IPM Question Paper 2023 | IPM Indore Quants

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IPMAT 2023 Question Paper Indore Quants. Solve questions from IPMAT 2023 Question Paper from IPM Indore and check the solutions to get adequate practice.

IPMAT 2023 Question Paper - IPM Indore Quants

Vinita drives a car which has four gears. The speed of the car in the fourth gear is five times its speed in the first gear. The car takes twice the time to travel a certain distance in the second gear as compared to the third gear. In a 100 km journey, if Vinita travels equal distances in each of the gears, she takes 585 minutes to complete the journey. Instead, if the distances covered in the first, second, third, and fourth gears are 4 km, 4 km, 32 km, and 60 km, respectively, then the total time taken, in minutes, to complete the journey, will be______.
312
IPMAT 2023 Question Paper - IPM Indore Quants

If three consecutive coefficients in the expansion of ( $x$ $+y)^n$ are in the ratio 1:9:63, then the value of $n$ is______ .
39
IPMAT 2023 Question Paper - IPM Indore Quants

The total number of positive integer solutions of $21 \leq$ $a + b + c \leq 25$ is______.
1160
IPMAT 2023 Question Paper - IPM Indore Quants

The product of the roots of the equation $\log _2 2^{\left(\log _2 x\right)^2}-5 \log _2 x+6=0$ is______.
32
IPMAT 2023 Question Paper - IPM Indore Quants

If f(1) = 1 and f(n) = 3n - f(n - 1) for all integers n > 1 , then the value of ƒ (2023) is _________.
3034
IPMAT 2023 Question Paper - IPM Indore Quants

If $f ( n )=1+2+3+\cdots+( n +1)$ and $g ( n )=\sum_{ k =1}^{ k = n } \frac{1}{ f ( k )}$ then the least value of $n$ for which $g(n)$ exceeds the value $\frac{99}{100}$ is______
199
IPMAT 2023 Question Paper - IPM Indore Quants

The polynomial $4 x^{10}-x^9+3 x^8-5 x^7+c x^6+2 x^5-$ $x^4+x^3-4 x^2+6 x-2$ when divided by $x-1$ leaves a remainder 2 . Then the value of $c +6$ is______.
5
IPMAT 2023 Question Paper - IPM Indore Quants

The remainder when 1! + 2! + 3! +∙∙∙+95! is divided by 15 is______.
3
IPMAT 2023 Question Paper - IPM Indore Quants

Let a, b, c, d be positive integers such that a + b + c + d = 2023. If a : b = 2 : 5 and c : d = 5 : 2 then the maximum possible value of a + c is________.
1442
IPMAT 2023 Question Paper - IPM Indore Quants

In the xy-plane let $A=(-2,0), B=(2,0)$ . Define the set $S$ as the collection of all points $C$ on the circle $x^2+y^2=$ 4 such that the area of the triangle $A B C$ is an integer. The number of points in the set $S$ is______.
14
IPMAT 2023 Question Paper - IPM Indore Quants

Amisha can complete a particular task in twenty days. After working for four days she fell sick for four days and resumed the work on the ninth day but with half of her original work rate. She completed the task in another twelve days with the help of a co-worker who joined her from the ninth day. The number of days required for the co-worker to complete the task alone would be ______.
24
IPMAT 2023 Question Paper - IPM Indore Quants

In an election with only two contesting candidates, 15% of the voters did not turn up to vote, and 50 voters cast invalid votes. It is known that 44% of all the voters in the voting list voted for the winner. If the winner got 200 votes more than the other candidate, then the number of voters in the voting list is_________.
5000
IPMAT 2023 Question Paper - IPM Indore Quants

Assume it is the beginning of the year today. Ankita will earn INR 10,000 at the end of the year, which she plans to invest in a bank deposit immediately at a fixed simple interest of 0.5% per annum. Her yearly income will increase by INR 10,000 every year, and the fixed simple interest offered by the bank on new deposits will also increase by 0.5% per annum every year. If Ankita continues to invest all her yearly income in new bank deposits at the end of each year, the total interest earned by her, in INR, in five years from today will be__________.
2500
IPMAT 2023 Question Paper - IPM Indore Quants

In a chess tournament, there are four groups, each containing an equal number of players. Each player plays
against every other player belonging to one's own group exactly once;
against each player belonging to one of the remaining three groups exactly twice;
against each player belonging to one of the remaining two groups exactly three times; and
against each player belonging to the remaining group exactly four times.
If there are more than 1000 matches being played in the tournament, the minimum possible number of players in each group is_______.
8
IPMAT 2023 Question Paper - IPM Indore Quants

The length of the line segment joining the two intersection points of the curves y = 4970 - |x| and y = x² is_________.
140
IPMAT 2023 Question Paper - IPM Indore Quants

If a three-digit number is chosen at random, what is the probability that it is divisible neither by 3 nor by 4?
1. 1/4
2. 2/3
3. 1/2
4. 1/3
Choice C
1/2
IPMAT 2023 Question Paper - IPM Indore Quants

A goldsmith bought a large solid golden ball at INR 1,000,000 and melted it to make a certain number of solid spherical beads such that the radius of each bead was one-fifth of the radius of the original ball. Assume that the cost of making golden beads is negligible. If the goldsmith sold all the beads at 20% discount on the listed price and made a total profit of 20%, then the listed price of each golden bead, in INR, was
1. 12000
2. 9600
3. 48000
4. 24000
Choice A
12000
IPMAT 2023 Question Paper - IPM Indore Quants

Let $a , b , c$ be real numbers greater than 1 , and n be a positive real number not equal to 1 . If $\log _n\left(\log _2 a\right)=1, \log _n\left(\log _2 b\right)=2$ and $\log _{ n }\left(\log _2 c \right)=3$ , then which of the following is true?
1. $a^n+b^n=c^n$
2. $\left(a^n+b\right)^n=a c$
3. $a+b=c$
4. $(b-a)^n=(c-b)$
Choice B
$\left(a^n+b\right)^n=a c$
IPMAT 2023 Question Paper - IPM Indore Quants

If the harmonic mean of the roots of the equation $(5+$ $\sqrt{2}) x^2-b x+8+2 \sqrt{5}=0$ is 4 then the value of $b$ is
1. $4-\sqrt{5}$
2. $2$
3. $4+\sqrt{5}$
4. $3$
Choice C
$4+\sqrt{5}$
IPMAT 2023 Question Paper - IPM Indore Quants

Consider an 8 × 8 chessboard. The number of ways 8 rooks can be placed on the board such that no two rooks are in the same row and no two are in the same column is
1. 7
2. 8
3. 7!
4. 8!
Choice D
8!
IPMAT 2023 Question Paper - IPM Indore Quants

The set of all real values of $x$ satisfying the inequality $\frac{x^2(x+1)}{(x-1)(2 x+1)^3}>0$ is
1. $\left(-1,-\frac{1}{2}\right) \cup(0,+\infty)$
2. $(-\infty,-1) \cup\left(-\frac{1}{2}, 0\right) \cup(1,+\infty)$
3. $(-1,0) \cup(1,+\infty)$
4. $\left(-1,-\frac{1}{2}\right) \cup(1,+\infty)$
Choice D
$\left(-1,-\frac{1}{2}\right) \cup(1,+\infty)$
IPMAT 2023 Question Paper - IPM Indore Quants

If $A=\left[\begin{array}{ll}1 & 2 \\ 3 & a\end{array}\right]$ where $a$ is a real number and $\operatorname{det}\left(A^3-\right.$ $\left.3 A^2-5 A\right)=0$ then one of the values of a can be
1. 1
2. 6
3. 4
4. 5
Choice B
6
IPMAT 2023 Question Paper - IPM Indore Quants

If the difference between compound interest and simple interest for a certain amount of money invested for 3 years at an annual interest rate of 10% is INR 527, then the amount invested in INR is
1. 170000
2. 15000
3. 150000
4. 17000
Choice D
17000
IPMAT 2023 Question Paper - IPM Indore Quants

In a group of 120 students, 80 students are from the Science stream and the rest are from the Commerce stream. It is known that 70 students support Mumbai Indians in the Indian Premier League; all the other students support Chennai Super Kings. The number of Science students who are supporters of Mumbai Indians is
1. Exactly 20
2. Between 15 and 25
3. Between 20 and 25
4. 30 or more
Choice D
30 or more
IPMAT 2023 Question Paper - IPM Indore Quants

The minimum number of times a fair coin must be tossed so that the probability of getting at least one head exceeds 0.8 is
1. 5
2. 7
3. 3
4. 6
Choice C
3
IPMAT 2023 Question Paper - IPM Indore Quants

A polynomial P(x) leaves a remainder 2 when divided by (x - 1) and a remainder 1 when divided by (x-2). The remainder when P(x) is divided by (x - 1) (x - 2) is
1. x − 3
2. 3 −x
3. 3
4. 2
Choice B
3 −x
IPMAT 2023 Question Paper - IPM Indore Quants

Let [x] denote the greatest integer not exceeding x and {x} = x –[x]. If n is a natural number, then the sum of all values of x satisfying the equation 2[x] = x + n{x} is
1. n
2. $\frac{ n ( n +1)}{2}$
3. $\frac{3}{2}$
4. $\frac{ n ( n +2)}{2}$
Choice D
$\frac{ n ( n +2)}{2}$
IPMAT 2023 Question Paper - IPM Indore Quants

If $\frac{a+b}{b+c}=\frac{c+d}{d+a}$ , which of the following statements is always true?
1. a = c
2. a = c, and b = d
3. a+ b+ c+ d = 0
4. a = c, or a+ b+ c+ d = 0
Choice D
a = c, or a+ b+ c+ d = 0
IPMAT 2023 Question Paper - IPM Indore Quants

If $\log _{\cos x}(\sin x)+\log _{\sin x}(\cos x)=2$ , then the value of $x$ is
1. $n \pi+\frac{\pi}{4}, n$ is an interger
2. $2 n \pi+\frac{\pi}{4}, n$ is an interger
3. $\frac{ n \pi}{4}+\frac{\pi}{4}, n$ is an interger
4. $\frac{4 \pi}{4}, n$ is an interger
Choice B
$2 n \pi+\frac{\pi}{4}, n$ is an interger
IPMAT 2023 Question Paper - IPM Indore Quants

A helicopter flies along the sides of a square field of side length 100 kms. The first side is covered at a speed of 100 kmph, and for each subsequent side the speed is increased by 100 kmph till it covers all the sides. The average speed of the helicopter is
1. 184 kmph
2. 200 kmph
3. 250 kmph
4. 192 kmph
Choice D
192 kmph
IPMAT 2023 Question Paper - IPM Indore Quants

In a triangle ABC, let D be the mid-point of BC, and AM be the altitude on BC. If the lengths of AB, BC and CA are in the ratio of 2:4:3, then the ratio of the lengths of BM and AD would be
1. $11: 12$
2. $11: 4 \sqrt{10}$
3. $12: 11$
4. $4 \sqrt{10}: 11$
Choice B
$11: 4 \sqrt{10}$
IPMAT 2023 Question Paper - IPM Indore Quants

In a chess tournament there are 5 contestants. Each player plays against all the others exactly once. No game results in a draw. The winner in a game gets one point and the loser gets zero point. Which of the following sequences cannot represent the scores of the five players?
1. 3, 2, 2, 2, 1
2. 4, 4, 1, 1, 0
3. 2, 2, 2, 2, 2
4. 3, 3, 2, 1, 1
Choice B
4, 4, 1, 1, 0
IPMAT 2023 Question Paper - IPM Indore Quants

A rabbit is sitting at the base of a staircase which has 10 steps. It proceeds to the top of the staircase by climbing either one step at a time or two steps at a time. The number of ways it can reach the top is
1. 34
2. 55
3. 144
4. 89
Choice D
89
IPMAT 2023 Question Paper - IPM Indore Quants

Let $a_1, a_2, a_3$ be three distinct real nubers in geometric progression. If the eqations $a_1 x^2+2 a_2 x+$ $a_3=0$ and $b_1 x^2+2 b_2 x+b_3+=0$ have a common root, then which of the following is necessarily ture?
1. $\frac{b_1}{a_1}, \frac{b_2}{a_2}, \frac{b_3}{a_3}$ are in arithmetic progression
2. $b _1, b_2, b_3$ are in arithmetic progression
3. $\frac{b_1}{a_1}, \frac{b_2}{a_2}, \frac{b_3}{a_3}$ are in geometric progression
4. $b _1, b_2, b_3$ are in geometric progression
Choice A
$\frac{b_1}{a_1}, \frac{b_2}{a_2}, \frac{b_3}{a_3}$ are in arithmetic progression
IPMAT 2023 Question Paper - IPM Indore Quants

Which of the following straight lines are both tangent to the circle $x^2+y^2-6 x+4 y-12=0$
1. $4 x+3 y+19=0,4 x+3 y-31=0$
2. $4 x+3 y+19=0,4 x+3 y+31=0$
3. $4 x+3 y-19=0,4 x+3 y-31=0$
4. $4 x+3 y-19=0,4 x+3 y+31=0$
Choice A
$4 x+3 y+19=0,4 x+3 y-31=0$
IPMAT 2023 Question Paper - IPM Indore Quants

A person standing at the center of an open ground first walks 32 meters towards the east, takes a right turn and walks 16 meters, takes another right turn and walks 8 meters, and so on. How far will the person be from the original starting point after an infinite number of such walks in this pattern?
1. $64 / \sqrt{5}$ meters
2. 64 meters
3. 32 meters
4. $32 / \sqrt{5}$ meters
Choice A
$64 / \sqrt{5}$ meters
IPMAT 2023 Question Paper - IPM Indore Quants

The equation $x^2+y^2-2 x-4 y+5=0$ represents
1. a point
2. a pair of straight lines
3. an ellipse
4. a circle
Choice A
a point
IPMAT 2023 Question Paper - IPM Indore Quants

If cosα+ cosβ = 1, then the maximum value of sinα − sinβ is
1. 1
2. 2
3. $\sqrt{3}$
4. $\sqrt{2}$
Choice C
$\sqrt{3}$
IPMAT 2023 Question Paper - IPM Indore Quants

Let p be a positive integer such that the unit digit of" $p ^3$ is 4 . What are the possible unit digits of $( p +3)^3$ ?
1. 1, 7, 9
2. 4, 7
3. 1, 3, 7
4. 3
Choice D
3
IPMAT 2023 Question Paper - IPM Indore Quants

The probability that a randomly chosen positive divisor of $10^{2023}$ is an integer multiple of $10^{2001}$ is
1. $\frac{23}{2024}$
2. $\frac{23^2}{2023^2}$
3. $\frac{23}{2023}$
4. $\frac{23^2}{2024^2}$
Choice D
$\frac{23^2}{2024^2}$

A pharmaceutical company has tested five drugs on three different organisms. The following incomplete table reports if a drug works on the given organism. For example, drug A works on organism R while B and C work on Q.
table

Following additional information is available:
- Each drug works on at least one organism but not more than two organisms.
- Each organism can be treated with at least two and at most three of these five drugs.
- On whichever organism A works, B also works. Similarly, on whichever organism C works, D also works.
- D and E do not work on the same organism

IPMAT 2023 Question Paper - IPM Indore Quants

Organism R can be treated with
1. Only A and E
2. A, B and E
3. A, B and C
4. Only A and B
Choice B
A, B and E
IPMAT 2023 Question Paper - IPM Indore Quants

Drug E works on
1. Only R
2. Q and R
3. Only P
4. P and R
Choice A
Only R
IPMAT 2023 Question Paper - IPM Indore Quants

The organism(s) that can be treated with three of these five drugs is(are)
1. Only Q
2. Only P
3. P and Q
4. Q and R
Choice D
Q and R
IPMAT 2023 Question Paper - IPM Indore Quants

Drug D works on
1. Only Q
2. P and Q
3. Q and R
4. Only P
Choice B
P and Q
IPMAT 2023 Question Paper - IPM Indore Quants

Organism P can be treated with
1. B, C and D
2. Only C and D
3. Only B and D
4. A, B, and D
Choice B
Only C and D