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IPMAT Indore 2024 Past Year Papers with Solutions filter tool

Q1:

If 4log⁡2x−4x+9log⁡3y−16y+68=04^{\log_2{x}} - 4x + 9^{\log_3{y}} - 16y + 68 = 0, then y−xy - x equals:
Explanation →

Q2:

A fruit seller has oranges, apples, and bananas in the ratio 3:6:73:6:7. If the number of oranges is a multiple of both 5 and 6, then the minimum number of fruits the seller has is:
Explanation →

Q3:

The number of real solutions of the equation (x2−15x+55)x2−5x+6=1(x^2 - 15x + 55)^{x^2-5x+6} = 1 is:
Explanation →

Q4:

The following table shows the number of employees and their median age in eight companies located in a district.
CompanyNumber of employeesMedian age
A3224
B2830
C4339
D3945
E3549
F2954
G2359
H1663
It is known that the age of all employees are integers. It is 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, ..., the age of every employee in G is strictly less than the age of every employee in H.
The highest possible age of an employee of company A is:
Explanation →

Q5:

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

Q6:

The number of triangles with integer sides and with perimeter 15 is:
Explanation →

Q7:

If A=[x1x27y1y2y3z183]A = \begin{bmatrix} x_1 & x_2 & 7 \\ y_1 & y_2 & y_3 \\ z_1 & 8 & 3 \end{bmatrix} is a matrix such that the sum of all three elements along any row, column or diagonal are equal to each other, then the value of determinant of A is:
Explanation →

Q8:

The number of factors of 1800 that are multiple of 6 is:
Explanation →

Q9:

The following table shows the number of employees and their median age in eight companies located in a district.
CompanyNumber of employeesMedian age
A3224
B2830
C4339
D3945
E3549
F2954
G2359
H1663
It is known that the age of all employees are integers. It is 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, ..., the age of every employee in G is strictly less than the age of every employee in H.
The median age of employees across the eight companies is:
Explanation →

Q10:

Let △ABC\triangle ABC be a triangle right-angled at BB with AB=BC=18AB = BC = 18. The area of the largest rectangle that can be inscribed in this triangle and has BB as one of the vertices is:
Explanation →

Q11:

The number of pairs (x,y)(x, y) of integers satisfying the inequality ∣x−5∣+∣y−5∣≤6|x - 5| + |y - 5| \leq 6 is:
Explanation →

Q12:

The following table shows the number of employees and their median age in eight companies located in a district.
CompanyNumber of employeesMedian age
A3224
B2830
C4339
D3945
E3549
F2954
G2359
H1663
It is known that the age of all employees are integers. It is 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, ..., 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:
Explanation →

Q13:

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:
Explanation →

Q14:

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:
Explanation →

Q15:

Let ff and gg be two functions defined by f(x)=∣x+∣x∣∣f(x) = |x + |x|| and g(x)=1xg(x) = \frac{1}{x} for x≠0x \neq 0. If f(a)+g(f(a))=136f(a) + g(f(a)) = \frac{13}{6} for some real aa, then the maximum possible value off(g(a)) f(g(a)) is:
Explanation →

IPMAT Indore 2024 SA - Past Year Questions (Free PDF Download)

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