC \) be a triangle right-angled at \( B \) with \( AB = BC = 18 \). The area of the largest rectangle that can be inscribed in this triangle and has \( B \) as one of the vertices is  _____________.

A fruit seller has oranges, apples, and bananas in the ratio 3:6:7. If the number of oranges is a multiple of both 5 and 6, then the minimum number of fruits the seller has is ______________.

The number of pairs \( (x, y) \) of integers satisfying the inequality \( |x - 5| + |y - 5| \leq 6 \) is ____________.

The price of a chocolate is increased by \( x% \) and then reduced by \( x% \). The new price is 96.76% of the original price. Then \( x \) is:

The following table shows the number of employees and their median age in eight companies located in a district. \[ \begin{array}{|l|l|l|} \hline \textbf{Company} & \textbf{Number of Employees} & \textbf{Median Age} \\ \hline A & 32 & 24 \\ B & 28 & 30 \\ C & 43 & 39 \\ D & 39 & 45 \\ E & 35 & 49 \\ F & 29 & 54 \\ G & 23 & 59 \\ H & 16 & 63 \\ \hline \end{array} \] It is known that the age of all employees are integers. It is also known that the age of every employee in A is strictly less than the age of every employee in B, the age of every employee in B is strictly less than the age of every employee in C, and the age of every employee in G is strictly less than the age of every employee in H. The median age of an employee across the eight companies is …………..

The following table shows the number of employees and their median age in eight companies located in a district. \[ \begin{array}{|l|l|l|} \hline \textbf{Company} & \textbf{Number of Employees} & \textbf{Median Age} \\ \hline A & 32 & 24 \\ B & 28 & 30 \\ C & 43 & 39 \\ D & 39 & 45 \\ E & 35 & 49 \\ F & 29 & 54 \\ G & 23 & 59 \\ H & 16 & 63 \\ \hline \end{array} \] It is known that the age of all employees are integers. It is also known that the age of every employee in A is strictly less than the age of every employee in B, the age of every employee in B is strictly less than the age of every employee in C, and the age of every employee in G is strictly less than the age of every employee in H. In company F, the lowest possible sum of the ages of all employees is ………….

If \(4 \log_2 x - 4 \log_3 x - 16 x + 68 = 0\), then \(x - 2\) equals ………...

Person A borrows rupees 4000 from another person B for a duration of 4 year rupee He borrows a portion of it at 3% simple interest per annum, while the rest at 4% simple interest per annum. If B gets rupees 520 as total interest, then the amount A borrowed at 3% per annum in rupee is …………….

The number of triangles with integer sides and with perimeter 15 is ………… .