IPM Question Paper 2024 | IPM Indore Quants

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IPMAT 2024 Question Paper Indore Quants. Solve questions from IPMAT 2024 Question Paper from IPM Indore and check the solutions to get adequate practice.

IPMAT 2024 Question Paper - IPM Indore Quants

The number of factors of 1800 that are multiple of 6 is ________
18
IPMAT 2024 Question Paper - IPM Indore Quants

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

IPMAT 2024 Question Paper - IPM Indore Quants

The following table shows the number of employees and their median age in eight companies located in a district.

Company	Number of employees	Median age
A	32	24
B	28	30
C	43	39
D	39	45
E	35	49
F	29	54
G	23	59
H	16	63

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 ______

IPMAT 2024 Question Paper - IPM Indore Quants

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 _____ .
12
IPMAT 2024 Question Paper - IPM Indore Quants

Let ABC be a triangle right-angled at B with AB = BC = 18. The area of largest rectangle that can be inscribed in this triangle and has B as one of the vertices is ______
81
IPMAT 2024 Question Paper - IPM Indore Quants

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 ______
160
IPMAT 2024 Question Paper - IPM Indore Quants

The number of pairs $(x, y)$ of integers satisfying the inequality $|x-5|+|y-5| \leq 6$ is $\qquad$ ______.
85
IPMAT 2024 Question Paper - IPM Indore Quants

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 _____ .
18
IPMAT 2024 Question Paper - IPM Indore Quants

Let $f$ and $g$ be two functions defined by $f(x)=|x+|x||$ and $g(x)=\frac{1}{x}$ for $x \neq 0$ . If $f(a)+g(f(a))=\frac{13}{6}$ for some real a, then the maximum possible value of $f(g(a))$ is $\qquad$ ________.
6

IPMAT 2024 Question Paper - IPM Indore Quants

The following table shows the number of employees and their median age in eight companies located in a district.

Company	Number of employees	Median age
A	32	24
B	28	30
C	43	39
D	39	45
E	35	49
F	29	54
G	23	59
H	16	63

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 an employee across the eight companies is______.

IPMAT 2024 Question Paper - IPM Indore Quants

The following table shows the number of employees and their median age in eight companies located in a district.

Company	Number of employees	Median age
A	32	24
B	28	30
C	43	39
D	39	45
E	35	49
F	29	54
G	23	59
H	16	63

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 ______

IPMAT 2024 Question Paper - IPM Indore Quants

If $4^{\log _2 x}-4 x+9^{\log _3 y}-16 y+68=0$ , then $y-x$ equals $\qquad$
6
IPMAT 2024 Question Paper - IPM Indore Quants

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 _______
3000
IPMAT 2024 Question Paper - IPM Indore Quants

The number of triangles with integer sides and with perimeter 15 is _______
7
IPMAT 2024 Question Paper - IPM Indore Quants

If $A=\left[\begin{array}{ccc}x_1 & x_2 & 7 \\ y_1 & y_2 & y_3 \\ z_1 & 8 & 3\end{array}\right]$ 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 $\qquad$
288
IPMAT 2024 Question Paper - IPM Indore Quants

The angle of elevation of the top of a pole from a point A on the ground is $30^{\circ}$ . The angle of elevation changes to $45^{\circ}$ , after moving 20 metres towards the base of the pole. Then the height of the pole, in metres, is
1. 30
2. $15(\sqrt{5}+1)$
3. $20(\sqrt{3}+1)$
4. $10(\sqrt{3}+1)$
Choice D
$10(\sqrt{3}+1)$
IPMAT 2024 Question Paper - IPM Indore Quants

If $|x+1|+(y+2)^2=0$ and $a x-3 a y=1$ , then the value of $a$ is
1. $\frac{1}{5}$
2. $\frac{1}{7}$
3. $\frac{1}{2}$
4. 2
Choice A
$\frac{1}{5}$
IPMAT 2024 Question Paper - IPM Indore Quants

If $\log _4 x=a$ and $\log _{25} x=b$ then $\log _x 10$ is
1. $\frac{a+b}{2(a-b)}$
2. $\frac{a+b}{2}$
3. $\frac{a+b}{2 a b}$
4. $\frac{a-b}{2 a b}$
Choice C
$\frac{a+b}{2 a b}$
IPMAT 2024 Question Paper - IPM Indore Quants

Let ABC be an equilateral triangle, with each side of length k. If a circle is drawn with diameter AB, then the area of the portion of the triangle lying inside the circle is
1. $(3 \sqrt{3}+\pi)\left(\frac{k^2}{6}\right)$
2. $(3 \sqrt{3}-\pi)\left(\frac{k^2}{24}\right)$
3. $(3 \sqrt{3}+\pi)\left(\frac{k^2}{24}\right)$
4. $(3 \sqrt{3}-\pi)\left(\frac{k^2}{6}\right)$
Choice C
$(3 \sqrt{3}+\pi)\left(\frac{k^2}{24}\right)$
IPMAT 2024 Question Paper - IPM Indore Quants

Let ABC be a triangle with $AB = AC$ and D be a point on $B C$ such that $\angle B A D=30^{\circ}$ . If $E$ is a point on $A C$ such that AD AE , then $\angle CDE$ equals
1. $15^{\circ}$
2. $60^{\circ}$
3. $30^{\circ}$
4. $10^{\circ}$
Choice A
$15^{\circ}$
IPMAT 2024 Question Paper - IPM Indore Quants

If 5 boys and 3 girls randomly sit around a circular table, the probability that there will be at least one boy sitting between any two girls, is
1. $\frac{2}{7}$
2. $\frac{1}{7}$
3. $\frac{1}{4}$
4. $\frac{1}{3}$
Choice A
$\frac{2}{7}$
IPMAT 2024 Question Paper - IPM Indore Quants

The side $A B$ of a triangle $A B C$ is $c$ . The median $B D$ is of length $k$ . If $\angle B D A=\theta<90^{\circ}\ ), then the area of triangle \(A B C$ is
1. $\frac{k^2 \cos 2 \theta}{2}+k \sin \theta \sqrt{\left(c^2-k^2 \cos ^2 \theta\right)}$
2. $\frac{k^2 \sin 2 \theta}{2}+k \sin \theta \sqrt{\left(c^2-k^2 \sin ^2 \theta\right)}$
3. $\frac{ k ^2 \cos \theta}{4}- k \sin \theta \sqrt{\left( c ^2+ k ^2 \sin ^2 \theta\right)}$
4. $\frac{k^2 \cos 2 \theta}{4}+k \sin \theta \sqrt{\left(c^2-k^2 \sin ^2 \theta\right)}$
Choice B
$\frac{k^2 \sin 2 \theta}{2}+k \sin \theta \sqrt{\left(c^2-k^2 \sin ^2 \theta\right)}$
IPMAT 2024 Question Paper - IPM Indore Quants

Let $a =\frac{\left(\log _7 4\right)\left(\log _7 5-\log _7 2\right)}{\left(\log _7 25\right)\left(\log _7 8-\log _7 4\right)}$ Then the value of $5^a$ is
1. $\frac{7}{2}$
2. 5
3. 8
4. $\frac{5}{2}$
Choice D
$\frac{5}{2}$
IPMAT 2024 Question Paper - IPM Indore Quants

For some non-zero real values of $a , b$ and $c$ , it is given that $\left|\frac{c}{a}\right|=4,\left|\frac{a}{b}\right|=\frac{1}{3}$ and $\frac{b}{c}=-\frac{3}{4}$ . If ac $>0$ , then $\left(\frac{b+c}{a}\right)$ equals
1. 7
2. -7
3. -1
4. 1
Choice D
1
IPMAT 2024 Question Paper - IPM Indore Quants

The difference between the maximum real root and the minimum real root of the equation $\left(x^2-5\right)^4+$ $\left(x^2-7\right)^4=16$ is
1. $2 \sqrt{5}$
2. $2 \sqrt{7}$
3. $\sqrt{7}$
4. $\sqrt{10}$
Choice B
$2 \sqrt{7}$
IPMAT 2024 Question Paper - IPM Indore Quants

If $\theta$ is the angle between the pair of tangents drawn from the point $A \left(0, \frac{7}{2}\right)$ to the circle $x^2+y^2-14 x+$ $16 y+88=0$ , then $\tan \theta$ equals
1. $\frac{5}{4}$
2. $\frac{20}{21}$
3. $\frac{2}{5}$
4. $\frac{4}{5}$
Choice B
$\frac{20}{21}$
IPMAT 2024 Question Paper - IPM Indore Quants

The numbers $2^{2024}$ and $5^{2024}$ are expanded and their digits are written out consecutively on one page. The total number of digits written on the page is
1. 1987
2. 2025
3. 2065
4. 2000
Choice B
2025
IPMAT 2024 Question Paper - IPM Indore Quants

A boat goes 96 km upstream in 8 hours and covers the same distance moving downstream in 6 hours. On the next day boat starts from point A, goes downstream for 1 hour, then upstream for 1 hour and repeats this four more time that is, 5 upstream and 5 downstream journeys. Then the boat would be
1. 22.5 km downstream of A
2. 15 km downstream of A
3. 12.5 km downstream of A
4. 20 km downstream of A
Choice D
20 km downstream of A
IPMAT 2024 Question Paper - IPM Indore Quants

If the shortest distance of a given point to a given circle is 4 cm and the longest distance is 9 cm, then the radius of the circle is
1. 2.5 cm or 6.5 cm.
2. 6.5 cm
3. 5 cm or 13 cm
4. 2.5 cm
Choice A
2.5 cm or 6.5 cm.
IPMAT 2024 Question Paper - IPM Indore Quants

In a survey of 500 people, it was found that 250 owned a 4-wheeler but not a 2-wheeler, 100 owned a 2-wheeler but not a 4-wheeler, and 100 owned neither a 4-wheeler nor a 2-wheeler. Then the number of people who owned both is
1. 75
2. 60
3. 50
4. 100
Choice C
50
IPMAT 2024 Question Paper - IPM Indore Quants

The sum of a given infinite geometric progression is 80 and the sum of its first two terms is 35. Then the value of n for which the sum of its first n terms is closest to 100, is
1. 6
2. 5
3. 7
4. 4
Choice B
5
IPMAT 2024 Question Paper - IPM Indore Quants

Let n be the number of ways in which 20 identical balloons can be distributed among 5 girls and 3 boys such that everyone gets at least one balloon and no girl gets fewer balloons than a boy does. Then
1. $8000 \leq n <9000$
2. $7000 \leq n <8000$
3. $9000 \leq n <10000$
4. $6000 \leq$ n $<7000$
Choice A
$8000 \leq n <9000$
IPMAT 2024 Question Paper - IPM Indore Quants

The greatest number among $2^{300}, 3^{200}, 4^{100}, 2^{100}+3^{100}$ is
1. $3^{200}$
2. $2^{100}+3^{100}$
3. $4^{100}$
4. $2^{300}$
Choice A
$3^{200}$
IPMAT 2024 Question Paper - IPM Indore Quants

The number of values of $x$ for which $C_{3 x+1}^{17-x}$ is defined as an integer is
1. 5
2. 6
3. 2
4. 4
Choice A
5
IPMAT 2024 Question Paper - IPM Indore Quants

The number of solutions of the equation $x_1+x_2+$ $x_3+x_4=50$ , where $x _1, x _2, x _3, x _4$ are integers with $x_1 \geq 1, x_2 \geq 2, x_3 \geq 0, x_4 \geq 0$ is
1. 19600
2. 19200
3. 20200
4. 20200
Choice A
19600
IPMAT 2024 Question Paper - IPM Indore Quants

Sagarika divides her savings of 10000 rupees to invest across two schemes A and B. Scheme A offers an interest rate of 10% per annum, compounded halfyearly, while scheme B offers a simple interest rate of 12% per annum. If at the end of first year, the value of her investment in scheme B exceeds the value of her investment in scheme A by 2310 rupees, then the total interest, in rupees, earned by Sagarika during the first year of investment is
1. 1100
2. 1130
3. 1111
4. 1000
Choice B
1130
IPMAT 2024 Question Paper - IPM Indore Quants

A fruit seller had a certain number of apples, bananas and oranges at the start of the day. The number of bananas was 10 more than the number of apples, and the total number of bananas and apples was a multiple of 11. She was able to sell 70% of apples, 60% of bananas, and 50% of oranges during the day. If she was able to sell 55% of the fruits she had at the start of the day, then the minimum number of oranges she had at the start of the day was
1. 220
2. 190
3. 210
4. 180
Choice C
210
IPMAT 2024 Question Paper - IPM Indore Quants

The terms of a geometric progression are real and positive. If the $p^{\text {th }}$ term of the progression is $q$ and the $q^{\text {th }}$ term is $p$ , then the logarithm of the first term is
1. $\frac{(1-q) \log (p)-(1-p) \log (q)}{(p-q)}$
2. $\frac{(1-q) \log (p)+(1-p) \log (q)}{(p-q)}$
3. $\frac{(1-q) \log ( q )+(1- p ) \log ( p )}{(p-q)}$
4. $\frac{(1-q) \log (q)-(1-p) \log (p)}{(p-q)}$
Choice D
$\frac{(1-q) \log (q)-(1-p) \log (p)}{(p-q)}$
IPMAT 2024 Question Paper - IPM Indore Quants

The number of real solutions of the equation $x^2-$ $10|x|-56=0$ is
1. 3
2. 4
3. 2
4. 1
Choice C
2
IPMAT 2024 Question Paper - IPM Indore Quants

The smallest possible number of students in a class if the girls in the class are less than 50% but more than 48% is
1. 25
2. 100
3. 27
4. 200
Choice C
27

In an election there were five constituencies S1, S2, S3, S4 and S5 with 20 voters each all of whom voted. Three parties A, B and C contested the elections.
The party that gets maximum number of votes in a constituency wins that seat. In every constituency there was a clear winner. The following additional information is available:

Total number of votes obtained by A, B and C across all constituencies are 49, 35 and 16 respectively
S2 and S3 were won by C while A won only S1.
Number of votes obtained by B in S1, S2, S3, S4 and S5 are distinct natural numbers in increasing order.

IPMAT 2024 Question Paper - IPM Indore Quants

The constituency in which B got lower number of votes compared to A and C is
1. S4
2. S1
3. S3
4. S2
Choice D
S2
IPMAT 2024 Question Paper - IPM Indore Quants

The number of votes obtained by B in S2 is
1. 5
2. 7
3. 4
4. 6
Choice D
6
IPMAT 2024 Question Paper - IPM Indore Quants

Assume that A and C had formed an alliance and any voter who voted for either A or C would have voted for this alliance. Then the number of seats this alliance would have won is
1. 3
2. 4
3. 5
4. 2
Choice D
2
IPMAT 2024 Question Paper - IPM Indore Quants

The number of votes obtained by A is S5 is
1. 7
2. 9
3. 6
4. 8
Choice D
8
IPMAT 2024 Question Paper - IPM Indore Quants

Comparing the number votes obtained by A across different constituencies, the lowest number of votes were in constituency
1. S2
2. S5
3. S3
4. S4
Choice C
S3