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IPMAT Indore 2023 Question Paper with Answers

Try practice questions from IPMAT Indore 2023 and check your answers. The preview order may differ from the original paper.

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Question 1

Given that cos⁡x+cos⁡y=1\cos x + \cos y = 1, the range of sin⁡x−sin⁡y\sin x - \sin y is
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Question 2

Let pp be a positive integer such that the unit digit of p3p ^ 3 is 44. What are the possible unit digits of (p+3)3(p + 3) ^ 3?
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Question 3

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 points. Which of the following sequences cannot represent the scores of the five players?
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Question 4

If the difference between compound interest and simple interest for a certain amount of money invested for 33 years at an annual interest rate of 10%10\% is INR 527527, then the amount invested in INR is
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Question 5

Let a1,a2,a3a_{1}, a_{2}, a_{3} be three distinct real numbers in geometric progression. If the equations a1x2+2a2x+a3=0a_{1} x ^ 2 + 2a_{2}x + a_{3} = 0 and b1x2+2b2x+b3=0b_{1} x ^ 2 + 2b_{2}x + b_{3} = 0 have a common root, then which of the following is necessarily true?
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Question 6

In a triangle ABC, let D be the midpoint 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
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Question 7

Let a,b,ca, b, c be real numbers greater than 1, and nn be a positive real number not equal to 1. If logn(log2a)=1;logn(log2b)=2log_n(log_2a) = 1; log_n(log_2b) = 2 and logn(log2c)=3log_n(log_2c) = 3 then which of the following is true?
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Question 8

Consider an 8×88 \times 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
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Question 9

The equation x2+y2−2x−4y+5=0x^2 + y^2 - 2x - 4y +5 = 0 represents
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Question 10

A person standing at the centre 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?
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Question 11

If log⁡(cosx)(sinx)+log⁡(sinx)(cosx)=2,\log_{(cos x)}(sin x) + \log_{(sin x)}(cos x) = 2, then the value of xx is
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Question 12

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
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Question 13

Let [x][x] denote the greatest integer not exceeding xx and {xx} =x−[x]= x - [x]. If nn is a natural number, then the sum of all values of xx satisfying the equation 2[x]=x+n2[x] = x + n{xx} is
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Question 14

The probability that a randomly chosen positive divisor of 10202310 ^ {2023} is an integer multiple of 10200110 ^ {2001} is
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Question 15

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
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Question 16

If a three-digit number is chosen at random, what is the probability that it is divisible neither by 3 nor by 4?
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Question 17

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
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Question 18

A polynomial P(x)P(x) leaves a remainder 22 when divided by (x−1)(x - 1) and a remainder 11 when divided by (x−2)(x - 2). The remainder when P(x)P(x) is divided by (x−1)(x−2)(x - 1)(x - 2) is
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Question 19

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.

DrugOrganism POrganism QOrganism R
A✔
B✔
C✔
D
E

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.

Drug E works on
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Question 20

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.

DrugOrganism POrganism QOrganism R
A✔
B✔
C✔
D
E

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.

Drug D works on:
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